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# Module: feature¶

 skimage.feature.canny(image[, sigma, …]) Edge filter an image using the Canny algorithm. skimage.feature.daisy(image[, step, radius, …]) Extract DAISY feature descriptors densely for the given image. skimage.feature.hog(image[, orientations, …]) Extract Histogram of Oriented Gradients (HOG) for a given image. skimage.feature.greycomatrix(image, …[, …]) Calculate the grey-level co-occurrence matrix. skimage.feature.greycoprops(P[, prop]) Calculate texture properties of a GLCM. skimage.feature.local_binary_pattern(image, P, R) Gray scale and rotation invariant LBP (Local Binary Patterns). skimage.feature.multiblock_lbp(int_image, r, …) Multi-block local binary pattern (MB-LBP). skimage.feature.draw_multiblock_lbp(image, …) Multi-block local binary pattern visualization. skimage.feature.peak_local_max(image[, …]) Find peaks in an image as coordinate list or boolean mask. skimage.feature.structure_tensor(image[, …]) Compute structure tensor using sum of squared differences. skimage.feature.structure_tensor_eigvals(…) Compute Eigen values of structure tensor. skimage.feature.hessian_matrix(image[, …]) Compute Hessian matrix. skimage.feature.hessian_matrix_det(image[, …]) Compute the approximate Hessian Determinant over an image. skimage.feature.hessian_matrix_eigvals(H_elems) Compute Eigenvalues of Hessian matrix. skimage.feature.shape_index(image[, sigma, …]) Compute the shape index. skimage.feature.corner_kitchen_rosenfeld(image) Compute Kitchen and Rosenfeld corner measure response image. skimage.feature.corner_harris(image[, …]) Compute Harris corner measure response image. skimage.feature.corner_shi_tomasi(image[, sigma]) Compute Shi-Tomasi (Kanade-Tomasi) corner measure response image. skimage.feature.corner_foerstner(image[, sigma]) Compute Foerstner corner measure response image. skimage.feature.corner_subpix(image, corners) Determine subpixel position of corners. skimage.feature.corner_peaks(image[, …]) Find corners in corner measure response image. skimage.feature.corner_moravec(image[, …]) Compute Moravec corner measure response image. skimage.feature.corner_fast(image[, n, …]) Extract FAST corners for a given image. skimage.feature.corner_orientations(image, …) Compute the orientation of corners. skimage.feature.match_template(image, template) Match a template to a 2-D or 3-D image using normalized correlation. skimage.feature.register_translation(…[, …]) Efficient subpixel image translation registration by cross-correlation. skimage.feature.match_descriptors(…[, …]) Brute-force matching of descriptors. skimage.feature.plot_matches(ax, image1, …) Plot matched features. skimage.feature.blob_dog(image[, min_sigma, …]) Finds blobs in the given grayscale image. skimage.feature.blob_doh(image[, min_sigma, …]) Finds blobs in the given grayscale image. skimage.feature.blob_log(image[, min_sigma, …]) Finds blobs in the given grayscale image. skimage.feature.haar_like_feature(int_image, …) Compute the Haar-like features for a region of interest (ROI) of an integral image. skimage.feature.haar_like_feature_coord(…) Compute the coordinates of Haar-like features. skimage.feature.draw_haar_like_feature(…) Visualization of Haar-like features. skimage.feature.BRIEF([descriptor_size, …]) BRIEF binary descriptor extractor. skimage.feature.CENSURE([min_scale, …]) CENSURE keypoint detector. skimage.feature.ORB([downscale, n_scales, …]) Oriented FAST and rotated BRIEF feature detector and binary descriptor extractor.

## canny¶

skimage.feature.canny(image, sigma=1.0, low_threshold=None, high_threshold=None, mask=None, use_quantiles=False)[source]

Edge filter an image using the Canny algorithm.

Parameters: image : 2D array Grayscale input image to detect edges on; can be of any dtype. sigma : float Standard deviation of the Gaussian filter. low_threshold : float Lower bound for hysteresis thresholding (linking edges). If None, low_threshold is set to 10% of dtype’s max. high_threshold : float Upper bound for hysteresis thresholding (linking edges). If None, high_threshold is set to 20% of dtype’s max. mask : array, dtype=bool, optional Mask to limit the application of Canny to a certain area. use_quantiles : bool, optional If True then treat low_threshold and high_threshold as quantiles of the edge magnitude image, rather than absolute edge magnitude values. If True then the thresholds must be in the range [0, 1]. output : 2D array (image) The binary edge map.

skimage.sobel

Notes

The steps of the algorithm are as follows:

• Smooth the image using a Gaussian with sigma width.
• Apply the horizontal and vertical Sobel operators to get the gradients within the image. The edge strength is the norm of the gradient.
• Thin potential edges to 1-pixel wide curves. First, find the normal to the edge at each point. This is done by looking at the signs and the relative magnitude of the X-Sobel and Y-Sobel to sort the points into 4 categories: horizontal, vertical, diagonal and antidiagonal. Then look in the normal and reverse directions to see if the values in either of those directions are greater than the point in question. Use interpolation to get a mix of points instead of picking the one that’s the closest to the normal.
• Perform a hysteresis thresholding: first label all points above the high threshold as edges. Then recursively label any point above the low threshold that is 8-connected to a labeled point as an edge.

References

 [1] Canny, J., A Computational Approach To Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679-714, 1986
 [2] William Green’s Canny tutorial http://dasl.unlv.edu/daslDrexel/alumni/bGreen/www.pages.drexel.edu/_weg22/can_tut.html

Examples

>>> from skimage import feature
>>> # Generate noisy image of a square
>>> im = np.zeros((256, 256))
>>> im[64:-64, 64:-64] = 1
>>> im += 0.2 * np.random.rand(*im.shape)
>>> # First trial with the Canny filter, with the default smoothing
>>> edges1 = feature.canny(im)
>>> # Increase the smoothing for better results
>>> edges2 = feature.canny(im, sigma=3)


## daisy¶

skimage.feature.daisy(image, step=4, radius=15, rings=3, histograms=8, orientations=8, normalization='l1', sigmas=None, ring_radii=None, visualize=False)[source]

Extract DAISY feature descriptors densely for the given image.

DAISY is a feature descriptor similar to SIFT formulated in a way that allows for fast dense extraction. Typically, this is practical for bag-of-features image representations.

The implementation follows Tola et al. [1] but deviate on the following points:

• Histogram bin contribution are smoothed with a circular Gaussian window over the tonal range (the angular range).
• The sigma values of the spatial Gaussian smoothing in this code do not match the sigma values in the original code by Tola et al. [2]. In their code, spatial smoothing is applied to both the input image and the center histogram. However, this smoothing is not documented in [1] and, therefore, it is omitted.
Parameters: image : (M, N) array Input image (grayscale). step : int, optional Distance between descriptor sampling points. radius : int, optional Radius (in pixels) of the outermost ring. rings : int, optional Number of rings. histograms : int, optional Number of histograms sampled per ring. orientations : int, optional Number of orientations (bins) per histogram. normalization : [ ‘l1’ | ‘l2’ | ‘daisy’ | ‘off’ ], optional How to normalize the descriptors ‘l1’: L1-normalization of each descriptor. ‘l2’: L2-normalization of each descriptor. ‘daisy’: L2-normalization of individual histograms. ‘off’: Disable normalization. sigmas : 1D array of float, optional Standard deviation of spatial Gaussian smoothing for the center histogram and for each ring of histograms. The array of sigmas should be sorted from the center and out. I.e. the first sigma value defines the spatial smoothing of the center histogram and the last sigma value defines the spatial smoothing of the outermost ring. Specifying sigmas overrides the following parameter. rings = len(sigmas) - 1 ring_radii : 1D array of int, optional Radius (in pixels) for each ring. Specifying ring_radii overrides the following two parameters. rings = len(ring_radii) radius = ring_radii[-1] If both sigmas and ring_radii are given, they must satisfy the following predicate since no radius is needed for the center histogram. len(ring_radii) == len(sigmas) + 1 visualize : bool, optional Generate a visualization of the DAISY descriptors descs : array Grid of DAISY descriptors for the given image as an array dimensionality (P, Q, R) where P = ceil((M - radius*2) / step) Q = ceil((N - radius*2) / step) R = (rings * histograms + 1) * orientations descs_img : (M, N, 3) array (only if visualize==True) Visualization of the DAISY descriptors.

References

 [1] (1, 2, 3) Tola et al. “Daisy: An efficient dense descriptor applied to wide- baseline stereo.” Pattern Analysis and Machine Intelligence, IEEE Transactions on 32.5 (2010): 815-830.

## hog¶

skimage.feature.hog(image, orientations=9, pixels_per_cell=(8, 8), cells_per_block=(3, 3), block_norm=None, visualize=False, visualise=None, transform_sqrt=False, feature_vector=True, multichannel=None)[source]

Extract Histogram of Oriented Gradients (HOG) for a given image.

Compute a Histogram of Oriented Gradients (HOG) by

1. (optional) global image normalization
2. computing the gradient image in row and col
4. normalizing across blocks
5. flattening into a feature vector
Parameters: image : (M, N[, C]) ndarray Input image. orientations : int, optional Number of orientation bins. pixels_per_cell : 2-tuple (int, int), optional Size (in pixels) of a cell. cells_per_block : 2-tuple (int, int), optional Number of cells in each block. block_norm : str {‘L1’, ‘L1-sqrt’, ‘L2’, ‘L2-Hys’}, optional Block normalization method: L1 Normalization using L1-norm. (default) L1-sqrt Normalization using L1-norm, followed by square root. L2 Normalization using L2-norm. L2-Hys Normalization using L2-norm, followed by limiting the maximum values to 0.2 (Hys stands for hysteresis) and renormalization using L2-norm. For details, see [3], [4]. visualize : bool, optional Also return an image of the HOG. For each cell and orientation bin, the image contains a line segment that is centered at the cell center, is perpendicular to the midpoint of the range of angles spanned by the orientation bin, and has intensity proportional to the corresponding histogram value. transform_sqrt : bool, optional Apply power law compression to normalize the image before processing. DO NOT use this if the image contains negative values. Also see notes section below. feature_vector : bool, optional Return the data as a feature vector by calling .ravel() on the result just before returning. multichannel : boolean, optional If True, the last image dimension is considered as a color channel, otherwise as spatial. out : (n_blocks_row, n_blocks_col, n_cells_row, n_cells_col, n_orient) ndarray HOG descriptor for the image. If feature_vector is True, a 1D (flattened) array is returned. hog_image : (M, N) ndarray, optional A visualisation of the HOG image. Only provided if visualize is True.

Notes

The presented code implements the HOG extraction method from [2] with the following changes: (I) blocks of (3, 3) cells are used ((2, 2) in the paper; (II) no smoothing within cells (Gaussian spatial window with sigma=8pix in the paper); (III) L1 block normalization is used (L2-Hys in the paper).

Power law compression, also known as Gamma correction, is used to reduce the effects of shadowing and illumination variations. The compression makes the dark regions lighter. When the kwarg transform_sqrt is set to True, the function computes the square root of each color channel and then applies the hog algorithm to the image.

References

 [2] (1, 2) Dalal, N and Triggs, B, Histograms of Oriented Gradients for Human Detection, IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2005 San Diego, CA, USA, https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf, DOI:10.1109/CVPR.2005.177
 [3] (1, 2) Lowe, D.G., Distinctive image features from scale-invatiant keypoints, International Journal of Computer Vision (2004) 60: 91, http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf, DOI:10.1023/B:VISI.0000029664.99615.94
 [4] (1, 2) Dalal, N, Finding People in Images and Videos, Human-Computer Interaction [cs.HC], Institut National Polytechnique de Grenoble - INPG, 2006, https://tel.archives-ouvertes.fr/tel-00390303/file/NavneetDalalThesis.pdf

## greycomatrix¶

skimage.feature.greycomatrix(image, distances, angles, levels=None, symmetric=False, normed=False)[source]

Calculate the grey-level co-occurrence matrix.

A grey level co-occurrence matrix is a histogram of co-occurring greyscale values at a given offset over an image.

Parameters: image : array_like Integer typed input image. Only positive valued images are supported. If type is other than uint8, the argument levels needs to be set. distances : array_like List of pixel pair distance offsets. angles : array_like List of pixel pair angles in radians. levels : int, optional The input image should contain integers in [0, levels-1], where levels indicate the number of grey-levels counted (typically 256 for an 8-bit image). This argument is required for 16-bit images or higher and is typically the maximum of the image. As the output matrix is at least levels x levels, it might be preferable to use binning of the input image rather than large values for levels. symmetric : bool, optional If True, the output matrix P[:, :, d, theta] is symmetric. This is accomplished by ignoring the order of value pairs, so both (i, j) and (j, i) are accumulated when (i, j) is encountered for a given offset. The default is False. normed : bool, optional If True, normalize each matrix P[:, :, d, theta] by dividing by the total number of accumulated co-occurrences for the given offset. The elements of the resulting matrix sum to 1. The default is False. P : 4-D ndarray The grey-level co-occurrence histogram. The value P[i,j,d,theta] is the number of times that grey-level j occurs at a distance d and at an angle theta from grey-level i. If normed is False, the output is of type uint32, otherwise it is float64. The dimensions are: levels x levels x number of distances x number of angles.

References

 [2] Pattern Recognition Engineering, Morton Nadler & Eric P. Smith

Examples

Compute 2 GLCMs: One for a 1-pixel offset to the right, and one for a 1-pixel offset upwards.

>>> image = np.array([[0, 0, 1, 1],
...                   [0, 0, 1, 1],
...                   [0, 2, 2, 2],
...                   [2, 2, 3, 3]], dtype=np.uint8)
>>> result = greycomatrix(image, [1], [0, np.pi/4, np.pi/2, 3*np.pi/4],
...                       levels=4)
>>> result[:, :, 0, 0]
array([[2, 2, 1, 0],
[0, 2, 0, 0],
[0, 0, 3, 1],
[0, 0, 0, 1]], dtype=uint32)
>>> result[:, :, 0, 1]
array([[1, 1, 3, 0],
[0, 1, 1, 0],
[0, 0, 0, 2],
[0, 0, 0, 0]], dtype=uint32)
>>> result[:, :, 0, 2]
array([[3, 0, 2, 0],
[0, 2, 2, 0],
[0, 0, 1, 2],
[0, 0, 0, 0]], dtype=uint32)
>>> result[:, :, 0, 3]
array([[2, 0, 0, 0],
[1, 1, 2, 0],
[0, 0, 2, 1],
[0, 0, 0, 0]], dtype=uint32)


## greycoprops¶

skimage.feature.greycoprops(P, prop='contrast')[source]

Calculate texture properties of a GLCM.

Compute a feature of a grey level co-occurrence matrix to serve as a compact summary of the matrix. The properties are computed as follows:

• ‘contrast’: $$\sum_{i,j=0}^{levels-1} P_{i,j}(i-j)^2$$

• ‘dissimilarity’: $$\sum_{i,j=0}^{levels-1}P_{i,j}|i-j|$$

• ‘homogeneity’: $$\sum_{i,j=0}^{levels-1}\frac{P_{i,j}}{1+(i-j)^2}$$

• ‘ASM’: $$\sum_{i,j=0}^{levels-1} P_{i,j}^2$$

• ‘energy’: $$\sqrt{ASM}$$

• ‘correlation’:
$\sum_{i,j=0}^{levels-1} P_{i,j}\left[\frac{(i-\mu_i) \ (j-\mu_j)}{\sqrt{(\sigma_i^2)(\sigma_j^2)}}\right]$
Parameters: P : ndarray Input array. P is the grey-level co-occurrence histogram for which to compute the specified property. The value P[i,j,d,theta] is the number of times that grey-level j occurs at a distance d and at an angle theta from grey-level i. prop : {‘contrast’, ‘dissimilarity’, ‘homogeneity’, ‘energy’, ‘correlation’, ‘ASM’}, optional The property of the GLCM to compute. The default is ‘contrast’. results : 2-D ndarray 2-dimensional array. results[d, a] is the property ‘prop’ for the d’th distance and the a’th angle.

References

Examples

Compute the contrast for GLCMs with distances [1, 2] and angles [0 degrees, 90 degrees]

>>> image = np.array([[0, 0, 1, 1],
...                   [0, 0, 1, 1],
...                   [0, 2, 2, 2],
...                   [2, 2, 3, 3]], dtype=np.uint8)
>>> g = greycomatrix(image, [1, 2], [0, np.pi/2], levels=4,
...                  normed=True, symmetric=True)
>>> contrast = greycoprops(g, 'contrast')
>>> contrast
array([[ 0.58333333,  1.        ],
[ 1.25      ,  2.75      ]])


## local_binary_pattern¶

skimage.feature.local_binary_pattern(image, P, R, method='default')[source]

Gray scale and rotation invariant LBP (Local Binary Patterns).

LBP is an invariant descriptor that can be used for texture classification.

Parameters: image : (N, M) array Graylevel image. P : int Number of circularly symmetric neighbour set points (quantization of the angular space). R : float Radius of circle (spatial resolution of the operator). method : {‘default’, ‘ror’, ‘uniform’, ‘var’} Method to determine the pattern. ‘default’: original local binary pattern which is gray scale but not rotation invariant. ‘ror’: extension of default implementation which is gray scale and rotation invariant. ‘uniform’: improved rotation invariance with uniform patterns and finer quantization of the angular space which is gray scale and rotation invariant. ‘nri_uniform’: non rotation-invariant uniform patterns variant which is only gray scale invariant [2]. ‘var’: rotation invariant variance measures of the contrast of local image texture which is rotation but not gray scale invariant. output : (N, M) array LBP image.

References

 [1] Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns. Timo Ojala, Matti Pietikainen, Topi Maenpaa. http://www.ee.oulu.fi/research/mvmp/mvg/files/pdf/pdf_94.pdf, 2002.
 [2] (1, 2) Face recognition with local binary patterns. Timo Ahonen, Abdenour Hadid, Matti Pietikainen, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.6851, 2004.

## multiblock_lbp¶

skimage.feature.multiblock_lbp(int_image, r, c, width, height)[source]

Multi-block local binary pattern (MB-LBP).

The features are calculated similarly to local binary patterns (LBPs), (See local_binary_pattern()) except that summed blocks are used instead of individual pixel values.

MB-LBP is an extension of LBP that can be computed on multiple scales in constant time using the integral image. Nine equally-sized rectangles are used to compute a feature. For each rectangle, the sum of the pixel intensities is computed. Comparisons of these sums to that of the central rectangle determine the feature, similarly to LBP.

Parameters: int_image : (N, M) array Integral image. r : int Row-coordinate of top left corner of a rectangle containing feature. c : int Column-coordinate of top left corner of a rectangle containing feature. width : int Width of one of the 9 equal rectangles that will be used to compute a feature. height : int Height of one of the 9 equal rectangles that will be used to compute a feature. output : int 8-bit MB-LBP feature descriptor.

References

 [1] Face Detection Based on Multi-Block LBP Representation. Lun Zhang, Rufeng Chu, Shiming Xiang, Shengcai Liao, Stan Z. Li http://www.cbsr.ia.ac.cn/users/scliao/papers/Zhang-ICB07-MBLBP.pdf

## draw_multiblock_lbp¶

skimage.feature.draw_multiblock_lbp(image, r, c, width, height, lbp_code=0, color_greater_block=(1, 1, 1), color_less_block=(0, 0.69, 0.96), alpha=0.5)[source]

Multi-block local binary pattern visualization.

Blocks with higher sums are colored with alpha-blended white rectangles, whereas blocks with lower sums are colored alpha-blended cyan. Colors and the alpha parameter can be changed.

Parameters: image : ndarray of float or uint Image on which to visualize the pattern. r : int Row-coordinate of top left corner of a rectangle containing feature. c : int Column-coordinate of top left corner of a rectangle containing feature. width : int Width of one of 9 equal rectangles that will be used to compute a feature. height : int Height of one of 9 equal rectangles that will be used to compute a feature. lbp_code : int The descriptor of feature to visualize. If not provided, the descriptor with 0 value will be used. color_greater_block : tuple of 3 floats Floats specifying the color for the block that has greater intensity value. They should be in the range [0, 1]. Corresponding values define (R, G, B) values. Default value is white (1, 1, 1). color_greater_block : tuple of 3 floats Floats specifying the color for the block that has greater intensity value. They should be in the range [0, 1]. Corresponding values define (R, G, B) values. Default value is cyan (0, 0.69, 0.96). alpha : float Value in the range [0, 1] that specifies opacity of visualization. 1 - fully transparent, 0 - opaque. output : ndarray of float Image with MB-LBP visualization.

References

 [1] Face Detection Based on Multi-Block LBP Representation. Lun Zhang, Rufeng Chu, Shiming Xiang, Shengcai Liao, Stan Z. Li http://www.cbsr.ia.ac.cn/users/scliao/papers/Zhang-ICB07-MBLBP.pdf

## peak_local_max¶

skimage.feature.peak_local_max(image, min_distance=1, threshold_abs=None, threshold_rel=None, exclude_border=True, indices=True, num_peaks=inf, footprint=None, labels=None, num_peaks_per_label=inf)[source]

Find peaks in an image as coordinate list or boolean mask.

Peaks are the local maxima in a region of 2 * min_distance + 1 (i.e. peaks are separated by at least min_distance).

If peaks are flat (i.e. multiple adjacent pixels have identical intensities), the coordinates of all such pixels are returned.

If both threshold_abs and threshold_rel are provided, the maximum of the two is chosen as the minimum intensity threshold of peaks.

Parameters: image : ndarray Input image. min_distance : int, optional Minimum number of pixels separating peaks in a region of 2 * min_distance + 1 (i.e. peaks are separated by at least min_distance). To find the maximum number of peaks, use min_distance=1. threshold_abs : float, optional Minimum intensity of peaks. By default, the absolute threshold is the minimum intensity of the image. threshold_rel : float, optional Minimum intensity of peaks, calculated as max(image) * threshold_rel. exclude_border : int, optional If nonzero, exclude_border excludes peaks from within exclude_border-pixels of the border of the image. indices : bool, optional If True, the output will be an array representing peak coordinates. If False, the output will be a boolean array shaped as image.shape with peaks present at True elements. num_peaks : int, optional Maximum number of peaks. When the number of peaks exceeds num_peaks, return num_peaks peaks based on highest peak intensity. footprint : ndarray of bools, optional If provided, footprint == 1 represents the local region within which to search for peaks at every point in image. Overrides min_distance (also for exclude_border). labels : ndarray of ints, optional If provided, each unique region labels == value represents a unique region to search for peaks. Zero is reserved for background. num_peaks_per_label : int, optional Maximum number of peaks for each label. output : ndarray or ndarray of bools If indices = True : (row, column, …) coordinates of peaks. If indices = False : Boolean array shaped like image, with peaks represented by True values.

Notes

The peak local maximum function returns the coordinates of local peaks (maxima) in an image. A maximum filter is used for finding local maxima. This operation dilates the original image. After comparison of the dilated and original image, this function returns the coordinates or a mask of the peaks where the dilated image equals the original image.

Examples

>>> img1 = np.zeros((7, 7))
>>> img1[3, 4] = 1
>>> img1[3, 2] = 1.5
>>> img1
array([[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
[ 0. ,  0. ,  1.5,  0. ,  1. ,  0. ,  0. ],
[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
[ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ]])

>>> peak_local_max(img1, min_distance=1)
array([[3, 4],
[3, 2]])

>>> peak_local_max(img1, min_distance=2)
array([[3, 2]])

>>> img2 = np.zeros((20, 20, 20))
>>> img2[10, 10, 10] = 1
>>> peak_local_max(img2, exclude_border=0)
array([[10, 10, 10]])


## structure_tensor¶

skimage.feature.structure_tensor(image, sigma=1, mode='constant', cval=0)[source]

Compute structure tensor using sum of squared differences.

The structure tensor A is defined as:

A = [Axx Axy]
[Axy Ayy]


which is approximated by the weighted sum of squared differences in a local window around each pixel in the image.

Parameters: image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as a weighting function for the local summation of squared differences. mode : {‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode ‘constant’, the value outside the image boundaries. Axx : ndarray Element of the structure tensor for each pixel in the input image. Axy : ndarray Element of the structure tensor for each pixel in the input image. Ayy : ndarray Element of the structure tensor for each pixel in the input image.

Examples

>>> from skimage.feature import structure_tensor
>>> square = np.zeros((5, 5))
>>> square[2, 2] = 1
>>> Axx, Axy, Ayy = structure_tensor(square, sigma=0.1)
>>> Axx
array([[ 0.,  0.,  0.,  0.,  0.],
[ 0.,  1.,  0.,  1.,  0.],
[ 0.,  4.,  0.,  4.,  0.],
[ 0.,  1.,  0.,  1.,  0.],
[ 0.,  0.,  0.,  0.,  0.]])


## structure_tensor_eigvals¶

skimage.feature.structure_tensor_eigvals(Axx, Axy, Ayy)[source]

Compute Eigen values of structure tensor.

Parameters: Axx : ndarray Element of the structure tensor for each pixel in the input image. Axy : ndarray Element of the structure tensor for each pixel in the input image. Ayy : ndarray Element of the structure tensor for each pixel in the input image. l1 : ndarray Larger eigen value for each input matrix. l2 : ndarray Smaller eigen value for each input matrix.

Examples

>>> from skimage.feature import structure_tensor, structure_tensor_eigvals
>>> square = np.zeros((5, 5))
>>> square[2, 2] = 1
>>> Axx, Axy, Ayy = structure_tensor(square, sigma=0.1)
>>> structure_tensor_eigvals(Axx, Axy, Ayy)[0]
array([[ 0.,  0.,  0.,  0.,  0.],
[ 0.,  2.,  4.,  2.,  0.],
[ 0.,  4.,  0.,  4.,  0.],
[ 0.,  2.,  4.,  2.,  0.],
[ 0.,  0.,  0.,  0.,  0.]])


## hessian_matrix¶

skimage.feature.hessian_matrix(image, sigma=1, mode='constant', cval=0, order=None)[source]

Compute Hessian matrix.

The Hessian matrix is defined as:

H = [Hrr Hrc]
[Hrc Hcc]


which is computed by convolving the image with the second derivatives of the Gaussian kernel in the respective x- and y-directions.

Parameters: image : ndarray Input image. sigma : float Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. mode : {‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode ‘constant’, the value outside the image boundaries. order : {‘xy’, ‘rc’}, optional This parameter allows for the use of reverse or forward order of the image axes in gradient computation. ‘xy’ indicates the usage of the last axis initially (Hxx, Hxy, Hyy), whilst ‘rc’ indicates the use of the first axis initially (Hrr, Hrc, Hcc). Hrr : ndarray Element of the Hessian matrix for each pixel in the input image. Hrc : ndarray Element of the Hessian matrix for each pixel in the input image. Hcc : ndarray Element of the Hessian matrix for each pixel in the input image.

Examples

>>> from skimage.feature import hessian_matrix
>>> square = np.zeros((5, 5))
>>> square[2, 2] = 4
>>> Hrr, Hrc, Hcc = hessian_matrix(square, sigma=0.1, order = 'rc')
>>> Hrc
array([[ 0.,  0.,  0.,  0.,  0.],
[ 0.,  1.,  0., -1.,  0.],
[ 0.,  0.,  0.,  0.,  0.],
[ 0., -1.,  0.,  1.,  0.],
[ 0.,  0.,  0.,  0.,  0.]])


## hessian_matrix_det¶

skimage.feature.hessian_matrix_det(image, sigma=1, approximate=True)[source]

Compute the approximate Hessian Determinant over an image.

The 2D approximate method uses box filters over integral images to compute the approximate Hessian Determinant, as described in [1].

Parameters: image : array The image over which to compute Hessian Determinant. sigma : float, optional Standard deviation used for the Gaussian kernel, used for the Hessian matrix. approximate : bool, optional If True and the image is 2D, use a much faster approximate computation. This argument has no effect on 3D and higher images. out : array The array of the Determinant of Hessians.

Notes

For 2D images when approximate=True, the running time of this method only depends on size of the image. It is independent of sigma as one would expect. The downside is that the result for sigma less than 3 is not accurate, i.e., not similar to the result obtained if someone computed the Hessian and took its determinant.

References

 [1] (1, 2) Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool, “SURF: Speeded Up Robust Features” ftp://ftp.vision.ee.ethz.ch/publications/articles/eth_biwi_00517.pdf

## hessian_matrix_eigvals¶

skimage.feature.hessian_matrix_eigvals(H_elems, Hxy=None, Hyy=None, Hxx=None)[source]

Compute Eigenvalues of Hessian matrix.

Parameters: H_elems : list of ndarray The upper-diagonal elements of the Hessian matrix, as returned by hessian_matrix. Hxy : ndarray, deprecated Element of the Hessian matrix for each pixel in the input image. Hyy : ndarray, deprecated Element of the Hessian matrix for each pixel in the input image. Hxx : ndarray, deprecated Element of the Hessian matrix for each pixel in the input image. eigs : ndarray The eigenvalues of the Hessian matrix, in decreasing order. The eigenvalues are the leading dimension. That is, eigs[i, j, k] contains the ith-largest eigenvalue at position (j, k).

Examples

>>> from skimage.feature import hessian_matrix, hessian_matrix_eigvals
>>> square = np.zeros((5, 5))
>>> square[2, 2] = 4
>>> H_elems = hessian_matrix(square, sigma=0.1, order='rc')
>>> hessian_matrix_eigvals(H_elems)[0]
array([[ 0.,  0.,  2.,  0.,  0.],
[ 0.,  1.,  0.,  1.,  0.],
[ 2.,  0., -2.,  0.,  2.],
[ 0.,  1.,  0.,  1.,  0.],
[ 0.,  0.,  2.,  0.,  0.]])


## shape_index¶

skimage.feature.shape_index(image, sigma=1, mode='constant', cval=0)[source]

Compute the shape index.

The shape index, as defined by Koenderink & van Doorn [1], is a single valued measure of local curvature, assuming the image as a 3D plane with intensities representing heights.

It is derived from the eigen values of the Hessian, and its value ranges from -1 to 1 (and is undefined (=NaN) in flat regions), with following ranges representing following shapes:

Ranges of the shape index and corresponding shapes.
Interval (s in …) Shape
[ -1, -7/8) Spherical cup
[-7/8, -5/8) Through
[-5/8, -3/8) Rut
[+3/8, +5/8) Ridge
[+5/8, +7/8) Dome
[+7/8, +1] Spherical cap
Parameters: image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used for smoothing the input data before Hessian eigen value calculation. mode : {‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional How to handle values outside the image borders cval : float, optional Used in conjunction with mode ‘constant’, the value outside the image boundaries. s : ndarray Shape index

References

 [1] (1, 2) Koenderink, J. J. & van Doorn, A. J., “Surface shape and curvature scales”, Image and Vision Computing, 1992, 10, 557-564. DOI:10.1016/0262-8856(92)90076-F

Examples

>>> from skimage.feature import shape_index
>>> square = np.zeros((5, 5))
>>> square[2, 2] = 4
>>> s = shape_index(square, sigma=0.1)
>>> s
array([[ nan,  nan, -0.5,  nan,  nan],
[ nan, -0. ,  nan, -0. ,  nan],
[-0.5,  nan, -1. ,  nan, -0.5],
[ nan, -0. ,  nan, -0. ,  nan],
[ nan,  nan, -0.5,  nan,  nan]])


## corner_kitchen_rosenfeld¶

skimage.feature.corner_kitchen_rosenfeld(image, mode='constant', cval=0)[source]

Compute Kitchen and Rosenfeld corner measure response image.

The corner measure is calculated as follows:

(imxx * imy**2 + imyy * imx**2 - 2 * imxy * imx * imy)
/ (imx**2 + imy**2)


Where imx and imy are the first and imxx, imxy, imyy the second derivatives.

Parameters: image : ndarray Input image. mode : {‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode ‘constant’, the value outside the image boundaries. response : ndarray Kitchen and Rosenfeld response image.

## corner_harris¶

skimage.feature.corner_harris(image, method='k', k=0.05, eps=1e-06, sigma=1)[source]

Compute Harris corner measure response image.

This corner detector uses information from the auto-correlation matrix A:

A = [(imx**2)   (imx*imy)] = [Axx Axy]
[(imx*imy)   (imy**2)]   [Axy Ayy]


Where imx and imy are first derivatives, averaged with a gaussian filter. The corner measure is then defined as:

det(A) - k * trace(A)**2


or:

2 * det(A) / (trace(A) + eps)

Parameters: image : ndarray Input image. method : {‘k’, ‘eps’}, optional Method to compute the response image from the auto-correlation matrix. k : float, optional Sensitivity factor to separate corners from edges, typically in range [0, 0.2]. Small values of k result in detection of sharp corners. eps : float, optional Normalisation factor (Noble’s corner measure). sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. response : ndarray Harris response image.

References

Examples

>>> from skimage.feature import corner_harris, corner_peaks
>>> square = np.zeros([10, 10])
>>> square[2:8, 2:8] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
>>> corner_peaks(corner_harris(square), min_distance=1)
array([[2, 2],
[2, 7],
[7, 2],
[7, 7]])


## corner_shi_tomasi¶

skimage.feature.corner_shi_tomasi(image, sigma=1)[source]

Compute Shi-Tomasi (Kanade-Tomasi) corner measure response image.

This corner detector uses information from the auto-correlation matrix A:

A = [(imx**2)   (imx*imy)] = [Axx Axy]
[(imx*imy)   (imy**2)]   [Axy Ayy]


Where imx and imy are first derivatives, averaged with a gaussian filter. The corner measure is then defined as the smaller eigenvalue of A:

((Axx + Ayy) - sqrt((Axx - Ayy)**2 + 4 * Axy**2)) / 2

Parameters: image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. response : ndarray Shi-Tomasi response image.

References

Examples

>>> from skimage.feature import corner_shi_tomasi, corner_peaks
>>> square = np.zeros([10, 10])
>>> square[2:8, 2:8] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
>>> corner_peaks(corner_shi_tomasi(square), min_distance=1)
array([[2, 2],
[2, 7],
[7, 2],
[7, 7]])


## corner_foerstner¶

skimage.feature.corner_foerstner(image, sigma=1)[source]

Compute Foerstner corner measure response image.

This corner detector uses information from the auto-correlation matrix A:

A = [(imx**2)   (imx*imy)] = [Axx Axy]
[(imx*imy)   (imy**2)]   [Axy Ayy]


Where imx and imy are first derivatives, averaged with a gaussian filter. The corner measure is then defined as:

w = det(A) / trace(A)           (size of error ellipse)
q = 4 * det(A) / trace(A)**2    (roundness of error ellipse)

Parameters: image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. w : ndarray Error ellipse sizes. q : ndarray Roundness of error ellipse.

References

Examples

>>> from skimage.feature import corner_foerstner, corner_peaks
>>> square = np.zeros([10, 10])
>>> square[2:8, 2:8] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
>>> w, q = corner_foerstner(square)
>>> accuracy_thresh = 0.5
>>> roundness_thresh = 0.3
>>> foerstner = (q > roundness_thresh) * (w > accuracy_thresh) * w
>>> corner_peaks(foerstner, min_distance=1)
array([[2, 2],
[2, 7],
[7, 2],
[7, 7]])


## corner_subpix¶

skimage.feature.corner_subpix(image, corners, window_size=11, alpha=0.99)[source]

Determine subpixel position of corners.

A statistical test decides whether the corner is defined as the intersection of two edges or a single peak. Depending on the classification result, the subpixel corner location is determined based on the local covariance of the grey-values. If the significance level for either statistical test is not sufficient, the corner cannot be classified, and the output subpixel position is set to NaN.

Parameters: image : ndarray Input image. corners : (N, 2) ndarray Corner coordinates (row, col). window_size : int, optional Search window size for subpixel estimation. alpha : float, optional Significance level for corner classification. positions : (N, 2) ndarray Subpixel corner positions. NaN for “not classified” corners.

References

Examples

>>> from skimage.feature import corner_harris, corner_peaks, corner_subpix
>>> img = np.zeros((10, 10))
>>> img[:5, :5] = 1
>>> img[5:, 5:] = 1
>>> img.astype(int)
array([[1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]])
>>> coords = corner_peaks(corner_harris(img), min_distance=2)
>>> coords_subpix = corner_subpix(img, coords, window_size=7)
>>> coords_subpix
array([[ 4.5,  4.5]])


## corner_peaks¶

skimage.feature.corner_peaks(image, min_distance=1, threshold_abs=None, threshold_rel=0.1, exclude_border=True, indices=True, num_peaks=inf, footprint=None, labels=None)[source]

Find corners in corner measure response image.

This differs from skimage.feature.peak_local_max in that it suppresses multiple connected peaks with the same accumulator value.

Parameters: * : *

Examples

>>> from skimage.feature import peak_local_max
>>> response = np.zeros((5, 5))
>>> response[2:4, 2:4] = 1
>>> response
array([[ 0.,  0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.,  0.],
[ 0.,  0.,  1.,  1.,  0.],
[ 0.,  0.,  1.,  1.,  0.],
[ 0.,  0.,  0.,  0.,  0.]])
>>> peak_local_max(response)
array([[3, 3],
[3, 2],
[2, 3],
[2, 2]])
>>> corner_peaks(response)
array([[2, 2]])


## corner_moravec¶

skimage.feature.corner_moravec(image, window_size=1)[source]

Compute Moravec corner measure response image.

This is one of the simplest corner detectors and is comparatively fast but has several limitations (e.g. not rotation invariant).

Parameters: image : ndarray Input image. window_size : int, optional Window size. response : ndarray Moravec response image.

References

Examples

>>> from skimage.feature import corner_moravec
>>> square = np.zeros([7, 7])
>>> square[3, 3] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> corner_moravec(square).astype(int)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 2, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])


## corner_fast¶

skimage.feature.corner_fast(image, n=12, threshold=0.15)[source]

Extract FAST corners for a given image.

Parameters: image : 2D ndarray Input image. n : int Minimum number of consecutive pixels out of 16 pixels on the circle that should all be either brighter or darker w.r.t testpixel. A point c on the circle is darker w.r.t test pixel p if Ic < Ip - threshold and brighter if Ic > Ip + threshold. Also stands for the n in FAST-n corner detector. threshold : float Threshold used in deciding whether the pixels on the circle are brighter, darker or similar w.r.t. the test pixel. Decrease the threshold when more corners are desired and vice-versa. response : ndarray FAST corner response image.

References

 [1] Edward Rosten and Tom Drummond “Machine Learning for high-speed corner detection”, http://www.edwardrosten.com/work/rosten_2006_machine.pdf
 [2] Wikipedia, “Features from accelerated segment test”, https://en.wikipedia.org/wiki/Features_from_accelerated_segment_test

Examples

>>> from skimage.feature import corner_fast, corner_peaks
>>> square = np.zeros((12, 12))
>>> square[3:9, 3:9] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
>>> corner_peaks(corner_fast(square, 9), min_distance=1)
array([[3, 3],
[3, 8],
[8, 3],
[8, 8]])


## corner_orientations¶

skimage.feature.corner_orientations(image, corners, mask)[source]

Compute the orientation of corners.

The orientation of corners is computed using the first order central moment i.e. the center of mass approach. The corner orientation is the angle of the vector from the corner coordinate to the intensity centroid in the local neighborhood around the corner calculated using first order central moment.

Parameters: image : 2D array Input grayscale image. corners : (N, 2) array Corner coordinates as (row, col). mask : 2D array Mask defining the local neighborhood of the corner used for the calculation of the central moment. orientations : (N, 1) array Orientations of corners in the range [-pi, pi].

References

 [1] Ethan Rublee, Vincent Rabaud, Kurt Konolige and Gary Bradski “ORB : An efficient alternative to SIFT and SURF” http://www.vision.cs.chubu.ac.jp/CV-R/pdf/Rublee_iccv2011.pdf
 [2] Paul L. Rosin, “Measuring Corner Properties” http://users.cs.cf.ac.uk/Paul.Rosin/corner2.pdf

Examples

>>> from skimage.morphology import octagon
>>> from skimage.feature import (corner_fast, corner_peaks,
...                              corner_orientations)
>>> square = np.zeros((12, 12))
>>> square[3:9, 3:9] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
>>> corners = corner_peaks(corner_fast(square, 9), min_distance=1)
>>> corners
array([[3, 3],
[3, 8],
[8, 3],
[8, 8]])
>>> orientations = corner_orientations(square, corners, octagon(3, 2))
array([  45.,  135.,  -45., -135.])


## match_template¶

skimage.feature.match_template(image, template, pad_input=False, mode='constant', constant_values=0)[source]

Match a template to a 2-D or 3-D image using normalized correlation.

The output is an array with values between -1.0 and 1.0. The value at a given position corresponds to the correlation coefficient between the image and the template.

For pad_input=True matches correspond to the center and otherwise to the top-left corner of the template. To find the best match you must search for peaks in the response (output) image.

Parameters: image : (M, N[, D]) array 2-D or 3-D input image. template : (m, n[, d]) array Template to locate. It must be (m <= M, n <= N[, d <= D]). pad_input : bool If True, pad image so that output is the same size as the image, and output values correspond to the template center. Otherwise, the output is an array with shape (M - m + 1, N - n + 1) for an (M, N) image and an (m, n) template, and matches correspond to origin (top-left corner) of the template. mode : see numpy.pad, optional Padding mode. constant_values : see numpy.pad, optional Constant values used in conjunction with mode='constant'. output : array Response image with correlation coefficients.

Notes

Details on the cross-correlation are presented in [1]. This implementation uses FFT convolutions of the image and the template. Reference [2] presents similar derivations but the approximation presented in this reference is not used in our implementation.

References

 [1] (1, 2) J. P. Lewis, “Fast Normalized Cross-Correlation”, Industrial Light and Magic.
 [2] (1, 2) Briechle and Hanebeck, “Template Matching using Fast Normalized Cross Correlation”, Proceedings of the SPIE (2001). DOI:10.1117/12.421129

Examples

>>> template = np.zeros((3, 3))
>>> template[1, 1] = 1
>>> template
array([[ 0.,  0.,  0.],
[ 0.,  1.,  0.],
[ 0.,  0.,  0.]])
>>> image = np.zeros((6, 6))
>>> image[1, 1] = 1
>>> image[4, 4] = -1
>>> image
array([[ 0.,  0.,  0.,  0.,  0.,  0.],
[ 0.,  1.,  0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0., -1.,  0.],
[ 0.,  0.,  0.,  0.,  0.,  0.]])
>>> result = match_template(image, template)
>>> np.round(result, 3)
array([[ 1.   , -0.125,  0.   ,  0.   ],
[-0.125, -0.125,  0.   ,  0.   ],
[ 0.   ,  0.   ,  0.125,  0.125],
[ 0.   ,  0.   ,  0.125, -1.   ]])
>>> result = match_template(image, template, pad_input=True)
>>> np.round(result, 3)
array([[-0.125, -0.125, -0.125,  0.   ,  0.   ,  0.   ],
[-0.125,  1.   , -0.125,  0.   ,  0.   ,  0.   ],
[-0.125, -0.125, -0.125,  0.   ,  0.   ,  0.   ],
[ 0.   ,  0.   ,  0.   ,  0.125,  0.125,  0.125],
[ 0.   ,  0.   ,  0.   ,  0.125, -1.   ,  0.125],
[ 0.   ,  0.   ,  0.   ,  0.125,  0.125,  0.125]])


## register_translation¶

skimage.feature.register_translation(src_image, target_image, upsample_factor=1, space='real')[source]

Efficient subpixel image translation registration by cross-correlation.

This code gives the same precision as the FFT upsampled cross-correlation in a fraction of the computation time and with reduced memory requirements. It obtains an initial estimate of the cross-correlation peak by an FFT and then refines the shift estimation by upsampling the DFT only in a small neighborhood of that estimate by means of a matrix-multiply DFT.

Parameters: src_image : ndarray Reference image. target_image : ndarray Image to register. Must be same dimensionality as src_image. upsample_factor : int, optional Upsampling factor. Images will be registered to within 1 / upsample_factor of a pixel. For example upsample_factor == 20 means the images will be registered within 1/20th of a pixel. Default is 1 (no upsampling) space : string, one of “real” or “fourier”, optional Defines how the algorithm interprets input data. “real” means data will be FFT’d to compute the correlation, while “fourier” data will bypass FFT of input data. Case insensitive. shifts : ndarray Shift vector (in pixels) required to register target_image with src_image. Axis ordering is consistent with numpy (e.g. Z, Y, X) error : float Translation invariant normalized RMS error between src_image and target_image. phasediff : float Global phase difference between the two images (should be zero if images are non-negative).

References

 [1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup, “Efficient subpixel image registration algorithms,” Optics Letters 33, 156-158 (2008). DOI:10.1364/OL.33.000156
 [2] James R. Fienup, “Invariant error metrics for image reconstruction” Optics Letters 36, 8352-8357 (1997). DOI:10.1364/AO.36.008352

## match_descriptors¶

skimage.feature.match_descriptors(descriptors1, descriptors2, metric=None, p=2, max_distance=inf, cross_check=True, max_ratio=1.0)[source]

Brute-force matching of descriptors.

For each descriptor in the first set this matcher finds the closest descriptor in the second set (and vice-versa in the case of enabled cross-checking).

Parameters: descriptors1 : (M, P) array Binary descriptors of size P about M keypoints in the first image. descriptors2 : (N, P) array Binary descriptors of size P about N keypoints in the second image. metric : {‘euclidean’, ‘cityblock’, ‘minkowski’, ‘hamming’, …} The metric to compute the distance between two descriptors. See scipy.spatial.distance.cdist for all possible types. The hamming distance should be used for binary descriptors. By default the L2-norm is used for all descriptors of dtype float or double and the Hamming distance is used for binary descriptors automatically. p : int The p-norm to apply for metric='minkowski'. max_distance : float Maximum allowed distance between descriptors of two keypoints in separate images to be regarded as a match. cross_check : bool If True, the matched keypoints are returned after cross checking i.e. a matched pair (keypoint1, keypoint2) is returned if keypoint2 is the best match for keypoint1 in second image and keypoint1 is the best match for keypoint2 in first image. max_ratio : float Maximum ratio of distances between first and second closest descriptor in the second set of descriptors. This threshold is useful to filter ambiguous matches between the two descriptor sets. The choice of this value depends on the statistics of the chosen descriptor, e.g., for SIFT descriptors a value of 0.8 is usually chosen, see D.G. Lowe, “Distinctive Image Features from Scale-Invariant Keypoints”, International Journal of Computer Vision, 2004. matches : (Q, 2) array Indices of corresponding matches in first and second set of descriptors, where matches[:, 0] denote the indices in the first and matches[:, 1] the indices in the second set of descriptors.

## plot_matches¶

skimage.feature.plot_matches(ax, image1, image2, keypoints1, keypoints2, matches, keypoints_color='k', matches_color=None, only_matches=False, alignment='horizontal')[source]

Plot matched features.

Parameters: ax : matplotlib.axes.Axes Matches and image are drawn in this ax. image1 : (N, M [, 3]) array First grayscale or color image. image2 : (N, M [, 3]) array Second grayscale or color image. keypoints1 : (K1, 2) array First keypoint coordinates as (row, col). keypoints2 : (K2, 2) array Second keypoint coordinates as (row, col). matches : (Q, 2) array Indices of corresponding matches in first and second set of descriptors, where matches[:, 0] denote the indices in the first and matches[:, 1] the indices in the second set of descriptors. keypoints_color : matplotlib color, optional Color for keypoint locations. matches_color : matplotlib color, optional Color for lines which connect keypoint matches. By default the color is chosen randomly. only_matches : bool, optional Whether to only plot matches and not plot the keypoint locations. alignment : {‘horizontal’, ‘vertical’}, optional Whether to show images side by side, 'horizontal', or one above the other, 'vertical'.

## blob_dog¶

skimage.feature.blob_dog(image, min_sigma=1, max_sigma=50, sigma_ratio=1.6, threshold=2.0, overlap=0.5)[source]

Finds blobs in the given grayscale image.

Blobs are found using the Difference of Gaussian (DoG) method [1]. For each blob found, the method returns its coordinates and the standard deviation of the Gaussian kernel that detected the blob.

Parameters: image : 2D or 3D ndarray Input grayscale image, blobs are assumed to be light on dark background (white on black). min_sigma : float, optional The minimum standard deviation for Gaussian Kernel. Keep this low to detect smaller blobs. max_sigma : float, optional The maximum standard deviation for Gaussian Kernel. Keep this high to detect larger blobs. sigma_ratio : float, optional The ratio between the standard deviation of Gaussian Kernels used for computing the Difference of Gaussians threshold : float, optional. The absolute lower bound for scale space maxima. Local maxima smaller than thresh are ignored. Reduce this to detect blobs with less intensities. overlap : float, optional A value between 0 and 1. If the area of two blobs overlaps by a fraction greater than threshold, the smaller blob is eliminated. A : (n, image.ndim + 1) ndarray A 2d array with each row representing 3 values for a 2D image, and 4 values for a 3D image: (r, c, sigma) or (p, r, c, sigma) where (r, c) or (p, r, c) are coordinates of the blob and sigma is the standard deviation of the Gaussian kernel which detected the blob.

Notes

The radius of each blob is approximately $$\sqrt{2}\sigma$$ for a 2-D image and $$\sqrt{3}\sigma$$ for a 3-D image.

References

Examples

>>> from skimage import data, feature
>>> feature.blob_dog(data.coins(), threshold=.5, max_sigma=40)
array([[ 267.      ,  359.      ,   16.777216],
[ 267.      ,  115.      ,   10.48576 ],
[ 263.      ,  302.      ,   16.777216],
[ 263.      ,  245.      ,   16.777216],
[ 261.      ,  173.      ,   16.777216],
[ 260.      ,   46.      ,   16.777216],
[ 198.      ,  155.      ,   10.48576 ],
[ 196.      ,   43.      ,   10.48576 ],
[ 195.      ,  102.      ,   16.777216],
[ 194.      ,  277.      ,   16.777216],
[ 193.      ,  213.      ,   16.777216],
[ 185.      ,  347.      ,   16.777216],
[ 128.      ,  154.      ,   10.48576 ],
[ 127.      ,  102.      ,   10.48576 ],
[ 125.      ,  208.      ,   10.48576 ],
[ 125.      ,   45.      ,   16.777216],
[ 124.      ,  337.      ,   10.48576 ],
[ 120.      ,  272.      ,   16.777216],
[  58.      ,  100.      ,   10.48576 ],
[  54.      ,  276.      ,   10.48576 ],
[  54.      ,   42.      ,   16.777216],
[  52.      ,  216.      ,   16.777216],
[  52.      ,  155.      ,   16.777216],
[  45.      ,  336.      ,   16.777216]])


## blob_doh¶

skimage.feature.blob_doh(image, min_sigma=1, max_sigma=30, num_sigma=10, threshold=0.01, overlap=0.5, log_scale=False)[source]

Finds blobs in the given grayscale image.

Blobs are found using the Determinant of Hessian method [1]. For each blob found, the method returns its coordinates and the standard deviation of the Gaussian Kernel used for the Hessian matrix whose determinant detected the blob. Determinant of Hessians is approximated using [2].

Parameters: image : 2D ndarray Input grayscale image.Blobs can either be light on dark or vice versa. min_sigma : float, optional The minimum standard deviation for Gaussian Kernel used to compute Hessian matrix. Keep this low to detect smaller blobs. max_sigma : float, optional The maximum standard deviation for Gaussian Kernel used to compute Hessian matrix. Keep this high to detect larger blobs. num_sigma : int, optional The number of intermediate values of standard deviations to consider between min_sigma and max_sigma. threshold : float, optional. The absolute lower bound for scale space maxima. Local maxima smaller than thresh are ignored. Reduce this to detect less prominent blobs. overlap : float, optional A value between 0 and 1. If the area of two blobs overlaps by a fraction greater than threshold, the smaller blob is eliminated. log_scale : bool, optional If set intermediate values of standard deviations are interpolated using a logarithmic scale to the base 10. If not, linear interpolation is used. A : (n, 3) ndarray A 2d array with each row representing 3 values, (y,x,sigma) where (y,x) are coordinates of the blob and sigma is the standard deviation of the Gaussian kernel of the Hessian Matrix whose determinant detected the blob.

Notes

The radius of each blob is approximately sigma. Computation of Determinant of Hessians is independent of the standard deviation. Therefore detecting larger blobs won’t take more time. In methods line blob_dog() and blob_log() the computation of Gaussians for larger sigma takes more time. The downside is that this method can’t be used for detecting blobs of radius less than 3px due to the box filters used in the approximation of Hessian Determinant.

References

 [2] (1, 2) Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool, “SURF: Speeded Up Robust Features” ftp://ftp.vision.ee.ethz.ch/publications/articles/eth_biwi_00517.pdf

Examples

>>> from skimage import data, feature
>>> img = data.coins()
>>> feature.blob_doh(img)
array([[ 270.        ,  363.        ,   30.        ],
[ 265.        ,  113.        ,   23.55555556],
[ 262.        ,  243.        ,   23.55555556],
[ 260.        ,  173.        ,   30.        ],
[ 197.        ,  153.        ,   20.33333333],
[ 197.        ,   44.        ,   20.33333333],
[ 195.        ,  100.        ,   23.55555556],
[ 193.        ,  275.        ,   23.55555556],
[ 192.        ,  212.        ,   23.55555556],
[ 185.        ,  348.        ,   30.        ],
[ 156.        ,  302.        ,   30.        ],
[ 126.        ,  153.        ,   20.33333333],
[ 126.        ,  101.        ,   20.33333333],
[ 124.        ,  336.        ,   20.33333333],
[ 123.        ,  205.        ,   20.33333333],
[ 123.        ,   44.        ,   23.55555556],
[ 121.        ,  271.        ,   30.        ]])


## blob_log¶

skimage.feature.blob_log(image, min_sigma=1, max_sigma=50, num_sigma=10, threshold=0.2, overlap=0.5, log_scale=False)[source]

Finds blobs in the given grayscale image.

Blobs are found using the Laplacian of Gaussian (LoG) method [1]. For each blob found, the method returns its coordinates and the standard deviation of the Gaussian kernel that detected the blob.

Parameters: image : 2D or 3D ndarray Input grayscale image, blobs are assumed to be light on dark background (white on black). min_sigma : float, optional The minimum standard deviation for Gaussian Kernel. Keep this low to detect smaller blobs. max_sigma : float, optional The maximum standard deviation for Gaussian Kernel. Keep this high to detect larger blobs. num_sigma : int, optional The number of intermediate values of standard deviations to consider between min_sigma and max_sigma. threshold : float, optional. The absolute lower bound for scale space maxima. Local maxima smaller than thresh are ignored. Reduce this to detect blobs with less intensities. overlap : float, optional A value between 0 and 1. If the area of two blobs overlaps by a fraction greater than threshold, the smaller blob is eliminated. log_scale : bool, optional If set intermediate values of standard deviations are interpolated using a logarithmic scale to the base 10. If not, linear interpolation is used. A : (n, image.ndim + 1) ndarray A 2d array with each row representing 3 values for a 2D image, and 4 values for a 3D image: (r, c, sigma) or (p, r, c, sigma) where (r, c) or (p, r, c) are coordinates of the blob and sigma is the standard deviation of the Gaussian kernel which detected the blob.

Notes

The radius of each blob is approximately $$\sqrt{2}\sigma$$ for a 2-D image and $$\sqrt{3}\sigma$$ for a 3-D image.

References

Examples

>>> from skimage import data, feature, exposure
>>> img = data.coins()
>>> img = exposure.equalize_hist(img)  # improves detection
>>> feature.blob_log(img, threshold = .3)
array([[ 266.        ,  115.        ,   11.88888889],
[ 263.        ,  302.        ,   17.33333333],
[ 263.        ,  244.        ,   17.33333333],
[ 260.        ,  174.        ,   17.33333333],
[ 198.        ,  155.        ,   11.88888889],
[ 198.        ,  103.        ,   11.88888889],
[ 197.        ,   44.        ,   11.88888889],
[ 194.        ,  276.        ,   17.33333333],
[ 194.        ,  213.        ,   17.33333333],
[ 185.        ,  344.        ,   17.33333333],
[ 128.        ,  154.        ,   11.88888889],
[ 127.        ,  102.        ,   11.88888889],
[ 126.        ,  208.        ,   11.88888889],
[ 126.        ,   46.        ,   11.88888889],
[ 124.        ,  336.        ,   11.88888889],
[ 121.        ,  272.        ,   17.33333333],
[ 113.        ,  323.        ,    1.        ]])


## haar_like_feature¶

skimage.feature.haar_like_feature(int_image, r, c, width, height, feature_type=None, feature_coord=None)[source]

Compute the Haar-like features for a region of interest (ROI) of an integral image.

Haar-like features have been successfully used for image classification and object detection [1]. It has been used for real-time face detection algorithm proposed in [2].

Parameters: int_image : (M, N) ndarray Integral image for which the features need to be computed. r : int Row-coordinate of top left corner of the detection window. c : int Column-coordinate of top left corner of the detection window. width : int Width of the detection window. height : int Height of the detection window. feature_type : str or list of str or None, optional The type of feature to consider: ‘type-2-x’: 2 rectangles varying along the x axis; ‘type-2-y’: 2 rectangles varying along the y axis; ‘type-3-x’: 3 rectangles varying along the x axis; ‘type-3-y’: 3 rectangles varying along the y axis; ‘type-4’: 4 rectangles varying along x and y axis. By default all features are extracted. If using with feature_coord, it should correspond to the feature type of each associated coordinate feature. feature_coord : ndarray of list of tuples or None, optional The array of coordinates to be extracted. This is useful when you want to recompute only a subset of features. In this case feature_type needs to be an array containing the type of each feature, as returned by haar_like_feature_coord(). By default, all coordinates are computed. haar_features : (n_features,) ndarray of int or float Resulting Haar-like features. Each value is equal to the subtraction of sums of the positive and negative rectangles. The data type depends of the data type of int_image: int when the data type of int_image is uint or int and float when the data type of int_image is float.

Notes

When extracting those features in parallel, be aware that the choice of the backend (i.e. multiprocessing vs threading) will have an impact on the performance. The rule of thumb is as follows: use multiprocessing when extracting features for all possible ROI in an image; use threading when extracting the feature at specific location for a limited number of ROIs. Refer to the example Face classification using Haar-like feature descriptor for more insights.

References

 [2] (1, 2) Oren, M., Papageorgiou, C., Sinha, P., Osuna, E., & Poggio, T. (1997, June). Pedestrian detection using wavelet templates. In Computer Vision and Pattern Recognition, 1997. Proceedings., 1997 IEEE Computer Society Conference on (pp. 193-199). IEEE. http://tinyurl.com/y6ulxfta DOI: 10.1109/CVPR.1997.609319
 [3] Viola, Paul, and Michael J. Jones. “Robust real-time face detection.” International journal of computer vision 57.2 (2004): 137-154. http://www.merl.com/publications/docs/TR2004-043.pdf DOI: 10.1109/CVPR.2001.990517

Examples

>>> import numpy as np
>>> from skimage.transform import integral_image
>>> from skimage.feature import haar_like_feature
>>> img = np.ones((5, 5), dtype=np.uint8)
>>> img_ii = integral_image(img)
>>> feature = haar_like_feature(img_ii, 0, 0, 5, 5, 'type-3-x')
>>> feature
array([-1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1,
-2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1,
-2, -1, -2, -1, -2, -1, -1, -1])


You can compute the feature for some pre-computed coordinates.

>>> from skimage.feature import haar_like_feature_coord
>>> feature_coord, feature_type = zip(
...     *[haar_like_feature_coord(5, 5, feat_t)
...       for feat_t in ('type-2-x', 'type-3-x')])
>>> # only select one feature over two
>>> feature_coord = np.concatenate([x[::2] for x in feature_coord])
>>> feature_type = np.concatenate([x[::2] for x in feature_type])
>>> feature = haar_like_feature(img_ii, 0, 0, 5, 5,
...                             feature_type=feature_type,
...                             feature_coord=feature_coord)
>>> feature
array([ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
0,  0,  0,  0,  0,  0,  0,  0, -1, -3, -1, -3, -1, -3, -1, -3, -1,
-3, -1, -3, -1, -3, -2, -1, -3, -2, -2, -2, -1])


## haar_like_feature_coord¶

skimage.feature.haar_like_feature_coord(width, height, feature_type=None)[source]

Compute the coordinates of Haar-like features.

Parameters: width : int Width of the detection window. height : int Height of the detection window. feature_type : str or list of str or None, optional The type of feature to consider: ‘type-2-x’: 2 rectangles varying along the x axis; ‘type-2-y’: 2 rectangles varying along the y axis; ‘type-3-x’: 3 rectangles varying along the x axis; ‘type-3-y’: 3 rectangles varying along the y axis; ‘type-4’: 4 rectangles varying along x and y axis. By default all features are extracted. feature_coord : (n_features, n_rectangles, 2, 2), ndarray of list of tuple coord Coordinates of the rectangles for each feature. feature_type : (n_features,), ndarray of str The corresponding type for each feature.

Examples

>>> import numpy as np
>>> from skimage.transform import integral_image
>>> from skimage.feature import haar_like_feature_coord
>>> feat_coord, feat_type = haar_like_feature_coord(2, 2, 'type-4')
>>> feat_coord # doctest: +SKIP
array([ list([[(0, 0), (0, 0)], [(0, 1), (0, 1)],
[(1, 1), (1, 1)], [(1, 0), (1, 0)]])], dtype=object)
>>> feat_type
array(['type-4'], dtype=object)


## draw_haar_like_feature¶

skimage.feature.draw_haar_like_feature(image, r, c, width, height, feature_coord, color_positive_block=(1.0, 0.0, 0.0), color_negative_block=(0.0, 1.0, 0.0), alpha=0.5, max_n_features=None, random_state=None)[source]

Visualization of Haar-like features.

Parameters: image : (M, N) ndarray The region of an integral image for which the features need to be computed. r : int Row-coordinate of top left corner of the detection window. c : int Column-coordinate of top left corner of the detection window. width : int Width of the detection window. height : int Height of the detection window. feature_coord : ndarray of list of tuples or None, optional The array of coordinates to be extracted. This is useful when you want to recompute only a subset of features. In this case feature_type needs to be an array containing the type of each feature, as returned by haar_like_feature_coord(). By default, all coordinates are computed. color_positive_rectangle : tuple of 3 floats Floats specifying the color for the positive block. Corresponding values define (R, G, B) values. Default value is red (1, 0, 0). color_negative_block : tuple of 3 floats Floats specifying the color for the negative block Corresponding values define (R, G, B) values. Default value is blue (0, 1, 0). alpha : float Value in the range [0, 1] that specifies opacity of visualization. 1 - fully transparent, 0 - opaque. max_n_features : int, default=None The maximum number of features to be returned. By default, all features are returned. random_state : int, RandomState instance or None, optional If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. The random state is used when generating a set of features smaller than the total number of available features. features : (M, N), ndarray An image in which the different features will be added.

Examples

>>> import numpy as np
>>> from skimage.feature import haar_like_feature_coord
>>> from skimage.feature import draw_haar_like_feature
>>> feature_coord, _ = haar_like_feature_coord(2, 2, 'type-4')
>>> image = draw_haar_like_feature(np.zeros((2, 2)),
...                                0, 0, 2, 2,
...                                feature_coord,
...                                max_n_features=1)
>>> image
array([[[ 0. ,  0.5,  0. ],
[ 0.5,  0. ,  0. ]],
<BLANKLINE>
[[ 0.5,  0. ,  0. ],
[ 0. ,  0.5,  0. ]]])


## BRIEF¶

class skimage.feature.BRIEF(descriptor_size=256, patch_size=49, mode='normal', sigma=1, sample_seed=1)[source]

Bases: skimage.feature.util.DescriptorExtractor

BRIEF binary descriptor extractor.

BRIEF (Binary Robust Independent Elementary Features) is an efficient feature point descriptor. It is highly discriminative even when using relatively few bits and is computed using simple intensity difference tests.

For each keypoint, intensity comparisons are carried out for a specifically distributed number N of pixel-pairs resulting in a binary descriptor of length N. For binary descriptors the Hamming distance can be used for feature matching, which leads to lower computational cost in comparison to the L2 norm.

Parameters: descriptor_size : int, optional Size of BRIEF descriptor for each keypoint. Sizes 128, 256 and 512 recommended by the authors. Default is 256. patch_size : int, optional Length of the two dimensional square patch sampling region around the keypoints. Default is 49. mode : {‘normal’, ‘uniform’}, optional Probability distribution for sampling location of decision pixel-pairs around keypoints. sample_seed : int, optional Seed for the random sampling of the decision pixel-pairs. From a square window with length patch_size, pixel pairs are sampled using the mode parameter to build the descriptors using intensity comparison. The value of sample_seed must be the same for the images to be matched while building the descriptors. sigma : float, optional Standard deviation of the Gaussian low-pass filter applied to the image to alleviate noise sensitivity, which is strongly recommended to obtain discriminative and good descriptors.

Examples

>>> from skimage.feature import (corner_harris, corner_peaks, BRIEF,
...                              match_descriptors)
>>> import numpy as np
>>> square1 = np.zeros((8, 8), dtype=np.int32)
>>> square1[2:6, 2:6] = 1
>>> square1
array([[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0]], dtype=int32)
>>> square2 = np.zeros((9, 9), dtype=np.int32)
>>> square2[2:7, 2:7] = 1
>>> square2
array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=int32)
>>> keypoints1 = corner_peaks(corner_harris(square1), min_distance=1)
>>> keypoints2 = corner_peaks(corner_harris(square2), min_distance=1)
>>> extractor = BRIEF(patch_size=5)
>>> extractor.extract(square1, keypoints1)
>>> descriptors1 = extractor.descriptors
>>> extractor.extract(square2, keypoints2)
>>> descriptors2 = extractor.descriptors
>>> matches = match_descriptors(descriptors1, descriptors2)
>>> matches
array([[0, 0],
[1, 1],
[2, 2],
[3, 3]])
>>> keypoints1[matches[:, 0]]
array([[2, 2],
[2, 5],
[5, 2],
[5, 5]])
>>> keypoints2[matches[:, 1]]
array([[2, 2],
[2, 6],
[6, 2],
[6, 6]])

Attributes: descriptors : (Q, descriptor_size) array of dtype bool 2D ndarray of binary descriptors of size descriptor_size for Q keypoints after filtering out border keypoints with value at an index (i, j) either being True or False representing the outcome of the intensity comparison for i-th keypoint on j-th decision pixel-pair. It is Q == np.sum(mask). mask : (N, ) array of dtype bool Mask indicating whether a keypoint has been filtered out (False) or is described in the descriptors array (True).
__init__(descriptor_size=256, patch_size=49, mode='normal', sigma=1, sample_seed=1)[source]

Initialize self. See help(type(self)) for accurate signature.

extract(image, keypoints)[source]

Extract BRIEF binary descriptors for given keypoints in image.

Parameters: image : 2D array Input image. keypoints : (N, 2) array Keypoint coordinates as (row, col).

## CENSURE¶

class skimage.feature.CENSURE(min_scale=1, max_scale=7, mode='DoB', non_max_threshold=0.15, line_threshold=10)[source]

Bases: skimage.feature.util.FeatureDetector

CENSURE keypoint detector.

min_scale : int, optional
Minimum scale to extract keypoints from.
max_scale : int, optional
Maximum scale to extract keypoints from. The keypoints will be extracted from all the scales except the first and the last i.e. from the scales in the range [min_scale + 1, max_scale - 1]. The filter sizes for different scales is such that the two adjacent scales comprise of an octave.
mode : {‘DoB’, ‘Octagon’, ‘STAR’}, optional
Type of bi-level filter used to get the scales of the input image. Possible values are ‘DoB’, ‘Octagon’ and ‘STAR’. The three modes represent the shape of the bi-level filters i.e. box(square), octagon and star respectively. For instance, a bi-level octagon filter consists of a smaller inner octagon and a larger outer octagon with the filter weights being uniformly negative in both the inner octagon while uniformly positive in the difference region. Use STAR and Octagon for better features and DoB for better performance.
non_max_threshold : float, optional
Threshold value used to suppress maximas and minimas with a weak magnitude response obtained after Non-Maximal Suppression.
line_threshold : float, optional
Threshold for rejecting interest points which have ratio of principal curvatures greater than this value.

References

 [1] Motilal Agrawal, Kurt Konolige and Morten Rufus Blas “CENSURE: Center Surround Extremas for Realtime Feature Detection and Matching”, https://link.springer.com/chapter/10.1007/978-3-540-88693-8_8 DOI:10.1007/978-3-540-88693-8_8
 [2] Adam Schmidt, Marek Kraft, Michal Fularz and Zuzanna Domagala “Comparative Assessment of Point Feature Detectors and Descriptors in the Context of Robot Navigation” http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-268aaf28-0faf-4872-a4df-7e2e61cb364c/c/Schmidt_comparative.pdf DOI:10.1.1.465.1117

Examples

>>> from skimage.data import astronaut
>>> from skimage.color import rgb2gray
>>> from skimage.feature import CENSURE
>>> img = rgb2gray(astronaut()[100:300, 100:300])
>>> censure = CENSURE()
>>> censure.detect(img)
>>> censure.keypoints
array([[  4, 148],
[ 12,  73],
[ 21, 176],
[ 91,  22],
[ 93,  56],
[ 94,  22],
[ 95,  54],
[100,  51],
[103,  51],
[106,  67],
[108,  15],
[117,  20],
[122,  60],
[125,  37],
[129,  37],
[133,  76],
[145,  44],
[146,  94],
[150, 114],
[153,  33],
[154, 156],
[155, 151],
[184,  63]])
>>> censure.scales
array([2, 6, 6, 2, 4, 3, 2, 3, 2, 6, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 4, 2, 2])

Attributes: keypoints : (N, 2) array Keypoint coordinates as (row, col). scales : (N, ) array Corresponding scales.
__init__(min_scale=1, max_scale=7, mode='DoB', non_max_threshold=0.15, line_threshold=10)[source]

Initialize self. See help(type(self)) for accurate signature.

detect(image)[source]

Detect CENSURE keypoints along with the corresponding scale.

Parameters: image : 2D ndarray Input image.

## ORB¶

class skimage.feature.ORB(downscale=1.2, n_scales=8, n_keypoints=500, fast_n=9, fast_threshold=0.08, harris_k=0.04)[source]

Bases: skimage.feature.util.FeatureDetector, skimage.feature.util.DescriptorExtractor

Oriented FAST and rotated BRIEF feature detector and binary descriptor extractor.

Parameters: n_keypoints : int, optional Number of keypoints to be returned. The function will return the best n_keypoints according to the Harris corner response if more than n_keypoints are detected. If not, then all the detected keypoints are returned. fast_n : int, optional The n parameter in skimage.feature.corner_fast. Minimum number of consecutive pixels out of 16 pixels on the circle that should all be either brighter or darker w.r.t test-pixel. A point c on the circle is darker w.r.t test pixel p if Ic < Ip - threshold and brighter if Ic > Ip + threshold. Also stands for the n in FAST-n corner detector. fast_threshold : float, optional The threshold parameter in feature.corner_fast. Threshold used to decide whether the pixels on the circle are brighter, darker or similar w.r.t. the test pixel. Decrease the threshold when more corners are desired and vice-versa. harris_k : float, optional The k parameter in skimage.feature.corner_harris. Sensitivity factor to separate corners from edges, typically in range [0, 0.2]. Small values of k result in detection of sharp corners. downscale : float, optional Downscale factor for the image pyramid. Default value 1.2 is chosen so that there are more dense scales which enable robust scale invariance for a subsequent feature description. n_scales : int, optional Maximum number of scales from the bottom of the image pyramid to extract the features from.

References

 [1] Ethan Rublee, Vincent Rabaud, Kurt Konolige and Gary Bradski “ORB: An efficient alternative to SIFT and SURF” http://www.vision.cs.chubu.ac.jp/CV-R/pdf/Rublee_iccv2011.pdf

Examples

>>> from skimage.feature import ORB, match_descriptors
>>> img1 = np.zeros((100, 100))
>>> img2 = np.zeros_like(img1)
>>> np.random.seed(1)
>>> square = np.random.rand(20, 20)
>>> img1[40:60, 40:60] = square
>>> img2[53:73, 53:73] = square
>>> detector_extractor1 = ORB(n_keypoints=5)
>>> detector_extractor2 = ORB(n_keypoints=5)
>>> detector_extractor1.detect_and_extract(img1)
>>> detector_extractor2.detect_and_extract(img2)
>>> matches = match_descriptors(detector_extractor1.descriptors,
...                             detector_extractor2.descriptors)
>>> matches
array([[0, 0],
[1, 1],
[2, 2],
[3, 3],
[4, 4]])
>>> detector_extractor1.keypoints[matches[:, 0]]
array([[ 42.,  40.],
[ 47.,  58.],
[ 44.,  40.],
[ 59.,  42.],
[ 45.,  44.]])
>>> detector_extractor2.keypoints[matches[:, 1]]
array([[ 55.,  53.],
[ 60.,  71.],
[ 57.,  53.],
[ 72.,  55.],
[ 58.,  57.]])

Attributes: keypoints : (N, 2) array Keypoint coordinates as (row, col). scales : (N, ) array Corresponding scales. orientations : (N, ) array Corresponding orientations in radians. responses : (N, ) array Corresponding Harris corner responses. descriptors : (Q, descriptor_size) array of dtype bool 2D array of binary descriptors of size descriptor_size for Q keypoints after filtering out border keypoints with value at an index (i, j) either being True or False representing the outcome of the intensity comparison for i-th keypoint on j-th decision pixel-pair. It is Q == np.sum(mask).
__init__(downscale=1.2, n_scales=8, n_keypoints=500, fast_n=9, fast_threshold=0.08, harris_k=0.04)[source]

Initialize self. See help(type(self)) for accurate signature.

detect(image)[source]

Detect oriented FAST keypoints along with the corresponding scale.

Parameters: image : 2D array Input image.
detect_and_extract(image)[source]

Detect oriented FAST keypoints and extract rBRIEF descriptors.

Note that this is faster than first calling detect and then extract.

Parameters: image : 2D array Input image.
extract(image, keypoints, scales, orientations)[source]

Extract rBRIEF binary descriptors for given keypoints in image.

Note that the keypoints must be extracted using the same downscale and n_scales parameters. Additionally, if you want to extract both keypoints and descriptors you should use the faster detect_and_extract.

Parameters: image : 2D array Input image. keypoints : (N, 2) array Keypoint coordinates as (row, col). scales : (N, ) array Corresponding scales. orientations : (N, ) array Corresponding orientations in radians.