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# Module: filters¶

 skimage.filters.inverse(data[, …]) Apply the filter in reverse to the given data. skimage.filters.wiener(data[, …]) Minimum Mean Square Error (Wiener) inverse filter. skimage.filters.gaussian(image[, sigma, …]) Multi-dimensional Gaussian filter. skimage.filters.median(image[, selem, out, …]) Return local median of an image. skimage.filters.sobel(image[, mask]) Find the edge magnitude using the Sobel transform. skimage.filters.sobel_h(image[, mask]) Find the horizontal edges of an image using the Sobel transform. skimage.filters.sobel_v(image[, mask]) Find the vertical edges of an image using the Sobel transform. skimage.filters.scharr(image[, mask]) Find the edge magnitude using the Scharr transform. skimage.filters.scharr_h(image[, mask]) Find the horizontal edges of an image using the Scharr transform. skimage.filters.scharr_v(image[, mask]) Find the vertical edges of an image using the Scharr transform. skimage.filters.prewitt(image[, mask]) Find the edge magnitude using the Prewitt transform. skimage.filters.prewitt_h(image[, mask]) Find the horizontal edges of an image using the Prewitt transform. skimage.filters.prewitt_v(image[, mask]) Find the vertical edges of an image using the Prewitt transform. skimage.filters.roberts(image[, mask]) Find the edge magnitude using Roberts’ cross operator. skimage.filters.roberts_pos_diag(image[, mask]) Find the cross edges of an image using Roberts’ cross operator. skimage.filters.roberts_neg_diag(image[, mask]) Find the cross edges of an image using the Roberts’ Cross operator. skimage.filters.laplace(image[, ksize, mask]) Find the edges of an image using the Laplace operator. skimage.filters.rank_order(image) Return an image of the same shape where each pixel is the index of the pixel value in the ascending order of the unique values of image, aka the rank-order value. skimage.filters.gabor_kernel(frequency[, …]) Return complex 2D Gabor filter kernel. skimage.filters.gabor(image, frequency[, …]) Return real and imaginary responses to Gabor filter. skimage.filters.try_all_threshold(image[, …]) Returns a figure comparing the outputs of different thresholding methods. skimage.filters.frangi(image[, scale_range, …]) Filter an image with the Frangi filter. skimage.filters.hessian(image[, …]) Filter an image with the Hessian filter. skimage.filters.threshold_otsu(image[, nbins]) Return threshold value based on Otsu’s method. skimage.filters.threshold_yen(image[, nbins]) Return threshold value based on Yen’s method. skimage.filters.threshold_isodata(image[, …]) Return threshold value(s) based on ISODATA method. skimage.filters.threshold_li(image, *[, …]) Compute threshold value by Li’s iterative Minimum Cross Entropy method. skimage.filters.threshold_local(image, …) Compute a threshold mask image based on local pixel neighborhood. skimage.filters.threshold_minimum(image[, …]) Return threshold value based on minimum method. skimage.filters.threshold_mean(image) Return threshold value based on the mean of grayscale values. skimage.filters.threshold_niblack(image[, …]) Applies Niblack local threshold to an array. skimage.filters.threshold_sauvola(image[, …]) Applies Sauvola local threshold to an array. skimage.filters.threshold_triangle(image[, …]) Return threshold value based on the triangle algorithm. skimage.filters.apply_hysteresis_threshold(…) Apply hysteresis thresholding to image. skimage.filters.unsharp_mask(image[, …]) Unsharp masking filter. skimage.filters.LPIFilter2D(…) Linear Position-Invariant Filter (2-dimensional) skimage.filters.rank

## inverse¶

skimage.filters.inverse(data, impulse_response=None, filter_params={}, max_gain=2, predefined_filter=None)[source]

Apply the filter in reverse to the given data.

Parameters: Other Parameters: data : (M,N) ndarray Input data. impulse_response : callable f(r, c, **filter_params) Impulse response of the filter. See LPIFilter2D.__init__. filter_params : dict Additional keyword parameters to the impulse_response function. max_gain : float Limit the filter gain. Often, the filter contains zeros, which would cause the inverse filter to have infinite gain. High gain causes amplification of artefacts, so a conservative limit is recommended. predefined_filter : LPIFilter2D If you need to apply the same filter multiple times over different images, construct the LPIFilter2D and specify it here.

## wiener¶

skimage.filters.wiener(data, impulse_response=None, filter_params={}, K=0.25, predefined_filter=None)[source]

Minimum Mean Square Error (Wiener) inverse filter.

Parameters: Other Parameters: data : (M,N) ndarray Input data. K : float or (M,N) ndarray Ratio between power spectrum of noise and undegraded image. impulse_response : callable f(r, c, **filter_params) Impulse response of the filter. See LPIFilter2D.__init__. filter_params : dict Additional keyword parameters to the impulse_response function. predefined_filter : LPIFilter2D If you need to apply the same filter multiple times over different images, construct the LPIFilter2D and specify it here.

## gaussian¶

skimage.filters.gaussian(image, sigma=1, output=None, mode='nearest', cval=0, multichannel=None, preserve_range=False, truncate=4.0)[source]

Multi-dimensional Gaussian filter.

Parameters: image : array-like Input image (grayscale or color) to filter. sigma : scalar or sequence of scalars, optional Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes. output : array, optional The output parameter passes an array in which to store the filter output. mode : {‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘nearest’. cval : scalar, optional Value to fill past edges of input if mode is ‘constant’. Default is 0.0 multichannel : bool, optional (default: None) Whether the last axis of the image is to be interpreted as multiple channels. If True, each channel is filtered separately (channels are not mixed together). Only 3 channels are supported. If None, the function will attempt to guess this, and raise a warning if ambiguous, when the array has shape (M, N, 3). preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html truncate : float, optional Truncate the filter at this many standard deviations. filtered_image : ndarray the filtered array

Notes

This function is a wrapper around scipy.ndi.gaussian_filter().

Integer arrays are converted to float.

The multi-dimensional filter is implemented as a sequence of one-dimensional convolution filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision.

Examples

>>> a = np.zeros((3, 3))
>>> a[1, 1] = 1
>>> a
array([[ 0.,  0.,  0.],
[ 0.,  1.,  0.],
[ 0.,  0.,  0.]])
>>> gaussian(a, sigma=0.4)  # mild smoothing
array([[ 0.00163116,  0.03712502,  0.00163116],
[ 0.03712502,  0.84496158,  0.03712502],
[ 0.00163116,  0.03712502,  0.00163116]])
>>> gaussian(a, sigma=1)  # more smoothing
array([[ 0.05855018,  0.09653293,  0.05855018],
[ 0.09653293,  0.15915589,  0.09653293],
[ 0.05855018,  0.09653293,  0.05855018]])
>>> # Several modes are possible for handling boundaries
>>> gaussian(a, sigma=1, mode='reflect')
array([[ 0.08767308,  0.12075024,  0.08767308],
[ 0.12075024,  0.16630671,  0.12075024],
[ 0.08767308,  0.12075024,  0.08767308]])
>>> # For RGB images, each is filtered separately
>>> from skimage.data import astronaut
>>> image = astronaut()
>>> filtered_img = gaussian(image, sigma=1, multichannel=True)


## median¶

skimage.filters.median(image, selem=None, out=None, mask=None, shift_x=False, shift_y=False, mode='nearest', cval=0.0, behavior='rank')[source]

Return local median of an image.

Parameters: image : array-like Input image. selem : ndarray, optional If behavior=='rank', selem is a 2-D array of 1’s and 0’s. If behavior=='ndimage', selem is a N-D array of 1’s and 0’s with the same number of dimension than image. If None, selem will be a N-D array with 3 elements for each dimension (e.g., vector, square, cube, etc.) out : ndarray, (same dtype as image), optional If None, a new array is allocated. mask : ndarray, optional Mask array that defines (>0) area of the image included in the local neighborhood. If None, the complete image is used (default). Only valid when behavior='rank' Deprecated since version 0.16: mask is deprecated in 0.16 and will be removed 0.17. shift_x, shift_y : int, optional Offset added to the structuring element center point. Shift is bounded by the structuring element sizes (center must be inside the given structuring element). Only valid when behavior='rank'. Deprecated since version 0.16: shift_x and shift_y are deprecated in 0.16 and will be removed in 0.17. mode : {‘reflect’, ‘constant’, ‘nearest’, ‘mirror’,’‘wrap’}, optional The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘nearest’. New in version 0.15: mode is used when behavior='ndimage'. cval : scalar, optional Value to fill past edges of input if mode is ‘constant’. Default is 0.0 New in version 0.15: cval was added in 0.15 is used when behavior='ndimage'. behavior : {‘rank’, ‘ndimage’}, optional Either to use the old behavior (i.e., < 0.15) or the new behavior. The old behavior will call the skimage.filters.rank.median(). The new behavior will call the scipy.ndimage.median_filter(). Default is ‘rank’. New in version 0.15: behavior is introduced in 0.15 Deprecated since version 0.15: Default behavior will change from ‘rank’ to ‘ndimage’ in 0.16 out : 2-D array (same dtype as input image) Output image.

skimage.filters.rank.median
Rank-based implementation of the median filtering offering more flexibility with additional parameters but dedicated for unsigned integer images.

Examples

>>> from skimage import data
>>> from skimage.morphology import disk
>>> from skimage.filters import median
>>> img = data.camera()
>>> med = median(img, disk(5))


## sobel¶

skimage.filters.sobel(image, mask=None)[source]

Find the edge magnitude using the Sobel transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Sobel edge map.

scharr, prewitt, roberts, feature.canny

Notes

Take the square root of the sum of the squares of the horizontal and vertical Sobels to get a magnitude that’s somewhat insensitive to direction.

The 3x3 convolution kernel used in the horizontal and vertical Sobels is an approximation of the gradient of the image (with some slight blurring since 9 pixels are used to compute the gradient at a given pixel). As an approximation of the gradient, the Sobel operator is not completely rotation-invariant. The Scharr operator should be used for a better rotation invariance.

Note that scipy.ndimage.sobel returns a directional Sobel which has to be further processed to perform edge detection.

Examples

>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.sobel(camera)


## sobel_h¶

skimage.filters.sobel_h(image, mask=None)[source]

Find the horizontal edges of an image using the Sobel transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Sobel edge map.

Notes

We use the following kernel:

 1   2   1
0   0   0
-1  -2  -1


## sobel_v¶

skimage.filters.sobel_v(image, mask=None)[source]

Find the vertical edges of an image using the Sobel transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Sobel edge map.

Notes

We use the following kernel:

1   0  -1
2   0  -2
1   0  -1


## scharr¶

skimage.filters.scharr(image, mask=None)[source]

Find the edge magnitude using the Scharr transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Scharr edge map.

sobel, prewitt, canny

Notes

Take the square root of the sum of the squares of the horizontal and vertical Scharrs to get a magnitude that is somewhat insensitive to direction. The Scharr operator has a better rotation invariance than other edge filters such as the Sobel or the Prewitt operators.

References

 [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.

Examples

>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.scharr(camera)


## scharr_h¶

skimage.filters.scharr_h(image, mask=None)[source]

Find the horizontal edges of an image using the Scharr transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Scharr edge map.

Notes

We use the following kernel:

 3   10   3
0    0   0
-3  -10  -3


References

 [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.

## scharr_v¶

skimage.filters.scharr_v(image, mask=None)[source]

Find the vertical edges of an image using the Scharr transform.

Parameters: image : 2-D array Image to process mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Scharr edge map.

Notes

We use the following kernel:

 3   0   -3
10   0  -10
3   0   -3


References

 [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives.

## prewitt¶

skimage.filters.prewitt(image, mask=None)[source]

Find the edge magnitude using the Prewitt transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Prewitt edge map.

Notes

Return the square root of the sum of squares of the horizontal and vertical Prewitt transforms. The edge magnitude depends slightly on edge directions, since the approximation of the gradient operator by the Prewitt operator is not completely rotation invariant. For a better rotation invariance, the Scharr operator should be used. The Sobel operator has a better rotation invariance than the Prewitt operator, but a worse rotation invariance than the Scharr operator.

Examples

>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.prewitt(camera)


## prewitt_h¶

skimage.filters.prewitt_h(image, mask=None)[source]

Find the horizontal edges of an image using the Prewitt transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Prewitt edge map.

Notes

We use the following kernel:

 1   1   1
0   0   0
-1  -1  -1


## prewitt_v¶

skimage.filters.prewitt_v(image, mask=None)[source]

Find the vertical edges of an image using the Prewitt transform.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Prewitt edge map.

Notes

We use the following kernel:

1   0  -1
1   0  -1
1   0  -1


## roberts¶

skimage.filters.roberts(image, mask=None)[source]

Find the edge magnitude using Roberts’ cross operator.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Roberts’ Cross edge map.

sobel, scharr, prewitt, feature.canny

Examples

>>> from skimage import data
>>> camera = data.camera()
>>> from skimage import filters
>>> edges = filters.roberts(camera)


## roberts_pos_diag¶

skimage.filters.roberts_pos_diag(image, mask=None)[source]

Find the cross edges of an image using Roberts’ cross operator.

The kernel is applied to the input image to produce separate measurements of the gradient component one orientation.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Robert’s edge map.

Notes

We use the following kernel:

1   0
0  -1


## roberts_neg_diag¶

skimage.filters.roberts_neg_diag(image, mask=None)[source]

Find the cross edges of an image using the Roberts’ Cross operator.

The kernel is applied to the input image to produce separate measurements of the gradient component one orientation.

Parameters: image : 2-D array Image to process. mask : 2-D array, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : 2-D array The Robert’s edge map.

Notes

We use the following kernel:

 0   1
-1   0


## laplace¶

skimage.filters.laplace(image, ksize=3, mask=None)[source]

Find the edges of an image using the Laplace operator.

Parameters: image : ndarray Image to process. ksize : int, optional Define the size of the discrete Laplacian operator such that it will have a size of (ksize,) * image.ndim. mask : ndarray, optional An optional mask to limit the application to a certain area. Note that pixels surrounding masked regions are also masked to prevent masked regions from affecting the result. output : ndarray The Laplace edge map.

Notes

The Laplacian operator is generated using the function skimage.restoration.uft.laplacian().

## rank_order¶

skimage.filters.rank_order(image)[source]

Return an image of the same shape where each pixel is the index of the pixel value in the ascending order of the unique values of image, aka the rank-order value.

Parameters: image: ndarray labels: ndarray of type np.uint32, of shape image.shape New array where each pixel has the rank-order value of the corresponding pixel in image. Pixel values are between 0 and n - 1, where n is the number of distinct unique values in image. original_values: 1-D ndarray Unique original values of image

Examples

>>> a = np.array([[1, 4, 5], [4, 4, 1], [5, 1, 1]])
>>> a
array([[1, 4, 5],
[4, 4, 1],
[5, 1, 1]])
>>> rank_order(a)
(array([[0, 1, 2],
[1, 1, 0],
[2, 0, 0]], dtype=uint32), array([1, 4, 5]))
>>> b = np.array([-1., 2.5, 3.1, 2.5])
>>> rank_order(b)
(array([0, 1, 2, 1], dtype=uint32), array([-1. ,  2.5,  3.1]))


## gabor_kernel¶

skimage.filters.gabor_kernel(frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None, n_stds=3, offset=0)[source]

Return complex 2D Gabor filter kernel.

Gabor kernel is a Gaussian kernel modulated by a complex harmonic function. Harmonic function consists of an imaginary sine function and a real cosine function. Spatial frequency is inversely proportional to the wavelength of the harmonic and to the standard deviation of a Gaussian kernel. The bandwidth is also inversely proportional to the standard deviation.

Parameters: frequency : float Spatial frequency of the harmonic function. Specified in pixels. theta : float, optional Orientation in radians. If 0, the harmonic is in the x-direction. bandwidth : float, optional The bandwidth captured by the filter. For fixed bandwidth, sigma_x and sigma_y will decrease with increasing frequency. This value is ignored if sigma_x and sigma_y are set by the user. sigma_x, sigma_y : float, optional Standard deviation in x- and y-directions. These directions apply to the kernel before rotation. If theta = pi/2, then the kernel is rotated 90 degrees so that sigma_x controls the vertical direction. n_stds : scalar, optional The linear size of the kernel is n_stds (3 by default) standard deviations offset : float, optional Phase offset of harmonic function in radians. g : complex array Complex filter kernel.

References

Examples

>>> from skimage.filters import gabor_kernel
>>> from skimage import io
>>> from matplotlib import pyplot as plt  # doctest: +SKIP

>>> gk = gabor_kernel(frequency=0.2)
>>> plt.figure()        # doctest: +SKIP
>>> io.imshow(gk.real)  # doctest: +SKIP
>>> io.show()           # doctest: +SKIP

>>> # more ripples (equivalent to increasing the size of the
>>> gk = gabor_kernel(frequency=0.2, bandwidth=0.1)
>>> plt.figure()        # doctest: +SKIP
>>> io.imshow(gk.real)  # doctest: +SKIP
>>> io.show()           # doctest: +SKIP


## gabor¶

skimage.filters.gabor(image, frequency, theta=0, bandwidth=1, sigma_x=None, sigma_y=None, n_stds=3, offset=0, mode='reflect', cval=0)[source]

Return real and imaginary responses to Gabor filter.

The real and imaginary parts of the Gabor filter kernel are applied to the image and the response is returned as a pair of arrays.

Gabor filter is a linear filter with a Gaussian kernel which is modulated by a sinusoidal plane wave. Frequency and orientation representations of the Gabor filter are similar to those of the human visual system. Gabor filter banks are commonly used in computer vision and image processing. They are especially suitable for edge detection and texture classification.

Parameters: image : 2-D array Input image. frequency : float Spatial frequency of the harmonic function. Specified in pixels. theta : float, optional Orientation in radians. If 0, the harmonic is in the x-direction. bandwidth : float, optional The bandwidth captured by the filter. For fixed bandwidth, sigma_x and sigma_y will decrease with increasing frequency. This value is ignored if sigma_x and sigma_y are set by the user. sigma_x, sigma_y : float, optional Standard deviation in x- and y-directions. These directions apply to the kernel before rotation. If theta = pi/2, then the kernel is rotated 90 degrees so that sigma_x controls the vertical direction. n_stds : scalar, optional The linear size of the kernel is n_stds (3 by default) standard deviations. offset : float, optional Phase offset of harmonic function in radians. mode : {‘constant’, ‘nearest’, ‘reflect’, ‘mirror’, ‘wrap’}, optional Mode used to convolve image with a kernel, passed to ndi.convolve cval : scalar, optional Value to fill past edges of input if mode of convolution is ‘constant’. The parameter is passed to ndi.convolve. real, imag : arrays Filtered images using the real and imaginary parts of the Gabor filter kernel. Images are of the same dimensions as the input one.

References

Examples

>>> from skimage.filters import gabor
>>> from skimage import data, io
>>> from matplotlib import pyplot as plt  # doctest: +SKIP

>>> image = data.coins()
>>> # detecting edges in a coin image
>>> filt_real, filt_imag = gabor(image, frequency=0.6)
>>> plt.figure()            # doctest: +SKIP
>>> io.imshow(filt_real)    # doctest: +SKIP
>>> io.show()               # doctest: +SKIP

>>> # less sensitivity to finer details with the lower frequency kernel
>>> filt_real, filt_imag = gabor(image, frequency=0.1)
>>> plt.figure()            # doctest: +SKIP
>>> io.imshow(filt_real)    # doctest: +SKIP
>>> io.show()               # doctest: +SKIP


## try_all_threshold¶

skimage.filters.try_all_threshold(image, figsize=(8, 5), verbose=True)[source]

Returns a figure comparing the outputs of different thresholding methods.

Parameters: image : (N, M) ndarray Input image. figsize : tuple, optional Figure size (in inches). verbose : bool, optional Print function name for each method. fig, ax : tuple Matplotlib figure and axes.

Notes

The following algorithms are used:

• isodata
• li
• mean
• minimum
• otsu
• triangle
• yen

Examples

>>> from skimage.data import text
>>> fig, ax = try_all_threshold(text(), figsize=(10, 6), verbose=False)


## frangi¶

skimage.filters.frangi(image, scale_range=(1, 10), scale_step=2, beta1=0.5, beta2=15, black_ridges=True)[source]

Filter an image with the Frangi filter.

This filter can be used to detect continuous edges, e.g. vessels, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects.

Calculates the eigenvectors of the Hessian to compute the similarity of an image region to vessels, according to the method described in [1].

Parameters: image : (N, M) ndarray Array with input image data. scale_range : 2-tuple of floats, optional The range of sigmas used. scale_step : float, optional Step size between sigmas. beta1 : float, optional Frangi correction constant that adjusts the filter’s sensitivity to deviation from a blob-like structure. beta2 : float, optional Frangi correction constant that adjusts the filter’s sensitivity to areas of high variance/texture/structure. black_ridges : boolean, optional When True (the default), the filter detects black ridges; when False, it detects white ridges. out : (N, M) ndarray Filtered image (maximum of pixels across all scales).

Notes

Written by Marc Schrijver, 2/11/2001 Re-Written by D. J. Kroon University of Twente (May 2009)

References

 [1] (1, 2) A. Frangi, W. Niessen, K. Vincken, and M. Viergever. “Multiscale vessel enhancement filtering,” In LNCS, vol. 1496, pages 130-137, Germany, 1998. Springer-Verlag.
 [2] Kroon, D.J.: Hessian based Frangi vesselness filter.

## hessian¶

skimage.filters.hessian(image, scale_range=(1, 10), scale_step=2, beta1=0.5, beta2=15)[source]

Filter an image with the Hessian filter.

This filter can be used to detect continuous edges, e.g. vessels, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects.

Almost equal to Frangi filter, but uses alternative method of smoothing. Refer to [1] to find the differences between Frangi and Hessian filters.

Parameters: image : (N, M) ndarray Array with input image data. scale_range : 2-tuple of floats, optional The range of sigmas used. scale_step : float, optional Step size between sigmas. beta1 : float, optional Frangi correction constant that adjusts the filter’s sensitivity to deviation from a blob-like structure. beta2 : float, optional Frangi correction constant that adjusts the filter’s sensitivity to areas of high variance/texture/structure. out : (N, M) ndarray Filtered image (maximum of pixels across all scales).

Notes

Written by Marc Schrijver, 2/11/2001 Re-Written by D. J. Kroon University of Twente (May 2009)

References

 [1] (1, 2) Choon-Ching Ng, Moi Hoon Yap, Nicholas Costen and Baihua Li, “Automatic Wrinkle Detection using Hybrid Hessian Filter”.

## threshold_otsu¶

skimage.filters.threshold_otsu(image, nbins=256)[source]

Return threshold value based on Otsu’s method.

Parameters: image : (N, M) ndarray Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. ValueError If image only contains a single grayscale value.

Notes

The input image must be grayscale.

References

Examples

>>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_otsu(image)
>>> binary = image <= thresh


## threshold_yen¶

skimage.filters.threshold_yen(image, nbins=256)[source]

Return threshold value based on Yen’s method.

Parameters: image : (N, M) ndarray Input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.

References

 [1] Yen J.C., Chang F.J., and Chang S. (1995) “A New Criterion for Automatic Multilevel Thresholding” IEEE Trans. on Image Processing, 4(3): 370-378. DOI:10.1109/83.366472
 [2] Sezgin M. and Sankur B. (2004) “Survey over Image Thresholding Techniques and Quantitative Performance Evaluation” Journal of Electronic Imaging, 13(1): 146-165, DOI:10.1117/1.1631315 http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf
 [3] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold

Examples

>>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_yen(image)
>>> binary = image <= thresh


## threshold_isodata¶

skimage.filters.threshold_isodata(image, nbins=256, return_all=False)[source]

Return threshold value(s) based on ISODATA method.

Histogram-based threshold, known as Ridler-Calvard method or inter-means. Threshold values returned satisfy the following equality:

threshold = (image[image <= threshold].mean() +
image[image > threshold].mean()) / 2.0


That is, returned thresholds are intensities that separate the image into two groups of pixels, where the threshold intensity is midway between the mean intensities of these groups.

For integer images, the above equality holds to within one; for floating- point images, the equality holds to within the histogram bin-width.

Parameters: image : (N, M) ndarray Input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. return_all: bool, optional If False (default), return only the lowest threshold that satisfies the above equality. If True, return all valid thresholds. threshold : float or int or array Threshold value(s).

References

 [1] Ridler, TW & Calvard, S (1978), “Picture thresholding using an iterative selection method” IEEE Transactions on Systems, Man and Cybernetics 8: 630-632, DOI:10.1109/TSMC.1978.4310039
 [2] Sezgin M. and Sankur B. (2004) “Survey over Image Thresholding Techniques and Quantitative Performance Evaluation” Journal of Electronic Imaging, 13(1): 146-165, http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf DOI:10.1117/1.1631315
 [3] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold

Examples

>>> from skimage.data import coins
>>> image = coins()
>>> thresh = threshold_isodata(image)
>>> binary = image > thresh


## threshold_li¶

skimage.filters.threshold_li(image, *, tolerance=None)[source]

Compute threshold value by Li’s iterative Minimum Cross Entropy method.

Parameters: image : ndarray Input image. tolerance : float, optional Finish the computation when the change in the threshold in an iteration is less than this value. By default, this is half of the range of the input image, divided by 256. threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.

References

 [1] Li C.H. and Lee C.K. (1993) “Minimum Cross Entropy Thresholding” Pattern Recognition, 26(4): 617-625 DOI:10.1016/0031-3203(93)90115-D
 [2] Li C.H. and Tam P.K.S. (1998) “An Iterative Algorithm for Minimum Cross Entropy Thresholding” Pattern Recognition Letters, 18(8): 771-776 DOI:10.1016/S0167-8655(98)00057-9
 [3] Sezgin M. and Sankur B. (2004) “Survey over Image Thresholding Techniques and Quantitative Performance Evaluation” Journal of Electronic Imaging, 13(1): 146-165 DOI:10.1117/1.1631315
 [4] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold

Examples

>>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_li(image)
>>> binary = image > thresh


## threshold_local¶

skimage.filters.threshold_local(image, block_size, method='gaussian', offset=0, mode='reflect', param=None, cval=0)[source]

Compute a threshold mask image based on local pixel neighborhood.

Also known as adaptive or dynamic thresholding. The threshold value is the weighted mean for the local neighborhood of a pixel subtracted by a constant. Alternatively the threshold can be determined dynamically by a given function, using the ‘generic’ method.

Parameters: image : (N, M) ndarray Input image. block_size : int Odd size of pixel neighborhood which is used to calculate the threshold value (e.g. 3, 5, 7, …, 21, …). method : {‘generic’, ‘gaussian’, ‘mean’, ‘median’}, optional Method used to determine adaptive threshold for local neighbourhood in weighted mean image. ‘generic’: use custom function (see param parameter) ‘gaussian’: apply gaussian filter (see param parameter for custom sigma value) ‘mean’: apply arithmetic mean filter ‘median’: apply median rank filter By default the ‘gaussian’ method is used. offset : float, optional Constant subtracted from weighted mean of neighborhood to calculate the local threshold value. Default offset is 0. mode : {‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘reflect’. param : {int, function}, optional Either specify sigma for ‘gaussian’ method or function object for ‘generic’ method. This functions takes the flat array of local neighbourhood as a single argument and returns the calculated threshold for the centre pixel. cval : float, optional Value to fill past edges of input if mode is ‘constant’. threshold : (N, M) ndarray Threshold image. All pixels in the input image higher than the corresponding pixel in the threshold image are considered foreground.

References

Examples

>>> from skimage.data import camera
>>> image = camera()[:50, :50]
>>> binary_image1 = image > threshold_local(image, 15, 'mean')
>>> func = lambda arr: arr.mean()
>>> binary_image2 = image > threshold_local(image, 15, 'generic',
...                                         param=func)


## threshold_minimum¶

skimage.filters.threshold_minimum(image, nbins=256, max_iter=10000)[source]

Return threshold value based on minimum method.

The histogram of the input image is computed and smoothed until there are only two maxima. Then the minimum in between is the threshold value.

Parameters: image : (M, N) ndarray Input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. max_iter: int, optional Maximum number of iterations to smooth the histogram. threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground. RuntimeError If unable to find two local maxima in the histogram or if the smoothing takes more than 1e4 iterations.

References

 [1] C. A. Glasbey, “An analysis of histogram-based thresholding algorithms,” CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993.
 [2] Prewitt, JMS & Mendelsohn, ML (1966), “The analysis of cell images”, Annals of the New York Academy of Sciences 128: 1035-1053 DOI:10.1111/j.1749-6632.1965.tb11715.x

Examples

>>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_minimum(image)
>>> binary = image > thresh


## threshold_mean¶

skimage.filters.threshold_mean(image)[source]

Return threshold value based on the mean of grayscale values.

Parameters: image : (N, M[, …, P]) ndarray Grayscale input image. threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.

References

 [1] C. A. Glasbey, “An analysis of histogram-based thresholding algorithms,” CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993. DOI:10.1006/cgip.1993.1040

Examples

>>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_mean(image)
>>> binary = image > thresh


## threshold_niblack¶

skimage.filters.threshold_niblack(image, window_size=15, k=0.2)[source]

Applies Niblack local threshold to an array.

A threshold T is calculated for every pixel in the image using the following formula:

T = m(x,y) - k * s(x,y)


where m(x,y) and s(x,y) are the mean and standard deviation of pixel (x,y) neighborhood defined by a rectangular window with size w times w centered around the pixel. k is a configurable parameter that weights the effect of standard deviation.

Parameters: image: ndarray Input image. window_size : int, or iterable of int, optional Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length image.ndim containing only odd integers (e.g. (1, 5, 5)). k : float, optional Value of parameter k in threshold formula. threshold : (N, M) ndarray Threshold mask. All pixels with an intensity higher than this value are assumed to be foreground.

Notes

This algorithm is originally designed for text recognition.

References

 [1] Niblack, W (1986), An introduction to Digital Image Processing, Prentice-Hall.

Examples

>>> from skimage import data
>>> image = data.page()
>>> binary_image = threshold_niblack(image, window_size=7, k=0.1)


## threshold_sauvola¶

skimage.filters.threshold_sauvola(image, window_size=15, k=0.2, r=None)[source]

Applies Sauvola local threshold to an array. Sauvola is a modification of Niblack technique.

In the original method a threshold T is calculated for every pixel in the image using the following formula:

T = m(x,y) * (1 + k * ((s(x,y) / R) - 1))


where m(x,y) and s(x,y) are the mean and standard deviation of pixel (x,y) neighborhood defined by a rectangular window with size w times w centered around the pixel. k is a configurable parameter that weights the effect of standard deviation. R is the maximum standard deviation of a greyscale image.

Parameters: image: ndarray Input image. window_size : int, or iterable of int, optional Window size specified as a single odd integer (3, 5, 7, …), or an iterable of length image.ndim containing only odd integers (e.g. (1, 5, 5)). k : float, optional Value of the positive parameter k. r : float, optional Value of R, the dynamic range of standard deviation. If None, set to the half of the image dtype range. threshold : (N, M) ndarray Threshold mask. All pixels with an intensity higher than this value are assumed to be foreground.

Notes

This algorithm is originally designed for text recognition.

References

 [1] J. Sauvola and M. Pietikainen, “Adaptive document image binarization,” Pattern Recognition 33(2), pp. 225-236, 2000. DOI:10.1016/S0031-3203(99)00055-2

Examples

>>> from skimage import data
>>> image = data.page()
>>> t_sauvola = threshold_sauvola(image, window_size=15, k=0.2)
>>> binary_image = image > t_sauvola


## threshold_triangle¶

skimage.filters.threshold_triangle(image, nbins=256)[source]

Return threshold value based on the triangle algorithm.

Parameters: image : (N, M[, …, P]) ndarray Grayscale input image. nbins : int, optional Number of bins used to calculate histogram. This value is ignored for integer arrays. threshold : float Upper threshold value. All pixels with an intensity higher than this value are assumed to be foreground.

References

 [1] Zack, G. W., Rogers, W. E. and Latt, S. A., 1977, Automatic Measurement of Sister Chromatid Exchange Frequency, Journal of Histochemistry and Cytochemistry 25 (7), pp. 741-753 DOI:10.1177/25.7.70454
 [2] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold

Examples

>>> from skimage.data import camera
>>> image = camera()
>>> thresh = threshold_triangle(image)
>>> binary = image > thresh


## apply_hysteresis_threshold¶

skimage.filters.apply_hysteresis_threshold(image, low, high)[source]

Apply hysteresis thresholding to image.

This algorithm finds regions where image is greater than high OR image is greater than low and that region is connected to a region greater than high.

Parameters: image : array, shape (M,[ N, …, P]) Grayscale input image. low : float, or array of same shape as image Lower threshold. high : float, or array of same shape as image Higher threshold. thresholded : array of bool, same shape as image Array in which True indicates the locations where image was above the hysteresis threshold.

References

 [1] J. Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986; vol. 8, pp.679-698. DOI:10.1109/TPAMI.1986.4767851

Examples

>>> image = np.array([1, 2, 3, 2, 1, 2, 1, 3, 2])
>>> apply_hysteresis_threshold(image, 1.5, 2.5).astype(int)
array([0, 1, 1, 1, 0, 0, 0, 1, 1])


### Examples using skimage.filters.apply_hysteresis_threshold¶

skimage.filters.unsharp_mask(image, radius=1.0, amount=1.0, multichannel=False, preserve_range=False)[source]

The sharp details are identified as the difference between the original image and its blurred version. These details are then scaled, and added back to the original image.

Parameters: image : [P, …, ]M[, N][, C] ndarray Input image. radius : scalar or sequence of scalars, optional If a scalar is given, then its value is used for all dimensions. If sequence is given, then there must be exactly one radius for each dimension except the last dimension for multichannel images. Note that 0 radius means no blurring, and negative values are not allowed. amount : scalar, optional The details will be amplified with this factor. The factor could be 0 or negative. Typically, it is a small positive number, e.g. 1.0. multichannel : bool, optional If True, the last image dimension is considered as a color channel, otherwise as spatial. Color channels are processed individually. preserve_range: bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html output : [P, …, ]M[, N][, C] ndarray of float Image with unsharp mask applied.

Notes

Unsharp masking is an image sharpening technique. It is a linear image operation, and numerically stable, unlike deconvolution which is an ill-posed problem. Because of this stability, it is often preferred over deconvolution.

The main idea is as follows: sharp details are identified as the difference between the original image and its blurred version. These details are added back to the original image after a scaling step:

enhanced image = original + amount * (original - blurred)

When applying this filter to several color layers independently, color bleeding may occur. More visually pleasing result can be achieved by processing only the brightness/lightness/intensity channel in a suitable color space such as HSV, HSL, YUV, or YCbCr.

Unsharp masking is described in most introductory digital image processing books. This implementation is based on [1].

References

 [1] (1, 2) Maria Petrou, Costas Petrou “Image Processing: The Fundamentals”, (2010), ed ii., page 357, ISBN 13: 9781119994398 DOI:10.1002/9781119994398

Examples

>>> array = np.ones(shape=(5,5), dtype=np.uint8)*100
>>> array[2,2] = 120
>>> array
array([[100, 100, 100, 100, 100],
[100, 100, 100, 100, 100],
[100, 100, 120, 100, 100],
[100, 100, 100, 100, 100],
[100, 100, 100, 100, 100]], dtype=uint8)
array([[ 0.39,  0.39,  0.39,  0.39,  0.39],
[ 0.39,  0.39,  0.38,  0.39,  0.39],
[ 0.39,  0.38,  0.53,  0.38,  0.39],
[ 0.39,  0.39,  0.38,  0.39,  0.39],
[ 0.39,  0.39,  0.39,  0.39,  0.39]])

>>> array = np.ones(shape=(5,5), dtype=np.int8)*100
>>> array[2,2] = 127
array([[ 0.79,  0.79,  0.79,  0.79,  0.79],
[ 0.79,  0.78,  0.75,  0.78,  0.79],
[ 0.79,  0.75,  1.  ,  0.75,  0.79],
[ 0.79,  0.78,  0.75,  0.78,  0.79],
[ 0.79,  0.79,  0.79,  0.79,  0.79]])

>>> np.around(unsharp_mask(array, radius=0.5, amount=2, preserve_range=True), 2)
array([[ 100.  ,  100.  ,   99.99,  100.  ,  100.  ],
[ 100.  ,   99.39,   95.48,   99.39,  100.  ],
[  99.99,   95.48,  147.59,   95.48,   99.99],
[ 100.  ,   99.39,   95.48,   99.39,  100.  ],
[ 100.  ,  100.  ,   99.99,  100.  ,  100.  ]])


## LPIFilter2D¶

class skimage.filters.LPIFilter2D(impulse_response, **filter_params)[source]

Bases: object

Linear Position-Invariant Filter (2-dimensional)

__init__(impulse_response, **filter_params)[source]
Parameters: impulse_response : callable f(r, c, **filter_params) Function that yields the impulse response. r and c are 1-dimensional vectors that represent row and column positions, in other words coordinates are (r[0],c[0]),(r[0],c[1]) etc. **filter_params are passed through. In other words, impulse_response would be called like this: >>> def impulse_response(r, c, **filter_params): ... pass >>> >>> r = [0,0,0,1,1,1,2,2,2] >>> c = [0,1,2,0,1,2,0,1,2] >>> filter_params = {'kw1': 1, 'kw2': 2, 'kw3': 3} >>> impulse_response(r, c, **filter_params) 

Examples

Gaussian filter: Use a 1-D gaussian in each direction without normalization coefficients.

>>> def filt_func(r, c, sigma = 1):
...     return np.exp(-np.hypot(r, c)/sigma)
>>> filter = LPIFilter2D(filt_func)