transform
¶

Perform a circular Hough transform. 

Perform an elliptical Hough transform. 

Perform a straight line Hough transform. 
Return lines from a progressive probabilistic line Hough transform. 

Return peaks in a circle Hough transform. 


Return peaks in a straight line Hough transform. 

Calculates the radon transform of an image given specified projection angles. 

Inverse radon transform. 

Inverse radon transform 
Order angles to reduce the amount of correlated information in subsequent projections. 

Compute the 2dimensional finite radon transform (FRT) for an n x n integer array. 

Compute the 2dimensional inverse finite radon transform (iFRT) for an (n+1) x n integer array. 

Integral image / summed area table. 


Use an integral image to integrate over a given window. 

Warp an image according to a given coordinate transformation. 

Build the source coordinates for the output of a 2D image warp. 

Estimate 2D geometric transformation parameters. 

Apply 2D matrix transform. 

Perform a swirl transformation. 

Resize image to match a certain size. 

Rotate image by a certain angle around its center. 

Scale image by a certain factor. 
Downsample Ndimensional image by local averaging. 


Smooth and then downsample image. 

Upsample and then smooth image. 

Yield images of the Gaussian pyramid formed by the input image. 

Yield images of the laplacian pyramid formed by the input image. 

Carve vertical or horizontal seams off an image. 
2D Euclidean transformation. 

2D similarity transformation. 


2D affine transformation. 

Projective transformation. 
Essential matrix transformation. 

Fundamental matrix transformation. 


2D polynomial transformation. 
2D piecewise affine transformation. 
skimage.transform.
hough_circle
(image, radius, normalize=True, full_output=False)[source]¶Perform a circular Hough transform.
Input image with nonzero values representing edges.
Radii at which to compute the Hough transform. Floats are converted to integers.
Normalize the accumulator with the number of pixels used to draw the radius.
Extend the output size by twice the largest radius in order to detect centers outside the input picture.
Hough transform accumulator for each radius. R designates the larger radius if full_output is True. Otherwise, R = 0.
Examples
>>> from skimage.transform import hough_circle
>>> from skimage.draw import circle_perimeter
>>> img = np.zeros((100, 100), dtype=np.bool_)
>>> rr, cc = circle_perimeter(25, 35, 23)
>>> img[rr, cc] = 1
>>> try_radii = np.arange(5, 50)
>>> res = hough_circle(img, try_radii)
>>> ridx, r, c = np.unravel_index(np.argmax(res), res.shape)
>>> r, c, try_radii[ridx]
(25, 35, 23)
skimage.transform.hough_circle
¶skimage.transform.
hough_ellipse
(image, threshold=4, accuracy=1, min_size=4, max_size=None)[source]¶Perform an elliptical Hough transform.
Input image with nonzero values representing edges.
Accumulator threshold value.
Bin size on the minor axis used in the accumulator.
Minimal major axis length.
Maximal minor axis length. If None, the value is set to the half of the smaller image dimension.
Where (yc, xc)
is the center, (a, b)
the major and minor
axes, respectively. The orientation value follows
skimage.draw.ellipse_perimeter convention.
Notes
The accuracy must be chosen to produce a peak in the accumulator distribution. In other words, a flat accumulator distribution with low values may be caused by a too low bin size.
References
Xie, Yonghong, and Qiang Ji. “A new efficient ellipse detection method.” Pattern Recognition, 2002. Proceedings. 16th International Conference on. Vol. 2. IEEE, 2002
Examples
>>> from skimage.transform import hough_ellipse
>>> from skimage.draw import ellipse_perimeter
>>> img = np.zeros((25, 25), dtype=np.uint8)
>>> rr, cc = ellipse_perimeter(10, 10, 6, 8)
>>> img[cc, rr] = 1
>>> result = hough_ellipse(img, threshold=8)
>>> result.tolist()
[(10, 10.0, 10.0, 8.0, 6.0, 0.0)]
skimage.transform.hough_ellipse
¶skimage.transform.
hough_line
(image, theta=None)[source]¶Perform a straight line Hough transform.
Input image with nonzero values representing edges.
Angles at which to compute the transform, in radians. Defaults to a vector of 180 angles evenly spaced from pi/2 to pi/2.
Hough transform accumulator.
Angles at which the transform is computed, in radians.
Distance values.
Notes
The origin is the top left corner of the original image. X and Y axis are horizontal and vertical edges respectively. The distance is the minimal algebraic distance from the origin to the detected line. The angle accuracy can be improved by decreasing the step size in the theta array.
Examples
Generate a test image:
>>> img = np.zeros((100, 150), dtype=bool)
>>> img[30, :] = 1
>>> img[:, 65] = 1
>>> img[35:45, 35:50] = 1
>>> for i in range(90):
... img[i, i] = 1
>>> img += np.random.random(img.shape) > 0.95
Apply the Hough transform:
>>> out, angles, d = hough_line(img)
import numpy as np
import matplotlib.pyplot as plt
from skimage.transform import hough_line
from skimage.draw import line
img = np.zeros((100, 150), dtype=bool)
img[30, :] = 1
img[:, 65] = 1
img[35:45, 35:50] = 1
rr, cc = line(60, 130, 80, 10)
img[rr, cc] = 1
img += np.random.random(img.shape) > 0.95
out, angles, d = hough_line(img)
fix, axes = plt.subplots(1, 2, figsize=(7, 4))
axes[0].imshow(img, cmap=plt.cm.gray)
axes[0].set_title('Input image')
axes[1].imshow(
out, cmap=plt.cm.bone,
extent=(np.rad2deg(angles[1]), np.rad2deg(angles[0]), d[1], d[0]))
axes[1].set_title('Hough transform')
axes[1].set_xlabel('Angle (degree)')
axes[1].set_ylabel('Distance (pixel)')
plt.tight_layout()
plt.show()
(Source code, png, pdf)
skimage.transform.hough_line
¶skimage.transform.
probabilistic_hough_line
(image, threshold=10, line_length=50, line_gap=10, theta=None, seed=None)[source]¶Return lines from a progressive probabilistic line Hough transform.
Input image with nonzero values representing edges.
Threshold
Minimum accepted length of detected lines. Increase the parameter to extract longer lines.
Maximum gap between pixels to still form a line. Increase the parameter to merge broken lines more aggresively.
Angles at which to compute the transform, in radians. If None, use a range from pi/2 to pi/2.
Seed to initialize the random number generator.
List of lines identified, lines in format ((x0, y0), (x1, y1)), indicating line start and end.
References
C. Galamhos, J. Matas and J. Kittler, “Progressive probabilistic Hough transform for line detection”, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999.
skimage.transform.probabilistic_hough_line
¶skimage.transform.
hough_circle_peaks
(hspaces, radii, min_xdistance=1, min_ydistance=1, threshold=None, num_peaks=inf, total_num_peaks=inf, normalize=False)[source]¶Return peaks in a circle Hough transform.
Identifies most prominent circles separated by certain distances in a Hough space. Nonmaximum suppression with different sizes is applied separately in the first and second dimension of the Hough space to identify peaks.
Hough spaces returned by the hough_circle function.
Radii corresponding to Hough spaces.
Minimum distance separating centers in the x dimension.
Minimum distance separating centers in the y dimension.
Minimum intensity of peaks in each Hough space. Default is 0.5 * max(hspace).
Maximum number of peaks in each Hough space. When the number of peaks exceeds num_peaks, only num_peaks coordinates based on peak intensity are considered for the corresponding radius.
Maximum number of peaks. When the number of peaks exceeds num_peaks, return num_peaks coordinates based on peak intensity.
If True, normalize the accumulator by the radius to sort the prominent peaks.
Peak values in Hough space, x and y center coordinates and radii.
Examples
>>> from skimage import transform, draw
>>> img = np.zeros((120, 100), dtype=int)
>>> radius, x_0, y_0 = (20, 99, 50)
>>> y, x = draw.circle_perimeter(y_0, x_0, radius)
>>> img[x, y] = 1
>>> hspaces = transform.hough_circle(img, radius)
>>> accum, cx, cy, rad = hough_circle_peaks(hspaces, [radius,])
skimage.transform.hough_circle_peaks
¶skimage.transform.
hough_line_peaks
(hspace, angles, dists, min_distance=9, min_angle=10, threshold=None, num_peaks=inf)[source]¶Return peaks in a straight line Hough transform.
Identifies most prominent lines separated by a certain angle and distance in a Hough transform. Nonmaximum suppression with different sizes is applied separately in the first (distances) and second (angles) dimension of the Hough space to identify peaks.
Hough space returned by the hough_line function.
Angles returned by the hough_line function. Assumed to be continuous. (angles[1]  angles[0] == PI).
Distances returned by the hough_line function.
Minimum distance separating lines (maximum filter size for first dimension of hough space).
Minimum angle separating lines (maximum filter size for second dimension of hough space).
Minimum intensity of peaks. Default is 0.5 * max(hspace).
Maximum number of peaks. When the number of peaks exceeds num_peaks, return num_peaks coordinates based on peak intensity.
Peak values in Hough space, angles and distances.
Examples
>>> from skimage.transform import hough_line, hough_line_peaks
>>> from skimage.draw import line
>>> img = np.zeros((15, 15), dtype=np.bool_)
>>> rr, cc = line(0, 0, 14, 14)
>>> img[rr, cc] = 1
>>> rr, cc = line(0, 14, 14, 0)
>>> img[cc, rr] = 1
>>> hspace, angles, dists = hough_line(img)
>>> hspace, angles, dists = hough_line_peaks(hspace, angles, dists)
>>> len(angles)
2
skimage.transform.hough_line_peaks
¶skimage.transform.
radon
(image, theta=None, circle=None)[source]¶Calculates the radon transform of an image given specified projection angles.
Input image. The rotation axis will be located in the pixel with
indices (image.shape[0] // 2, image.shape[1] // 2)
.
Projection angles (in degrees).
Assume image is zero outside the inscribed circle, making the
width of each projection (the first dimension of the sinogram)
equal to min(image.shape)
.
The default behavior (None) is equivalent to False.
Radon transform (sinogram). The tomography rotation axis will lie
at the pixel index radon_image.shape[0] // 2
along the 0th
dimension of radon_image
.
Notes
Based on code of Justin K. Romberg (http://www.clear.rice.edu/elec431/projects96/DSP/bpanalysis.html)
References
AC Kak, M Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1988.
B.R. Ramesh, N. Srinivasa, K. Rajgopal, “An Algorithm for Computing the Discrete Radon Transform With Some Applications”, Proceedings of the Fourth IEEE Region 10 International Conference, TENCON ‘89, 1989
skimage.transform.radon
¶skimage.transform.
iradon
(radon_image, theta=None, output_size=None, filter='ramp', interpolation='linear', circle=None)[source]¶Inverse radon transform.
Reconstruct an image from the radon transform, using the filtered back projection algorithm.
Image containing radon transform (sinogram). Each column of
the image corresponds to a projection along a different angle. The
tomography rotation axis should lie at the pixel index
radon_image.shape[0] // 2
along the 0th dimension of
radon_image
.
Reconstruction angles (in degrees). Default: m angles evenly spaced between 0 and 180 (if the shape of radon_image is (N, M)).
Number of rows and columns in the reconstruction.
Filter used in frequency domain filtering. Ramp filter used by default. Filters available: ramp, shepplogan, cosine, hamming, hann. Assign None to use no filter.
Interpolation method used in reconstruction. Methods available: ‘linear’, ‘nearest’, and ‘cubic’ (‘cubic’ is slow).
Assume the reconstructed image is zero outside the inscribed circle.
Also changes the default output_size to match the behaviour of
radon
called with circle=True
.
The default behavior (None) is equivalent to False.
Reconstructed image. The rotation axis will be located in the pixel
with indices
(reconstructed.shape[0] // 2, reconstructed.shape[1] // 2)
.
Notes
It applies the Fourier slice theorem to reconstruct an image by multiplying the frequency domain of the filter with the FFT of the projection data. This algorithm is called filtered back projection.
References
AC Kak, M Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1988.
B.R. Ramesh, N. Srinivasa, K. Rajgopal, “An Algorithm for Computing the Discrete Radon Transform With Some Applications”, Proceedings of the Fourth IEEE Region 10 International Conference, TENCON ‘89, 1989
skimage.transform.iradon
¶skimage.transform.
iradon_sart
(radon_image, theta=None, image=None, projection_shifts=None, clip=None, relaxation=0.15)[source]¶Inverse radon transform
Reconstruct an image from the radon transform, using a single iteration of the Simultaneous Algebraic Reconstruction Technique (SART) algorithm.
Image containing radon transform (sinogram). Each column of
the image corresponds to a projection along a different angle. The
tomography rotation axis should lie at the pixel index
radon_image.shape[0] // 2
along the 0th dimension of
radon_image
.
Reconstruction angles (in degrees). Default: m angles evenly spaced between 0 and 180 (if the shape of radon_image is (N, M)).
Image containing an initial reconstruction estimate. Shape of this
array should be (radon_image.shape[0], radon_image.shape[0])
. The
default is an array of zeros.
Shift the projections contained in radon_image
(the sinogram) by
this many pixels before reconstructing the image. The i’th value
defines the shift of the i’th column of radon_image
.
Force all values in the reconstructed tomogram to lie in the range
[clip[0], clip[1]]
Relaxation parameter for the update step. A higher value can improve the convergence rate, but one runs the risk of instabilities. Values close to or higher than 1 are not recommended.
Reconstructed image. The rotation axis will be located in the pixel
with indices
(reconstructed.shape[0] // 2, reconstructed.shape[1] // 2)
.
Notes
Algebraic Reconstruction Techniques are based on formulating the tomography reconstruction problem as a set of linear equations. Along each ray, the projected value is the sum of all the values of the cross section along the ray. A typical feature of SART (and a few other variants of algebraic techniques) is that it samples the cross section at equidistant points along the ray, using linear interpolation between the pixel values of the cross section. The resulting set of linear equations are then solved using a slightly modified Kaczmarz method.
When using SART, a single iteration is usually sufficient to obtain a good reconstruction. Further iterations will tend to enhance highfrequency information, but will also often increase the noise.
References
AC Kak, M Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1988.
AH Andersen, AC Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm”, Ultrasonic Imaging 6 pp 81–94 (1984)
S Kaczmarz, “Angenäherte auflösung von systemen linearer gleichungen”, Bulletin International de l’Academie Polonaise des Sciences et des Lettres 35 pp 355–357 (1937)
Kohler, T. “A projection access scheme for iterative reconstruction based on the golden section.” Nuclear Science Symposium Conference Record, 2004 IEEE. Vol. 6. IEEE, 2004.
Kaczmarz’ method, Wikipedia, http://en.wikipedia.org/wiki/Kaczmarz_method
skimage.transform.iradon_sart
¶skimage.transform.
order_angles_golden_ratio
(theta)[source]¶Order angles to reduce the amount of correlated information in subsequent projections.
Projection angles in degrees. Duplicate angles are not allowed.
The returned generator yields indices into theta
such that
theta[indices]
gives the approximate golden ratio ordering
of the projections. In total, len(theta)
indices are yielded.
All nonnegative integers < len(theta)
are yielded exactly once.
Notes
The method used here is that of the golden ratio introduced by T. Kohler.
References
Kohler, T. “A projection access scheme for iterative reconstruction based on the golden section.” Nuclear Science Symposium Conference Record, 2004 IEEE. Vol. 6. IEEE, 2004.
Winkelmann, Stefanie, et al. “An optimal radial profile order based on the Golden Ratio for timeresolved MRI.” Medical Imaging, IEEE Transactions on 26.1 (2007): 6876.
skimage.transform.
frt2
(a)[source]¶Compute the 2dimensional finite radon transform (FRT) for an n x n integer array.
A 2D square n x n integer array.
Finite Radon Transform array of (n+1) x n integer coefficients.
See also
ifrt2
The twodimensional inverse FRT.
Notes
The FRT has a unique inverse if and only if n is prime. [FRT] The idea for this algorithm is due to Vlad Negnevitski.
References
A. Kingston and I. Svalbe, “Projective transforms on periodic discrete image arrays,” in P. Hawkes (Ed), Advances in Imaging and Electron Physics, 139 (2006)
Examples
Generate a test image: Use a prime number for the array dimensions
>>> SIZE = 59
>>> img = np.tri(SIZE, dtype=np.int32)
Apply the Finite Radon Transform:
>>> f = frt2(img)
skimage.transform.
ifrt2
(a)[source]¶Compute the 2dimensional inverse finite radon transform (iFRT) for an (n+1) x n integer array.
A 2D (n+1) row x n column integer array.
Inverse Finite Radon Transform array of n x n integer coefficients.
See also
frt2
The twodimensional FRT
Notes
The FRT has a unique inverse if and only if n is prime. See [1] for an overview. The idea for this algorithm is due to Vlad Negnevitski.
References
A. Kingston and I. Svalbe, “Projective transforms on periodic discrete image arrays,” in P. Hawkes (Ed), Advances in Imaging and Electron Physics, 139 (2006)
Examples
>>> SIZE = 59
>>> img = np.tri(SIZE, dtype=np.int32)
Apply the Finite Radon Transform:
>>> f = frt2(img)
Apply the Inverse Finite Radon Transform to recover the input
>>> fi = ifrt2(f)
Check that it’s identical to the original
>>> assert len(np.nonzero(imgfi)[0]) == 0
skimage.transform.
integral_image
(image)[source]¶Integral image / summed area table.
The integral image contains the sum of all elements above and to the left of it, i.e.:
Input image.
Integral image/summed area table of same shape as input image.
References
F.C. Crow, “Summedarea tables for texture mapping,” ACM SIGGRAPH Computer Graphics, vol. 18, 1984, pp. 207212.
skimage.transform.
integrate
(ii, start, end)[source]¶Use an integral image to integrate over a given window.
Integral image.
Coordinates of top left corner of window(s). Each tuple in the list contains the starting row, col, … index i.e [(row_win1, col_win1, …), (row_win2, col_win2,…), …].
Coordinates of bottom right corner of window(s). Each tuple in the list containing the end row, col, … index i.e [(row_win1, col_win1, …), (row_win2, col_win2, …), …].
Integral (sum) over the given window(s).
Examples
>>> arr = np.ones((5, 6), dtype=np.float)
>>> ii = integral_image(arr)
>>> integrate(ii, (1, 0), (1, 2)) # sum from (1, 0) to (1, 2)
array([ 3.])
>>> integrate(ii, [(3, 3)], [(4, 5)]) # sum from (3, 3) to (4, 5)
array([ 6.])
>>> # sum from (1, 0) to (1, 2) and from (3, 3) to (4, 5)
>>> integrate(ii, [(1, 0), (3, 3)], [(1, 2), (4, 5)])
array([ 3., 6.])
skimage.transform.
warp
(image, inverse_map, map_args={}, output_shape=None, order=1, mode='constant', cval=0.0, clip=True, preserve_range=False)[source]¶Warp an image according to a given coordinate transformation.
Input image.
cr = f(cr, **kwargs)
, or ndarrayInverse coordinate map, which transforms coordinates in the output images into their corresponding coordinates in the input image.
There are a number of different options to define this map, depending on the dimensionality of the input image. A 2D image can have 2 dimensions for grayscale images, or 3 dimensions with color information.
For 2D images, you can directly pass a transformation object, e.g. skimage.transform.SimilarityTransform, or its inverse.
For 2D images, you can pass a
(3, 3)
homogeneous transformation matrix, e.g. skimage.transform.SimilarityTransform.params.For 2D images, a function that transforms a
(M, 2)
array of(col, row)
coordinates in the output image to their corresponding coordinates in the input image. Extra parameters to the function can be specified through map_args.For ND images, you can directly pass an array of coordinates. The first dimension specifies the coordinates in the input image, while the subsequent dimensions determine the position in the output image. E.g. in case of 2D images, you need to pass an array of shape
(2, rows, cols)
, where rows and cols determine the shape of the output image, and the first dimension contains the(row, col)
coordinate in the input image. See scipy.ndimage.map_coordinates for further documentation.
Note, that a (3, 3)
matrix is interpreted as a homogeneous
transformation matrix, so you cannot interpolate values from a 3D
input, if the output is of shape (3,)
.
See example section for usage.
Keyword arguments passed to inverse_map.
Shape of the output image generated. By default the shape of the input image is preserved. Note that, even for multiband images, only rows and columns need to be specified.
0: Nearestneighbor
1: Bilinear (default)
2: Biquadratic
3: Bicubic
4: Biquartic
5: Biquintic
Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad.
Used in conjunction with mode ‘constant’, the value outside the image boundaries.
Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range.
Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float.
The warped input image.
Notes
The input image is converted to a double image.
In case of a SimilarityTransform, AffineTransform and ProjectiveTransform and order in [0, 3] this function uses the underlying transformation matrix to warp the image with a much faster routine.
Examples
>>> from skimage.transform import warp
>>> from skimage import data
>>> image = data.camera()
The following image warps are all equal but differ substantially in execution time. The image is shifted to the bottom.
Use a geometric transform to warp an image (fast):
>>> from skimage.transform import SimilarityTransform
>>> tform = SimilarityTransform(translation=(0, 10))
>>> warped = warp(image, tform)
Use a callable (slow):
>>> def shift_down(xy):
... xy[:, 1] = 10
... return xy
>>> warped = warp(image, shift_down)
Use a transformation matrix to warp an image (fast):
>>> matrix = np.array([[1, 0, 0], [0, 1, 10], [0, 0, 1]])
>>> warped = warp(image, matrix)
>>> from skimage.transform import ProjectiveTransform
>>> warped = warp(image, ProjectiveTransform(matrix=matrix))
You can also use the inverse of a geometric transformation (fast):
>>> warped = warp(image, tform.inverse)
For ND images you can pass a coordinate array, that specifies the coordinates in the input image for every element in the output image. E.g. if you want to rescale a 3D cube, you can do:
>>> cube_shape = np.array([30, 30, 30])
>>> cube = np.random.rand(*cube_shape)
Setup the coordinate array, that defines the scaling:
>>> scale = 0.1
>>> output_shape = (scale * cube_shape).astype(int)
>>> coords0, coords1, coords2 = np.mgrid[:output_shape[0],
... :output_shape[1], :output_shape[2]]
>>> coords = np.array([coords0, coords1, coords2])
Assume that the cube contains spatial data, where the first array element center is at coordinate (0.5, 0.5, 0.5) in real space, i.e. we have to account for this extra offset when scaling the image:
>>> coords = (coords + 0.5) / scale  0.5
>>> warped = warp(cube, coords)
skimage.transform.
warp_coords
(coord_map, shape, dtype=<class 'numpy.float64'>)[source]¶Build the source coordinates for the output of a 2D image warp.
Return input coordinates for given output coordinates.
Coordinates are in the shape (P, 2), where P is the number
of coordinates and each element is a (row, col)
pair.
Shape of output image (rows, cols[, bands])
.
dtype for return value (sane choices: float32 or float64).
Coordinates for scipy.ndimage.map_coordinates, that will yield an image of shape (orows, ocols, bands) by drawing from source points according to the coord_transform_fn.
Notes
This is a lowerlevel routine that produces the source coordinates for 2D images used by warp().
It is provided separately from warp to give additional flexibility to users who would like, for example, to reuse a particular coordinate mapping, to use specific dtypes at various points along the the imagewarping process, or to implement different postprocessing logic than warp performs after the call to ndi.map_coordinates.
Examples
Produce a coordinate map that shifts an image up and to the right:
>>> from skimage import data
>>> from scipy.ndimage import map_coordinates
>>>
>>> def shift_up10_left20(xy):
... return xy  np.array([20, 10])[None, :]
>>>
>>> image = data.astronaut().astype(np.float32)
>>> coords = warp_coords(shift_up10_left20, image.shape)
>>> warped_image = map_coordinates(image, coords)
skimage.transform.
estimate_transform
(ttype, src, dst, **kwargs)[source]¶Estimate 2D geometric transformation parameters.
You can determine the over, well and underdetermined parameters with the total leastsquares method.
Number of source and destination coordinates must match.
Type of transform.
Function parameters (src, dst, n, angle):
NAME / TTYPE FUNCTION PARAMETERS
'euclidean' `src, `dst`
'similarity' `src, `dst`
'affine' `src, `dst`
'piecewiseaffine' `src, `dst`
'projective' `src, `dst`
'polynomial' `src, `dst`, `order` (polynomial order,
default order is 2)
Also see examples below.
GeometricTransform
Transform object containing the transformation parameters and providing access to forward and inverse transformation functions.
Examples
>>> import numpy as np
>>> from skimage import transform as tf
>>> # estimate transformation parameters
>>> src = np.array([0, 0, 10, 10]).reshape((2, 2))
>>> dst = np.array([12, 14, 1, 20]).reshape((2, 2))
>>> tform = tf.estimate_transform('similarity', src, dst)
>>> np.allclose(tform.inverse(tform(src)), src)
True
>>> # warp image using the estimated transformation
>>> from skimage import data
>>> image = data.camera()
>>> warp(image, inverse_map=tform.inverse) # doctest: +SKIP
>>> # create transformation with explicit parameters
>>> tform2 = tf.SimilarityTransform(scale=1.1, rotation=1,
... translation=(10, 20))
>>> # unite transformations, applied in order from left to right
>>> tform3 = tform + tform2
>>> np.allclose(tform3(src), tform2(tform(src)))
True
skimage.transform.
swirl
(image, center=None, strength=1, radius=100, rotation=0, output_shape=None, order=1, mode=None, cval=0, clip=True, preserve_range=False)[source]¶Perform a swirl transformation.
Input image.
Center coordinate of transformation.
The amount of swirling applied.
The extent of the swirl in pixels. The effect dies out rapidly beyond radius.
Additional rotation applied to the image.
Swirled version of the input.
Shape of the output image generated. By default the shape of the input image is preserved.
The order of the spline interpolation, default is 1. The order has to be in the range 05. See skimage.transform.warp for detail.
Points outside the boundaries of the input are filled according to the given mode, with ‘constant’ used as the default. Modes match the behaviour of numpy.pad.
Used in conjunction with mode ‘constant’, the value outside the image boundaries.
Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range.
Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float.
skimage.transform.swirl
¶skimage.transform.
resize
(image, output_shape, order=1, mode=None, cval=0, clip=True, preserve_range=False, anti_aliasing=None, anti_aliasing_sigma=None)[source]¶Resize image to match a certain size.
Performs interpolation to upsize or downsize images. Note that anti aliasing should be enabled when downsizing images to avoid aliasing artifacts. For downsampling Ndimensional images with an integer factor also see skimage.transform.downscale_local_mean.
Input image.
Size of the generated output image (rows, cols[, …][, dim]). If dim is not provided, the number of channels is preserved. In case the number of input channels does not equal the number of output channels a ndimensional interpolation is applied.
Resized version of the input.
The order of the spline interpolation, default is 1. The order has to be in the range 05. See skimage.transform.warp for detail.
Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad. The default mode is ‘constant’.
Used in conjunction with mode ‘constant’, the value outside the image boundaries.
Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range.
Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float.
Whether to apply a Gaussian filter to smooth the image prior to downscaling. It is crucial to filter when downsampling the image to avoid aliasing artifacts.
Standard deviation for Gaussian filtering to avoid aliasing artifacts. By default, this value is chosen as (1  s) / 2 where s is the downscaling factor.
Notes
Modes ‘reflect’ and ‘symmetric’ are similar, but differ in whether the edge pixels are duplicated during the reflection. As an example, if an array has values [0, 1, 2] and was padded to the right by four values using symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it would be [0, 1, 2, 1, 0, 1, 2].
Examples
>>> from skimage import data
>>> from skimage.transform import resize
>>> image = data.camera()
>>> resize(image, (100, 100), mode='reflect').shape
(100, 100)
skimage.transform.
rotate
(image, angle, resize=False, center=None, order=1, mode='constant', cval=0, clip=True, preserve_range=False)[source]¶Rotate image by a certain angle around its center.
Input image.
Rotation angle in degrees in counterclockwise direction.
Determine whether the shape of the output image will be automatically calculated, so the complete rotated image exactly fits. Default is False.
The rotation center. If center=None
, the image is rotated around
its center, i.e. center=(cols / 2  0.5, rows / 2  0.5)
. Please
note that this parameter is (cols, rows), contrary to normal skimage
ordering.
Rotated version of the input.
The order of the spline interpolation, default is 1. The order has to be in the range 05. See skimage.transform.warp for detail.
Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad.
Used in conjunction with mode ‘constant’, the value outside the image boundaries.
Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range.
Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float.
Notes
Modes ‘reflect’ and ‘symmetric’ are similar, but differ in whether the edge pixels are duplicated during the reflection. As an example, if an array has values [0, 1, 2] and was padded to the right by four values using symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it would be [0, 1, 2, 1, 0, 1, 2].
Examples
>>> from skimage import data
>>> from skimage.transform import rotate
>>> image = data.camera()
>>> rotate(image, 2).shape
(512, 512)
>>> rotate(image, 2, resize=True).shape
(530, 530)
>>> rotate(image, 90, resize=True).shape
(512, 512)
skimage.transform.
rescale
(image, scale, order=1, mode=None, cval=0, clip=True, preserve_range=False, multichannel=None, anti_aliasing=None, anti_aliasing_sigma=None)[source]¶Scale image by a certain factor.
Performs interpolation to upscale or downscale images. Note that anti aliasing should be enabled when downsizing images to avoid aliasing artifacts. For downsampling Ndimensional images with an integer factor also see skimage.transform.downscale_local_mean.
Input image.
Scale factors. Separate scale factors can be defined as (rows, cols[, …][, dim]).
Scaled version of the input.
The order of the spline interpolation, default is 1. The order has to be in the range 05. See skimage.transform.warp for detail.
Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad. The default mode is ‘constant’.
Used in conjunction with mode ‘constant’, the value outside the image boundaries.
Whether to clip the output to the range of values of the input image. This is enabled by default, since higher order interpolation may produce values outside the given input range.
Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of img_as_float.
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. By default, is set to True for 3D (2D+color) inputs, and False for others. Starting in release 0.16, this will always default to False.
Whether to apply a Gaussian filter to smooth the image prior to downscaling. It is crucial to filter when downsampling the image to avoid aliasing artifacts.
Standard deviation for Gaussian filtering to avoid aliasing artifacts. By default, this value is chosen as (1  s) / 2 where s is the downscaling factor.
Notes
Modes ‘reflect’ and ‘symmetric’ are similar, but differ in whether the edge pixels are duplicated during the reflection. As an example, if an array has values [0, 1, 2] and was padded to the right by four values using symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it would be [0, 1, 2, 1, 0, 1, 2].
Examples
>>> from skimage import data
>>> from skimage.transform import rescale
>>> image = data.camera()
>>> rescale(image, 0.1, mode='reflect').shape
(51, 51)
>>> rescale(image, 0.5, mode='reflect').shape
(256, 256)
skimage.transform.
downscale_local_mean
(image, factors, cval=0, clip=True)[source]¶Downsample Ndimensional image by local averaging.
The image is padded with cval if it is not perfectly divisible by the integer factors.
In contrast to the 2D interpolation in skimage.transform.resize and skimage.transform.rescale this function may be applied to Ndimensional images and calculates the local mean of elements in each block of size factors in the input image.
Ndimensional input image.
Array containing downsampling integer factor along each axis.
Constant padding value if image is not perfectly divisible by the integer factors.
Downsampled image with same number of dimensions as input image.
Examples
>>> a = np.arange(15).reshape(3, 5)
>>> a
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
>>> downscale_local_mean(a, (2, 3))
array([[ 3.5, 4. ],
[ 5.5, 4.5]])
skimage.transform.downscale_local_mean
¶skimage.transform.
pyramid_reduce
(image, downscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=None)[source]¶Smooth and then downsample image.
Input image.
Downscale factor.
Sigma for Gaussian filter. Default is 2 * downscale / 6.0 which corresponds to a filter mask twice the size of the scale factor that covers more than 99% of the Gaussian distribution.
Order of splines used in interpolation of downsampling. See skimage.transform.warp for detail.
The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
Value to fill past edges of input if mode is ‘constant’.
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. By default, is set to True for 3D (2D+color) inputs, and False for others. Starting in release 0.16, this will always default to False.
Smoothed and downsampled float image.
References
skimage.transform.
pyramid_expand
(image, upscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=None)[source]¶Upsample and then smooth image.
Input image.
Upscale factor.
Sigma for Gaussian filter. Default is 2 * upscale / 6.0 which corresponds to a filter mask twice the size of the scale factor that covers more than 99% of the Gaussian distribution.
Order of splines used in interpolation of upsampling. See skimage.transform.warp for detail.
The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
Value to fill past edges of input if mode is ‘constant’.
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. By default, is set to True for 3D (2D+color) inputs, and False for others. Starting in release 0.16, this will always default to False.
Upsampled and smoothed float image.
References
skimage.transform.
pyramid_gaussian
(image, max_layer=1, downscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=None)[source]¶Yield images of the Gaussian pyramid formed by the input image.
Recursively applies the pyramid_reduce function to the image, and yields the downscaled images.
Note that the first image of the pyramid will be the original, unscaled image. The total number of images is max_layer + 1. In case all layers are computed, the last image is either a onepixel image or the image where the reduction does not change its shape.
Input image.
Number of layers for the pyramid. 0th layer is the original image. Default is 1 which builds all possible layers.
Downscale factor.
Sigma for Gaussian filter. Default is 2 * downscale / 6.0 which corresponds to a filter mask twice the size of the scale factor that covers more than 99% of the Gaussian distribution.
Order of splines used in interpolation of downsampling. See skimage.transform.warp for detail.
The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
Value to fill past edges of input if mode is ‘constant’.
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. By default, is set to True for 3D (2D+color) inputs, and False for others. Starting in release 0.16, this will always default to False.
Generator yielding pyramid layers as float images.
References
skimage.transform.pyramid_gaussian
¶skimage.transform.
pyramid_laplacian
(image, max_layer=1, downscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=None)[source]¶Yield images of the laplacian pyramid formed by the input image.
Each layer contains the difference between the downsampled and the downsampled, smoothed image:
layer = resize(prev_layer)  smooth(resize(prev_layer))
Note that the first image of the pyramid will be the difference between the original, unscaled image and its smoothed version. The total number of images is max_layer + 1. In case all layers are computed, the last image is either a onepixel image or the image where the reduction does not change its shape.
Input image.
Number of layers for the pyramid. 0th layer is the original image. Default is 1 which builds all possible layers.
Downscale factor.
Sigma for Gaussian filter. Default is 2 * downscale / 6.0 which corresponds to a filter mask twice the size of the scale factor that covers more than 99% of the Gaussian distribution.
Order of splines used in interpolation of downsampling. See skimage.transform.warp for detail.
The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
Value to fill past edges of input if mode is ‘constant’.
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. By default, is set to True for 3D (2D+color) inputs, and False for others. Starting in release 0.16, this will always default to False.
Generator yielding pyramid layers as float images.
References
skimage.transform.
seam_carve
(image, energy_map, mode, num, border=1, force_copy=True)[source]¶Carve vertical or horizontal seams off an image.
Carves out vertical/horizontal seams from an image while using the given energy map to decide the importance of each pixel.
Input image whose seams are to be removed.
The array to decide the importance of each pixel. The higher the value corresponding to a pixel, the more the algorithm will try to keep it in the image.
Indicates whether seams are to be removed vertically or horizontally. Removing seams horizontally will decrease the height whereas removing vertically will decrease the width.
Number of seams are to be removed.
The number of pixels in the right, left and bottom end of the image to be excluded from being considered for a seam. This is important as certain filters just ignore image boundaries and set them to 0. By default border is set to 1.
If set, the image and energy_map are copied before being used by the method which modifies it in place. Set this to False if the original image and the energy map are no longer needed after this operation.
The cropped image with the seams removed.
References
Shai Avidan and Ariel Shamir “Seam Carving for ContentAware Image Resizing” http://www.cs.jhu.edu/~misha/ReadingSeminar/Papers/Avidan07.pdf
skimage.transform.seam_carve
¶EuclideanTransform
¶skimage.transform.
EuclideanTransform
(matrix=None, rotation=None, translation=None)[source]¶Bases: skimage.transform._geometric.ProjectiveTransform
2D Euclidean transformation.
Has the following form:
X = a0 * x  b0 * y + a1 =
= x * cos(rotation)  y * sin(rotation) + a1
Y = b0 * x + a0 * y + b1 =
= x * sin(rotation) + y * cos(rotation) + b1
where the homogeneous transformation matrix is:
[[a0 b0 a1]
[b0 a0 b1]
[0 0 1]]
The Euclidean transformation is a rigid transformation with rotation and translation parameters. The similarity transformation extends the Euclidean transformation with a single scaling factor.
Homogeneous transformation matrix.
Rotation angle in counterclockwise direction as radians.
x, y translation parameters.
Homogeneous transformation matrix.
__init__
(self, matrix=None, rotation=None, translation=None)[source]¶Initialize self. See help(type(self)) for accurate signature.
estimate
(self, src, dst)[source]¶Estimate the transformation from a set of corresponding points.
You can determine the over, well and underdetermined parameters with the total leastsquares method.
Number of source and destination coordinates must match.
Source coordinates.
Destination coordinates.
True, if model estimation succeeds.
rotation
¶translation
¶SimilarityTransform
¶skimage.transform.
SimilarityTransform
(matrix=None, scale=None, rotation=None, translation=None)[source]¶Bases: skimage.transform._geometric.EuclideanTransform
2D similarity transformation.
Has the following form:
X = a0 * x  b0 * y + a1 =
= s * x * cos(rotation)  s * y * sin(rotation) + a1
Y = b0 * x + a0 * y + b1 =
= s * x * sin(rotation) + s * y * cos(rotation) + b1
where s
is a scale factor and the homogeneous transformation matrix is:
[[a0 b0 a1]
[b0 a0 b1]
[0 0 1]]
The similarity transformation extends the Euclidean transformation with a single scaling factor in addition to the rotation and translation parameters.
Homogeneous transformation matrix.
Scale factor.
Rotation angle in counterclockwise direction as radians.
x, y translation parameters.
Homogeneous transformation matrix.
__init__
(self, matrix=None, scale=None, rotation=None, translation=None)[source]¶Initialize self. See help(type(self)) for accurate signature.
estimate
(self, src, dst)[source]¶Estimate the transformation from a set of corresponding points.
You can determine the over, well and underdetermined parameters with the total leastsquares method.
Number of source and destination coordinates must match.
Source coordinates.
Destination coordinates.
True, if model estimation succeeds.
scale
¶AffineTransform
¶skimage.transform.
AffineTransform
(matrix=None, scale=None, rotation=None, shear=None, translation=None)[source]¶Bases: skimage.transform._geometric.ProjectiveTransform
2D affine transformation.
Has the following form:
X = a0*x + a1*y + a2 =
= sx*x*cos(rotation)  sy*y*sin(rotation + shear) + a2
Y = b0*x + b1*y + b2 =
= sx*x*sin(rotation) + sy*y*cos(rotation + shear) + b2
where sx
and sy
are scale factors in the x and y directions,
and the homogeneous transformation matrix is:
[[a0 a1 a2]
[b0 b1 b2]
[0 0 1]]
Homogeneous transformation matrix.
Scale factors.
Rotation angle in counterclockwise direction as radians.
Shear angle in counterclockwise direction as radians.
Translation parameters.
Homogeneous transformation matrix.
__init__
(self, matrix=None, scale=None, rotation=None, shear=None, translation=None)[source]¶Initialize self. See help(type(self)) for accurate signature.
rotation
¶scale
¶shear
¶translation
¶ProjectiveTransform
¶skimage.transform.
ProjectiveTransform
(matrix=None)[source]¶Bases: skimage.transform._geometric.GeometricTransform
Projective transformation.
Apply a projective transformation (homography) on coordinates.
For each homogeneous coordinate \(\mathbf{x} = [x, y, 1]^T\), its target position is calculated by multiplying with the given matrix, \(H\), to give \(H \mathbf{x}\):
[[a0 a1 a2]
[b0 b1 b2]
[c0 c1 1 ]].
E.g., to rotate by theta degrees clockwise, the matrix should be:
[[cos(theta) sin(theta) 0]
[sin(theta) cos(theta) 0]
[0 0 1]]
or, to translate x by 10 and y by 20:
[[1 0 10]
[0 1 20]
[0 0 1 ]].
Homogeneous transformation matrix.
Homogeneous transformation matrix.
estimate
(self, src, dst)[source]¶Estimate the transformation from a set of corresponding points.
You can determine the over, well and underdetermined parameters with the total leastsquares method.
Number of source and destination coordinates must match.
The transformation is defined as:
X = (a0*x + a1*y + a2) / (c0*x + c1*y + 1)
Y = (b0*x + b1*y + b2) / (c0*x + c1*y + 1)
These equations can be transformed to the following form:
0 = a0*x + a1*y + a2  c0*x*X  c1*y*X  X
0 = b0*x + b1*y + b2  c0*x*Y  c1*y*Y  Y
which exist for each set of corresponding points, so we have a set of N * 2 equations. The coefficients appear linearly so we can write A x = 0, where:
A = [[x y 1 0 0 0 x*X y*X X]
[0 0 0 x y 1 x*Y y*Y Y]
...
...
]
x.T = [a0 a1 a2 b0 b1 b2 c0 c1 c3]
In case of total leastsquares the solution of this homogeneous system of equations is the right singular vector of A which corresponds to the smallest singular value normed by the coefficient c3.
In case of the affine transformation the coefficients c0 and c1 are 0. Thus the system of equations is:
A = [[x y 1 0 0 0 X]
[0 0 0 x y 1 Y]
...
...
]
x.T = [a0 a1 a2 b0 b1 b2 c3]
Source coordinates.
Destination coordinates.
True, if model estimation succeeds.
EssentialMatrixTransform
¶skimage.transform.
EssentialMatrixTransform
(rotation=None, translation=None, matrix=None)[source]¶Bases: skimage.transform._geometric.FundamentalMatrixTransform
Essential matrix transformation.
The essential matrix relates corresponding points between a pair of calibrated images. The matrix transforms normalized, homogeneous image points in one image to epipolar lines in the other image.
The essential matrix is only defined for a pair of moving images capturing a nonplanar scene. In the case of pure rotation or planar scenes, the homography describes the geometric relation between two images (ProjectiveTransform). If the intrinsic calibration of the images is unknown, the fundamental matrix describes the projective relation between the two images (FundamentalMatrixTransform).
Rotation matrix of the relative camera motion.
Translation vector of the relative camera motion. The vector must have unit length.
Essential matrix.
References
Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003.
Essential matrix.
__init__
(self, rotation=None, translation=None, matrix=None)[source]¶Initialize self. See help(type(self)) for accurate signature.
estimate
(self, src, dst)[source]¶Estimate essential matrix using 8point algorithm.
The 8point algorithm requires at least 8 corresponding point pairs for a wellconditioned solution, otherwise the overdetermined solution is estimated.
Source coordinates.
Destination coordinates.
True, if model estimation succeeds.
FundamentalMatrixTransform
¶skimage.transform.
FundamentalMatrixTransform
(matrix=None)[source]¶Bases: skimage.transform._geometric.GeometricTransform
Fundamental matrix transformation.
The fundamental matrix relates corresponding points between a pair of uncalibrated images. The matrix transforms homogeneous image points in one image to epipolar lines in the other image.
The fundamental matrix is only defined for a pair of moving images. In the case of pure rotation or planar scenes, the homography describes the geometric relation between two images (ProjectiveTransform). If the intrinsic calibration of the images is known, the essential matrix describes the metric relation between the two images (EssentialMatrixTransform).
Fundamental matrix.
References
Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003.
Fundamental matrix.
estimate
(self, src, dst)[source]¶Estimate fundamental matrix using 8point algorithm.
The 8point algorithm requires at least 8 corresponding point pairs for a wellconditioned solution, otherwise the overdetermined solution is estimated.
Source coordinates.
Destination coordinates.
True, if model estimation succeeds.
PolynomialTransform
¶skimage.transform.
PolynomialTransform
(params=None)[source]¶Bases: skimage.transform._geometric.GeometricTransform
2D polynomial transformation.
Has the following form:
X = sum[j=0:order]( sum[i=0:j]( a_ji * x**(j  i) * y**i ))
Y = sum[j=0:order]( sum[i=0:j]( b_ji * x**(j  i) * y**i ))
Polynomial coefficients where N * 2 = (order + 1) * (order + 2). So, a_ji is defined in params[0, :] and b_ji in params[1, :].
Polynomial coefficients where N * 2 = (order + 1) * (order + 2). So, a_ji is defined in params[0, :] and b_ji in params[1, :].
estimate
(self, src, dst, order=2)[source]¶Estimate the transformation from a set of corresponding points.
You can determine the over, well and underdetermined parameters with the total leastsquares method.
Number of source and destination coordinates must match.
The transformation is defined as:
X = sum[j=0:order]( sum[i=0:j]( a_ji * x**(j  i) * y**i ))
Y = sum[j=0:order]( sum[i=0:j]( b_ji * x**(j  i) * y**i ))
These equations can be transformed to the following form:
0 = sum[j=0:order]( sum[i=0:j]( a_ji * x**(j  i) * y**i ))  X
0 = sum[j=0:order]( sum[i=0:j]( b_ji * x**(j  i) * y**i ))  Y
which exist for each set of corresponding points, so we have a set of N * 2 equations. The coefficients appear linearly so we can write A x = 0, where:
A = [[1 x y x**2 x*y y**2 ... 0 ... 0 X]
[0 ... 0 1 x y x**2 x*y y**2 Y]
...
...
]
x.T = [a00 a10 a11 a20 a21 a22 ... ann
b00 b10 b11 b20 b21 b22 ... bnn c3]
In case of total leastsquares the solution of this homogeneous system of equations is the right singular vector of A which corresponds to the smallest singular value normed by the coefficient c3.
Source coordinates.
Destination coordinates.
Polynomial order (number of coefficients is order + 1).
True, if model estimation succeeds.
PiecewiseAffineTransform
¶skimage.transform.
PiecewiseAffineTransform
[source]¶Bases: skimage.transform._geometric.GeometricTransform
2D piecewise affine transformation.
Control points are used to define the mapping. The transform is based on a Delaunay triangulation of the points to form a mesh. Each triangle is used to find a local affine transform.
Affine transformations for each triangle in the mesh.
Inverse affine transformations for each triangle in the mesh.