skimage.segmentation.random_walker(data, labels, beta=130, mode='cg_j', tol=0.001, copy=True, multichannel=False, return_full_prob=False, spacing=None, *, prob_tol=0.001) [source]

Random walker algorithm for segmentation from markers. Random walker algorithm is implemented for gray-level or multichannel images.  Parameters

dataarray_like

Image to be segmented in phases. Gray-level data can be two- or three-dimensional; multichannel data can be three- or four- dimensional (multichannel=True) with the highest dimension denoting channels. Data spacing is assumed isotropic unless the spacing keyword argument is used.
labelsarray of ints, of same shape as data without channels dimension

Array of seed markers labeled with different positive integers for different phases. Zero-labeled pixels are unlabeled pixels. Negative labels correspond to inactive pixels that are not taken into account (they are removed from the graph). If labels are not consecutive integers, the labels array will be transformed so that labels are consecutive. In the multichannel case, labels should have the same shape as a single channel of data, i.e. without the final dimension denoting channels.
betafloat, optional

Penalization coefficient for the random walker motion (the greater beta, the more difficult the diffusion).
modestring, available options {‘cg’, ‘cg_j’, ‘cg_mg’, ‘bf’}

Mode for solving the linear system in the random walker algorithm.  ‘bf’ (brute force): an LU factorization of the Laplacian is computed. This is fast for small images (<1024x1024), but very slow and memory-intensive for large images (e.g., 3-D volumes). ‘cg’ (conjugate gradient): the linear system is solved iteratively using the Conjugate Gradient method from scipy.sparse.linalg. This is less memory-consuming than the brute force method for large images, but it is quite slow. ‘cg_j’ (conjugate gradient with Jacobi preconditionner): the Jacobi preconditionner is applyed during the Conjugate gradient method iterations. This may accelerate the convergence of the ‘cg’ method. ‘cg_mg’ (conjugate gradient with multigrid preconditioner): a preconditioner is computed using a multigrid solver, then the solution is computed with the Conjugate Gradient method. This mode requires that the pyamg module is installed.
tolfloat, optional

Tolerance to achieve when solving the linear system using the conjugate gradient based modes (‘cg’, ‘cg_j’ and ‘cg_mg’).
copybool, optional

If copy is False, the labels array will be overwritten with the result of the segmentation. Use copy=False if you want to save on memory.
multichannelbool, optional

If True, input data is parsed as multichannel data (see ‘data’ above for proper input format in this case).
return_full_probbool, optional

If True, the probability that a pixel belongs to each of the labels will be returned, instead of only the most likely label.
spacingiterable of floats, optional

Spacing between voxels in each spatial dimension. If None, then the spacing between pixels/voxels in each dimension is assumed 1.
prob_tolfloat, optional

Tolerance on the resulting probability to be in the interval [0, 1]. If the tolerance is not satisfied, a warning is displayed.    Returns

outputndarray

 If return_full_prob is False, array of ints of same shape and data type as labels, in which each pixel has been labeled according to the marker that reached the pixel first by anisotropic diffusion. If return_full_prob is True, array of floats of shape (nlabels, labels.shape). output[label_nb, i, j] is the probability that label label_nb reaches the pixel (i, j) first.       See also
skimage.morphology.watershed

watershed segmentation A segmentation algorithm based on mathematical morphology and “flooding” of regions from markers.    Notes Multichannel inputs are scaled with all channel data combined. Ensure all channels are separately normalized prior to running this algorithm. The spacing argument is specifically for anisotropic datasets, where data points are spaced differently in one or more spatial dimensions. Anisotropic data is commonly encountered in medical imaging. The algorithm was first proposed in [1]. The algorithm solves the diffusion equation at infinite times for sources placed on markers of each phase in turn. A pixel is labeled with the phase that has the greatest probability to diffuse first to the pixel. The diffusion equation is solved by minimizing x.T L x for each phase, where L is the Laplacian of the weighted graph of the image, and x is the probability that a marker of the given phase arrives first at a pixel by diffusion (x=1 on markers of the phase, x=0 on the other markers, and the other coefficients are looked for). Each pixel is attributed the label for which it has a maximal value of x. The Laplacian L of the image is defined as:  L_ii = d_i, the number of neighbors of pixel i (the degree of i) L_ij = -w_ij if i and j are adjacent pixels  The weight w_ij is a decreasing function of the norm of the local gradient. This ensures that diffusion is easier between pixels of similar values. When the Laplacian is decomposed into blocks of marked and unmarked pixels: L = M B.T
    B A
 with first indices corresponding to marked pixels, and then to unmarked pixels, minimizing x.T L x for one phase amount to solving: A x = - B x_m
 where x_m = 1 on markers of the given phase, and 0 on other markers. This linear system is solved in the algorithm using a direct method for small images, and an iterative method for larger images. References
1
Leo Grady, Random walks for image segmentation, IEEE Trans Pattern Anal Mach Intell. 2006 Nov;28(11):1768-83. DOI:10.1109/TPAMI.2006.233.   Examples >>> np.random.seed(0)
>>> a = np.zeros((10, 10)) + 0.2 * np.random.rand(10, 10)
>>> a[5:8, 5:8] += 1
>>> b = np.zeros_like(a, dtype=np.int32)
>>> b[3, 3] = 1  # Marker for first phase
>>> b[6, 6] = 2  # Marker for second phase
>>> random_walker(a, b)
array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 2, 2, 2, 1, 1],
       [1, 1, 1, 1, 1, 2, 2, 2, 1, 1],
       [1, 1, 1, 1, 1, 2, 2, 2, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=int32)


skimage.segmentation.relabel_sequential(label_field, offset=1) [source]

Relabel arbitrary labels to {offset, … offset + number_of_labels}. This function also returns the forward map (mapping the original labels to the reduced labels) and the inverse map (mapping the reduced labels back to the original ones).  Parameters

label_fieldnumpy array of int, arbitrary shape

An array of labels, which must be non-negative integers.
offsetint, optional

The return labels will start at offset, which should be strictly positive.    Returns

relabelednumpy array of int, same shape as label_field

The input label field with labels mapped to {offset, …, number_of_labels + offset - 1}. The data type will be the same as label_field, except when offset + number_of_labels causes overflow of the current data type.
forward_mapArrayMap

The map from the original label space to the returned label space. Can be used to re-apply the same mapping. See examples for usage. The output data type will be the same as relabeled.
inverse_mapArrayMap

The map from the new label space to the original space. This can be used to reconstruct the original label field from the relabeled one. The output data type will be the same as label_field.     Notes The label 0 is assumed to denote the background and is never remapped. The forward map can be extremely big for some inputs, since its length is given by the maximum of the label field. However, in most situations, label_field.max() is much smaller than label_field.size, and in these cases the forward map is guaranteed to be smaller than either the input or output images. Examples >>> from skimage.segmentation import relabel_sequential
>>> label_field = np.array([1, 1, 5, 5, 8, 99, 42])
>>> relab, fw, inv = relabel_sequential(label_field)
>>> relab
array([1, 1, 2, 2, 3, 5, 4])
>>> print(fw)
ArrayMap:
  1 → 1
  5 → 2
  8 → 3
  42 → 4
  99 → 5
>>> np.array(fw)
array([0, 1, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5])
>>> np.array(inv)
array([ 0,  1,  5,  8, 42, 99])
>>> (fw[label_field] == relab).all()
True
>>> (inv[relab] == label_field).all()
True
>>> relab, fw, inv = relabel_sequential(label_field, offset=5)
>>> relab
array([5, 5, 6, 6, 7, 9, 8])


skimage.segmentation.slic(image, n_segments=100, compactness=10.0, max_iter=10, sigma=0, spacing=None, multichannel=True, convert2lab=None, enforce_connectivity=True, min_size_factor=0.5, max_size_factor=3, slic_zero=False, start_label=None, mask=None) [source]

Segments image using k-means clustering in Color-(x,y,z) space.  Parameters

image2D, 3D or 4D ndarray

Input image, which can be 2D or 3D, and grayscale or multichannel (see multichannel parameter). Input image must either be NaN-free or the NaN’s must be masked out
n_segmentsint, optional

The (approximate) number of labels in the segmented output image.
compactnessfloat, optional

Balances color proximity and space proximity. Higher values give more weight to space proximity, making superpixel shapes more square/cubic. In SLICO mode, this is the initial compactness. This parameter depends strongly on image contrast and on the shapes of objects in the image. We recommend exploring possible values on a log scale, e.g., 0.01, 0.1, 1, 10, 100, before refining around a chosen value.
max_iterint, optional

Maximum number of iterations of k-means.
sigmafloat or (3,) array-like of floats, optional

Width of Gaussian smoothing kernel for pre-processing for each dimension of the image. The same sigma is applied to each dimension in case of a scalar value. Zero means no smoothing. Note, that sigma is automatically scaled if it is scalar and a manual voxel spacing is provided (see Notes section).
spacing(3,) array-like of floats, optional

The voxel spacing along each image dimension. By default, slic assumes uniform spacing (same voxel resolution along z, y and x). This parameter controls the weights of the distances along z, y, and x during k-means clustering.
multichannelbool, optional

Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
convert2labbool, optional

Whether the input should be converted to Lab colorspace prior to segmentation. The input image must be RGB. Highly recommended. This option defaults to True when multichannel=True and image.shape[-1] == 3.
enforce_connectivitybool, optional

Whether the generated segments are connected or not
min_size_factorfloat, optional

Proportion of the minimum segment size to be removed with respect to the supposed segment size `depth*width*height/n_segments`
max_size_factorfloat, optional

Proportion of the maximum connected segment size. A value of 3 works in most of the cases.
slic_zerobool, optional

Run SLIC-zero, the zero-parameter mode of SLIC. [2]  start_label: int, optional

The labels’ index start. Should be 0 or 1.  New in version 0.17: start_label was introduced in 0.17
mask2D ndarray, optional

If provided, superpixels are computed only where mask is True, and seed points are homogeneously distributed over the mask using a K-means clustering strategy.  New in version 0.17: mask was introduced in 0.17     Returns

labels2D or 3D array

Integer mask indicating segment labels.    Raises
 ValueError

If convert2lab is set to True but the last array dimension is not of length 3.  ValueError

If start_label is not 0 or 1.     Notes  If sigma > 0, the image is smoothed using a Gaussian kernel prior to segmentation. If sigma is scalar and spacing is provided, the kernel width is divided along each dimension by the spacing. For example, if sigma=1 and spacing=[5, 1, 1], the effective sigma is [0.2, 1, 1]. This ensures sensible smoothing for anisotropic images. The image is rescaled to be in [0, 1] prior to processing. Images of shape (M, N, 3) are interpreted as 2D RGB images by default. To interpret them as 3D with the last dimension having length 3, use multichannel=False.
start_label is introduced to handle the issue [4]. The labels indexing starting at 0 will be deprecated in future versions. If mask is not None labels indexing starts at 1 and masked area is set to 0.  References
1
Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süsstrunk, SLIC Superpixels Compared to State-of-the-art Superpixel Methods, TPAMI, May 2012. DOI:10.1109/TPAMI.2012.120
2
https://www.epfl.ch/labs/ivrl/research/slic-superpixels/#SLICO
3
Irving, Benjamin. “maskSLIC: regional superpixel generation with application to local pathology characterisation in medical images.”, 2016, arXiv:1606.09518
4
https://github.com/scikit-image/scikit-image/issues/3722   Examples >>> from skimage.segmentation import slic
>>> from skimage.data import astronaut
>>> img = astronaut()
>>> segments = slic(img, n_segments=100, compactness=10)
 Increasing the compactness parameter yields more square regions: >>> segments = slic(img, n_segments=100, compactness=20)


skimage.segmentation.watershed(image, markers=None, connectivity=1, offset=None, mask=None, compactness=0, watershed_line=False) [source]

Find watershed basins in image flooded from given markers.  Parameters

imagendarray (2-D, 3-D, …) of integers

Data array where the lowest value points are labeled first.
markersint, or ndarray of int, same shape as image, optional

The desired number of markers, or an array marking the basins with the values to be assigned in the label matrix. Zero means not a marker. If None (no markers given), the local minima of the image are used as markers.
connectivityndarray, optional

An array with the same number of dimensions as image whose non-zero elements indicate neighbors for connection. Following the scipy convention, default is a one-connected array of the dimension of the image.
offsetarray_like of shape image.ndim, optional

offset of the connectivity (one offset per dimension)
maskndarray of bools or 0s and 1s, optional

Array of same shape as image. Only points at which mask == True will be labeled.
compactnessfloat, optional

Use compact watershed [3] with given compactness parameter. Higher values result in more regularly-shaped watershed basins.
watershed_linebool, optional

If watershed_line is True, a one-pixel wide line separates the regions obtained by the watershed algorithm. The line has the label 0.    Returns

outndarray

A labeled matrix of the same type and shape as markers      See also
skimage.segmentation.random_walker

random walker segmentation A segmentation algorithm based on anisotropic diffusion, usually slower than the watershed but with good results on noisy data and boundaries with holes.    Notes This function implements a watershed algorithm [1] [2] that apportions pixels into marked basins. The algorithm uses a priority queue to hold the pixels with the metric for the priority queue being pixel value, then the time of entry into the queue - this settles ties in favor of the closest marker. Some ideas taken from Soille, “Automated Basin Delineation from Digital Elevation Models Using Mathematical Morphology”, Signal Processing 20 (1990) 171-182 The most important insight in the paper is that entry time onto the queue solves two problems: a pixel should be assigned to the neighbor with the largest gradient or, if there is no gradient, pixels on a plateau should be split between markers on opposite sides. This implementation converts all arguments to specific, lowest common denominator types, then passes these to a C algorithm. Markers can be determined manually, or automatically using for example the local minima of the gradient of the image, or the local maxima of the distance function to the background for separating overlapping objects (see example). References
1
https://en.wikipedia.org/wiki/Watershed_%28image_processing%29
2
http://cmm.ensmp.fr/~beucher/wtshed.html
3
Peer Neubert & Peter Protzel (2014). Compact Watershed and Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation Algorithms. ICPR 2014, pp 996-1001. DOI:10.1109/ICPR.2014.181 https://www.tu-chemnitz.de/etit/proaut/publications/cws_pSLIC_ICPR.pdf   Examples The watershed algorithm is useful to separate overlapping objects. We first generate an initial image with two overlapping circles: >>> x, y = np.indices((80, 80))
>>> x1, y1, x2, y2 = 28, 28, 44, 52
>>> r1, r2 = 16, 20
>>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2
>>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2
>>> image = np.logical_or(mask_circle1, mask_circle2)
 Next, we want to separate the two circles. We generate markers at the maxima of the distance to the background: >>> from scipy import ndimage as ndi
>>> distance = ndi.distance_transform_edt(image)
>>> from skimage.feature import peak_local_max
>>> local_maxi = peak_local_max(distance, labels=image,
...                             footprint=np.ones((3, 3)),
...                             indices=False)
>>> markers = ndi.label(local_maxi)[0]
 Finally, we run the watershed on the image and markers: >>> labels = watershed(-distance, markers, mask=image)
 The algorithm works also for 3-D images, and can be used for example to separate overlapping spheres.


skimage Image Processing for Python scikit-image (a.k.a. skimage) is a collection of algorithms for image processing and computer vision. The main package of skimage only provides a few utilities for converting between image data types; for most features, you need to import one of the following subpackages: Subpackages  color

Color space conversion.  data

Test images and example data.  draw

Drawing primitives (lines, text, etc.) that operate on NumPy arrays.  exposure

Image intensity adjustment, e.g., histogram equalization, etc.  feature

Feature detection and extraction, e.g., texture analysis corners, etc.  filters

Sharpening, edge finding, rank filters, thresholding, etc.  graph

Graph-theoretic operations, e.g., shortest paths.  io

Reading, saving, and displaying images and video.  measure

Measurement of image properties, e.g., region properties and contours.  metrics

Metrics corresponding to images, e.g. distance metrics, similarity, etc.  morphology

Morphological operations, e.g., opening or skeletonization.  restoration

Restoration algorithms, e.g., deconvolution algorithms, denoising, etc.  segmentation

Partitioning an image into multiple regions.  transform

Geometric and other transforms, e.g., rotation or the Radon transform.  util

Generic utilities.  viewer

A simple graphical user interface for visualizing results and exploring parameters.   Utility Functions  img_as_float

Convert an image to floating point format, with values in [0, 1]. Is similar to img_as_float64, but will not convert lower-precision floating point arrays to float64.  img_as_float32

Convert an image to single-precision (32-bit) floating point format, with values in [0, 1].  img_as_float64

Convert an image to double-precision (64-bit) floating point format, with values in [0, 1].  img_as_uint

Convert an image to unsigned integer format, with values in [0, 65535].  img_as_int

Convert an image to signed integer format, with values in [-32768, 32767].  img_as_ubyte

Convert an image to unsigned byte format, with values in [0, 255].  img_as_bool

Convert an image to boolean format, with values either True or False.  dtype_limits

Return intensity limits, i.e. (min, max) tuple, of the image’s dtype.
skimage.dtype_limits(image[, clip_negative]) Return intensity limits, i.e.
skimage.ensure_python_version(min_version)
skimage.img_as_bool(image[, force_copy]) Convert an image to boolean format.
skimage.img_as_float(image[, force_copy]) Convert an image to floating point format.
skimage.img_as_float32(image[, force_copy]) Convert an image to single-precision (32-bit) floating point format.
skimage.img_as_float64(image[, force_copy]) Convert an image to double-precision (64-bit) floating point format.
skimage.img_as_int(image[, force_copy]) Convert an image to 16-bit signed integer format.
skimage.img_as_ubyte(image[, force_copy]) Convert an image to 8-bit unsigned integer format.
skimage.img_as_uint(image[, force_copy]) Convert an image to 16-bit unsigned integer format.
skimage.lookfor(what) Do a keyword search on scikit-image docstrings.
skimage.data Standard test images.
skimage.util    dtype_limits
skimage.dtype_limits(image, clip_negative=False) [source]

Return intensity limits, i.e. (min, max) tuple, of the image’s dtype.  Parameters

imagendarray

Input image.
clip_negativebool, optional

If True, clip the negative range (i.e. return 0 for min intensity) even if the image dtype allows negative values.    Returns

imin, imaxtuple

Lower and upper intensity limits.
 ensure_python_version
skimage.ensure_python_version(min_version) [source]

 img_as_bool
skimage.img_as_bool(image, force_copy=False) [source]

Convert an image to boolean format.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of bool (bool_)

Output image.     Notes The upper half of the input dtype’s positive range is True, and the lower half is False. All negative values (if present) are False.
 img_as_float
skimage.img_as_float(image, force_copy=False) [source]

Convert an image to floating point format. This function is similar to img_as_float64, but will not convert lower-precision floating point arrays to float64.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of float

Output image.     Notes The range of a floating point image is [0.0, 1.0] or [-1.0, 1.0] when converting from unsigned or signed datatypes, respectively. If the input image has a float type, intensity values are not modified and can be outside the ranges [0.0, 1.0] or [-1.0, 1.0].
 Examples using skimage.img_as_float

  Tinting gray-scale images

  3D adaptive histogram equalization

  Phase Unwrapping

  Finding local maxima

  Use rolling-ball algorithm for estimating background intensity

  Explore 3D images (of cells)   img_as_float32
skimage.img_as_float32(image, force_copy=False) [source]

Convert an image to single-precision (32-bit) floating point format.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of float32

Output image.     Notes The range of a floating point image is [0.0, 1.0] or [-1.0, 1.0] when converting from unsigned or signed datatypes, respectively. If the input image has a float type, intensity values are not modified and can be outside the ranges [0.0, 1.0] or [-1.0, 1.0].
 img_as_float64
skimage.img_as_float64(image, force_copy=False) [source]

Convert an image to double-precision (64-bit) floating point format.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of float64

Output image.     Notes The range of a floating point image is [0.0, 1.0] or [-1.0, 1.0] when converting from unsigned or signed datatypes, respectively. If the input image has a float type, intensity values are not modified and can be outside the ranges [0.0, 1.0] or [-1.0, 1.0].
 img_as_int
skimage.img_as_int(image, force_copy=False) [source]

Convert an image to 16-bit signed integer format.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of int16

Output image.     Notes The values are scaled between -32768 and 32767. If the input data-type is positive-only (e.g., uint8), then the output image will still only have positive values.
 img_as_ubyte
skimage.img_as_ubyte(image, force_copy=False) [source]

Convert an image to 8-bit unsigned integer format.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of ubyte (uint8)

Output image.     Notes Negative input values will be clipped. Positive values are scaled between 0 and 255.
 Examples using skimage.img_as_ubyte

  Local Histogram Equalization

  Entropy

  Markers for watershed transform

  Segment human cells (in mitosis)

  Rank filters   img_as_uint
skimage.img_as_uint(image, force_copy=False) [source]

Convert an image to 16-bit unsigned integer format.  Parameters

imagendarray

Input image.
force_copybool, optional

Force a copy of the data, irrespective of its current dtype.    Returns

outndarray of uint16

Output image.     Notes Negative input values will be clipped. Positive values are scaled between 0 and 65535.
 lookfor
skimage.lookfor(what) [source]

Do a keyword search on scikit-image docstrings.  Parameters

whatstr

Words to look for.     Examples >>> import skimage
>>> skimage.lookfor('regular_grid')
Search results for 'regular_grid'
---------------------------------
skimage.lookfor
    Do a keyword search on scikit-image docstrings.
skimage.util.regular_grid
    Find `n_points` regularly spaced along `ar_shape`.


Module: transform
skimage.transform.downscale_local_mean(…) Down-sample N-dimensional image by local averaging.
skimage.transform.estimate_transform(ttype, …) Estimate 2D geometric transformation parameters.
skimage.transform.frt2(a) Compute the 2-dimensional finite radon transform (FRT) for an n x n integer array.
skimage.transform.hough_circle(image, radius) Perform a circular Hough transform.
skimage.transform.hough_circle_peaks(…[, …]) Return peaks in a circle Hough transform.
skimage.transform.hough_ellipse(image[, …]) Perform an elliptical Hough transform.
skimage.transform.hough_line(image[, theta]) Perform a straight line Hough transform.
skimage.transform.hough_line_peaks(hspace, …) Return peaks in a straight line Hough transform.
skimage.transform.ifrt2(a) Compute the 2-dimensional inverse finite radon transform (iFRT) for an (n+1) x n integer array.
skimage.transform.integral_image(image) Integral image / summed area table.
skimage.transform.integrate(ii, start, end) Use an integral image to integrate over a given window.
skimage.transform.iradon(radon_image[, …]) Inverse radon transform.
skimage.transform.iradon_sart(radon_image[, …]) Inverse radon transform.
skimage.transform.matrix_transform(coords, …) Apply 2D matrix transform.
skimage.transform.order_angles_golden_ratio(theta) Order angles to reduce the amount of correlated information in subsequent projections.
skimage.transform.probabilistic_hough_line(image) Return lines from a progressive probabilistic line Hough transform.
skimage.transform.pyramid_expand(image[, …]) Upsample and then smooth image.
skimage.transform.pyramid_gaussian(image[, …]) Yield images of the Gaussian pyramid formed by the input image.
skimage.transform.pyramid_laplacian(image[, …]) Yield images of the laplacian pyramid formed by the input image.
skimage.transform.pyramid_reduce(image[, …]) Smooth and then downsample image.
skimage.transform.radon(image[, theta, …]) Calculates the radon transform of an image given specified projection angles.
skimage.transform.rescale(image, scale[, …]) Scale image by a certain factor.
skimage.transform.resize(image, output_shape) Resize image to match a certain size.
skimage.transform.rotate(image, angle[, …]) Rotate image by a certain angle around its center.
skimage.transform.swirl(image[, center, …]) Perform a swirl transformation.
skimage.transform.warp(image, inverse_map[, …]) Warp an image according to a given coordinate transformation.
skimage.transform.warp_coords(coord_map, shape) Build the source coordinates for the output of a 2-D image warp.
skimage.transform.warp_polar(image[, …]) Remap image to polar or log-polar coordinates space.
skimage.transform.AffineTransform([matrix, …]) 2D affine transformation.
skimage.transform.EssentialMatrixTransform([…]) Essential matrix transformation.
skimage.transform.EuclideanTransform([…]) 2D Euclidean transformation.
skimage.transform.FundamentalMatrixTransform([…]) Fundamental matrix transformation.
skimage.transform.PiecewiseAffineTransform() 2D piecewise affine transformation.
skimage.transform.PolynomialTransform([params]) 2D polynomial transformation.
skimage.transform.ProjectiveTransform([matrix]) Projective transformation.
skimage.transform.SimilarityTransform([…]) 2D similarity transformation.   downscale_local_mean
skimage.transform.downscale_local_mean(image, factors, cval=0, clip=True) [source]

Down-sample N-dimensional image by local averaging. The image is padded with cval if it is not perfectly divisible by the integer factors. In contrast to interpolation in skimage.transform.resize and skimage.transform.rescale this function calculates the local mean of elements in each block of size factors in the input image.  Parameters

imagendarray

N-dimensional input image.
factorsarray_like

Array containing down-sampling integer factor along each axis.
cvalfloat, optional

Constant padding value if image is not perfectly divisible by the integer factors.
clipbool, optional

Unused, but kept here for API consistency with the other transforms in this module. (The local mean will never fall outside the range of values in the input image, assuming the provided cval also falls within that range.)    Returns

imagendarray

Down-sampled image with same number of dimensions as input image. For integer inputs, the output dtype will be float64. See numpy.mean() for details.     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]])

 estimate_transform
skimage.transform.estimate_transform(ttype, src, dst, **kwargs) [source]

Estimate 2D geometric transformation parameters. You can determine the over-, well- and under-determined parameters with the total least-squares method. Number of source and destination coordinates must match.  Parameters

ttype{‘euclidean’, similarity’, ‘affine’, ‘piecewise-affine’, ‘projective’, ‘polynomial’}

Type of transform.
kwargsarray or int

Function parameters (src, dst, n, angle): NAME / TTYPE        FUNCTION PARAMETERS
'euclidean'         `src, `dst`
'similarity'        `src, `dst`
'affine'            `src, `dst`
'piecewise-affine'  `src, `dst`
'projective'        `src, `dst`
'polynomial'        `src, `dst`, `order` (polynomial order,
                                          default order is 2)
 Also see examples below.    Returns

tformGeometricTransform

Transform object containing the transformation parameters and providing access to forward and inverse transformation functions.     Examples >>> import numpy as np
>>> from skimage import transform
 >>> # estimate transformation parameters
>>> src = np.array([0, 0, 10, 10]).reshape((2, 2))
>>> dst = np.array([12, 14, 1, -20]).reshape((2, 2))
 >>> tform = transform.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)
 >>> # create transformation with explicit parameters
>>> tform2 = transform.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

 frt2
skimage.transform.frt2(a) [source]

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

aarray_like

A 2-D square n x n integer array.    Returns

FRT2-D ndarray

Finite Radon Transform array of (n+1) x n integer coefficients.      See also
ifrt2

The two-dimensional 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
FRT
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)

 hough_circle
skimage.transform.hough_circle(image, radius, normalize=True, full_output=False) [source]

Perform a circular Hough transform.  Parameters

image(M, N) ndarray

Input image with nonzero values representing edges.
radiusscalar or sequence of scalars

Radii at which to compute the Hough transform. Floats are converted to integers.
normalizeboolean, optional (default True)

Normalize the accumulator with the number of pixels used to draw the radius.
full_outputboolean, optional (default False)

Extend the output size by twice the largest radius in order to detect centers outside the input picture.    Returns

H3D ndarray (radius index, (M + 2R, N + 2R) ndarray)

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=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)

 hough_circle_peaks
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 given Hough spaces. Non-maximum suppression with different sizes is applied separately in the first and second dimension of the Hough space to identify peaks. For circles with different radius but close in distance, only the one with highest peak is kept.  Parameters

hspaces(N, M) array

Hough spaces returned by the hough_circle function.
radii(M,) array

Radii corresponding to Hough spaces.
min_xdistanceint, optional

Minimum distance separating centers in the x dimension.
min_ydistanceint, optional

Minimum distance separating centers in the y dimension.
thresholdfloat, optional

Minimum intensity of peaks in each Hough space. Default is 0.5 * max(hspace).
num_peaksint, optional

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.
total_num_peaksint, optional

Maximum number of peaks. When the number of peaks exceeds num_peaks, return num_peaks coordinates based on peak intensity.
normalizebool, optional

If True, normalize the accumulator by the radius to sort the prominent peaks.    Returns

accum, cx, cy, radtuple of array

Peak values in Hough space, x and y center coordinates and radii.     Notes Circles with bigger radius have higher peaks in Hough space. If larger circles are preferred over smaller ones, normalize should be False. Otherwise, circles will be returned in the order of decreasing voting number. 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,])

 hough_ellipse
skimage.transform.hough_ellipse(image, threshold=4, accuracy=1, min_size=4, max_size=None) [source]

Perform an elliptical Hough transform.  Parameters

image(M, N) ndarray

Input image with nonzero values representing edges.
thresholdint, optional

Accumulator threshold value.
accuracydouble, optional

Bin size on the minor axis used in the accumulator.
min_sizeint, optional

Minimal major axis length.
max_sizeint, optional

Maximal minor axis length. If None, the value is set to the half of the smaller image dimension.    Returns

resultndarray with fields [(accumulator, yc, xc, a, b, orientation)].

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
1
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)]

 hough_line
skimage.transform.hough_line(image, theta=None) [source]

Perform a straight line Hough transform.  Parameters

image(M, N) ndarray

Input image with nonzero values representing edges.
theta1D ndarray of double, optional

Angles at which to compute the transform, in radians. Defaults to a vector of 180 angles evenly spaced from -pi/2 to pi/2.    Returns

hspace2-D ndarray of uint64

Hough transform accumulator.
anglesndarray

Angles at which the transform is computed, in radians.
distancesndarray

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)
 hough_line_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. Non-maximum suppression with different sizes is applied separately in the first (distances) and second (angles) dimension of the Hough space to identify peaks.  Parameters

hspace(N, M) array

Hough space returned by the hough_line function.
angles(M,) array

Angles returned by the hough_line function. Assumed to be continuous. (angles[-1] - angles[0] == PI).
dists(N, ) array

Distances returned by the hough_line function.
min_distanceint, optional

Minimum distance separating lines (maximum filter size for first dimension of hough space).
min_angleint, optional

Minimum angle separating lines (maximum filter size for second dimension of hough space).
thresholdfloat, optional

Minimum intensity of peaks. Default is 0.5 * max(hspace).
num_peaksint, optional

Maximum number of peaks. When the number of peaks exceeds num_peaks, return num_peaks coordinates based on peak intensity.    Returns

accum, angles, diststuple of array

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=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

 ifrt2
skimage.transform.ifrt2(a) [source]

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

aarray_like

A 2-D (n+1) row x n column integer array.    Returns

iFRT2-D n x n ndarray

Inverse Finite Radon Transform array of n x n integer coefficients.      See also
frt2

The two-dimensional 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
1
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(img-fi)[0]) == 0

 integral_image
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.:  \[S[m, n] = \sum_{i \leq m} \sum_{j \leq n} X[i, j]\]  Parameters

imagendarray

Input image.    Returns

Sndarray

Integral image/summed area table of same shape as input image.     References
1
F.C. Crow, “Summed-area tables for texture mapping,” ACM SIGGRAPH Computer Graphics, vol. 18, 1984, pp. 207-212.
 integrate
skimage.transform.integrate(ii, start, end) [source]

Use an integral image to integrate over a given window.  Parameters

iindarray

Integral image.
startList of tuples, each tuple of length equal to dimension of ii

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,…), …].
endList of tuples, each tuple of length equal to dimension of ii

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, …), …].    Returns

Sscalar or ndarray

Integral (sum) over the given window(s).     Examples >>> arr = np.ones((5, 6), dtype=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.])

 iradon
skimage.transform.iradon(radon_image, theta=None, output_size=None, filter_name='ramp', interpolation='linear', circle=True, preserve_range=True) [source]

Inverse radon transform. Reconstruct an image from the radon transform, using the filtered back projection algorithm.  Parameters

radon_imagearray

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.
thetaarray_like, optional

Reconstruction angles (in degrees). Default: m angles evenly spaced between 0 and 180 (if the shape of radon_image is (N, M)).
output_sizeint, optional

Number of rows and columns in the reconstruction.
filter_namestr, optional

Filter used in frequency domain filtering. Ramp filter used by default. Filters available: ramp, shepp-logan, cosine, hamming, hann. Assign None to use no filter.
interpolationstr, optional

Interpolation method used in reconstruction. Methods available: ‘linear’, ‘nearest’, and ‘cubic’ (‘cubic’ is slow).
circleboolean, optional

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.
preserve_rangebool, 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    Returns

reconstructedndarray

Reconstructed image. The rotation axis will be located in the pixel with indices (reconstructed.shape[0] // 2, reconstructed.shape[1] // 2).    Changed in version 0.19: In iradon, filter argument is deprecated in favor of filter_name.    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
1
AC Kak, M Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1988.
2
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
 iradon_sart
skimage.transform.iradon_sart(radon_image, theta=None, image=None, projection_shifts=None, clip=None, relaxation=0.15, dtype=None) [source]

Inverse radon transform. Reconstruct an image from the radon transform, using a single iteration of the Simultaneous Algebraic Reconstruction Technique (SART) algorithm.  Parameters

radon_image2D array

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.
theta1D array, optional

Reconstruction angles (in degrees). Default: m angles evenly spaced between 0 and 180 (if the shape of radon_image is (N, M)).
image2D array, optional

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.
projection_shifts1D array, optional

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.
cliplength-2 sequence of floats, optional

Force all values in the reconstructed tomogram to lie in the range [clip[0], clip[1]]
relaxationfloat, optional

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.
dtypedtype, optional

Output data type, must be floating point. By default, if input data type is not float, input is cast to double, otherwise dtype is set to input data type.    Returns

reconstructedndarray

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 high-frequency information, but will also often increase the noise. References
1
AC Kak, M Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1988.
2
AH Andersen, AC Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm”, Ultrasonic Imaging 6 pp 81–94 (1984)
3
S Kaczmarz, “Angenäherte auflösung von systemen linearer gleichungen”, Bulletin International de l’Academie Polonaise des Sciences et des Lettres 35 pp 355–357 (1937)
4
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.
5
Kaczmarz’ method, Wikipedia, https://en.wikipedia.org/wiki/Kaczmarz_method
 matrix_transform
skimage.transform.matrix_transform(coords, matrix) [source]

Apply 2D matrix transform.  Parameters

coords(N, 2) array

x, y coordinates to transform
matrix(3, 3) array

Homogeneous transformation matrix.    Returns

coords(N, 2) array

Transformed coordinates.
 order_angles_golden_ratio
skimage.transform.order_angles_golden_ratio(theta) [source]

Order angles to reduce the amount of correlated information in subsequent projections.  Parameters

theta1D array of floats

Projection angles in degrees. Duplicate angles are not allowed.    Returns

indices_generatorgenerator yielding unsigned integers

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 non-negative integers < len(theta) are yielded exactly once.     Notes The method used here is that of the golden ratio introduced by T. Kohler. References
1
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.
2
Winkelmann, Stefanie, et al. “An optimal radial profile order based on the Golden Ratio for time-resolved MRI.” Medical Imaging, IEEE Transactions on 26.1 (2007): 68-76.
 probabilistic_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.  Parameters

image(M, N) ndarray

Input image with nonzero values representing edges.
thresholdint, optional

Threshold
line_lengthint, optional

Minimum accepted length of detected lines. Increase the parameter to extract longer lines.
line_gapint, optional

Maximum gap between pixels to still form a line. Increase the parameter to merge broken lines more aggressively.
theta1D ndarray, dtype=double, optional

Angles at which to compute the transform, in radians. If None, use a range from -pi/2 to pi/2.
seedint, optional

Seed to initialize the random number generator.    Returns

lineslist

List of lines identified, lines in format ((x0, y0), (x1, y1)), indicating line start and end.     References
1
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.
 pyramid_expand
skimage.transform.pyramid_expand(image, upscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=False, preserve_range=False) [source]

Upsample and then smooth image.  Parameters

imagendarray

Input image.
upscalefloat, optional

Upscale factor.
sigmafloat, optional

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.
orderint, optional

Order of splines used in interpolation of upsampling. See skimage.transform.warp for detail.
mode{‘reflect’, ‘constant’, ‘edge’, ‘symmetric’, ‘wrap’}, optional

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
cvalfloat, optional

Value to fill past edges of input if mode is ‘constant’.
multichannelbool, optional

Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
preserve_rangebool, 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    Returns

outarray

Upsampled and smoothed float image.     References
1
http://persci.mit.edu/pub_pdfs/pyramid83.pdf
 pyramid_gaussian
skimage.transform.pyramid_gaussian(image, max_layer=-1, downscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=False, preserve_range=False) [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 one-pixel image or the image where the reduction does not change its shape.  Parameters

imagendarray

Input image.
max_layerint, optional

Number of layers for the pyramid. 0th layer is the original image. Default is -1 which builds all possible layers.
downscalefloat, optional

Downscale factor.
sigmafloat, optional

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.
orderint, optional

Order of splines used in interpolation of downsampling. See skimage.transform.warp for detail.
mode{‘reflect’, ‘constant’, ‘edge’, ‘symmetric’, ‘wrap’}, optional

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
cvalfloat, optional

Value to fill past edges of input if mode is ‘constant’.
multichannelbool, optional

Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
preserve_rangebool, 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    Returns

pyramidgenerator

Generator yielding pyramid layers as float images.     References
1
http://persci.mit.edu/pub_pdfs/pyramid83.pdf
 pyramid_laplacian
skimage.transform.pyramid_laplacian(image, max_layer=-1, downscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=False, preserve_range=False) [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 one-pixel image or the image where the reduction does not change its shape.  Parameters

imagendarray

Input image.
max_layerint, optional

Number of layers for the pyramid. 0th layer is the original image. Default is -1 which builds all possible layers.
downscalefloat, optional

Downscale factor.
sigmafloat, optional

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.
orderint, optional

Order of splines used in interpolation of downsampling. See skimage.transform.warp for detail.
mode{‘reflect’, ‘constant’, ‘edge’, ‘symmetric’, ‘wrap’}, optional

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
cvalfloat, optional

Value to fill past edges of input if mode is ‘constant’.
multichannelbool, optional

Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
preserve_rangebool, 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    Returns

pyramidgenerator

Generator yielding pyramid layers as float images.     References
1
http://persci.mit.edu/pub_pdfs/pyramid83.pdf
2
http://sepwww.stanford.edu/data/media/public/sep/morgan/texturematch/paper_html/node3.html
 pyramid_reduce
skimage.transform.pyramid_reduce(image, downscale=2, sigma=None, order=1, mode='reflect', cval=0, multichannel=False, preserve_range=False) [source]

Smooth and then downsample image.  Parameters

imagendarray

Input image.
downscalefloat, optional

Downscale factor.
sigmafloat, optional

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.
orderint, optional

Order of splines used in interpolation of downsampling. See skimage.transform.warp for detail.
mode{‘reflect’, ‘constant’, ‘edge’, ‘symmetric’, ‘wrap’}, optional

The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’.
cvalfloat, optional

Value to fill past edges of input if mode is ‘constant’.
multichannelbool, optional

Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
preserve_rangebool, 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    Returns

outarray

Smoothed and downsampled float image.     References
1
http://persci.mit.edu/pub_pdfs/pyramid83.pdf
 radon
skimage.transform.radon(image, theta=None, circle=True, *, preserve_range=False) [source]

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

imagearray_like

Input image. The rotation axis will be located in the pixel with indices (image.shape[0] // 2, image.shape[1] // 2).
thetaarray_like, optional

Projection angles (in degrees). If None, the value is set to np.arange(180).
circleboolean, optional

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).
preserve_rangebool, 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    Returns

radon_imagendarray

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 (https://www.clear.rice.edu/elec431/projects96/DSP/bpanalysis.html) References
1
AC Kak, M Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1988.
2
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
 rescale
skimage.transform.rescale(image, scale, order=None, mode='reflect', cval=0, clip=True, preserve_range=False, multichannel=False, anti_aliasing=None, anti_aliasing_sigma=None) [source]

Scale image by a certain factor. Performs interpolation to up-scale or down-scale N-dimensional images. Note that anti-aliasing should be enabled when down-sizing images to avoid aliasing artifacts. For down-sampling with an integer factor also see skimage.transform.downscale_local_mean.  Parameters

imagendarray

Input image.
scale{float, tuple of floats}

Scale factors. Separate scale factors can be defined as (rows, cols[, …][, dim]).    Returns

scaledndarray

Scaled version of the input.    Other Parameters

orderint, optional

The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See skimage.transform.warp for detail.
mode{‘constant’, ‘edge’, ‘symmetric’, ‘reflect’, ‘wrap’}, optional

Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad.
cvalfloat, optional

Used in conjunction with mode ‘constant’, the value outside the image boundaries.
clipbool, optional

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.
preserve_rangebool, 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
multichannelbool, optional

Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
anti_aliasingbool, optional

Whether to apply a Gaussian filter to smooth the image prior to down-scaling. It is crucial to filter when down-sampling the image to avoid aliasing artifacts. If input image data type is bool, no anti-aliasing is applied.
anti_aliasing_sigma{float, tuple of floats}, optional

Standard deviation for Gaussian filtering to avoid aliasing artifacts. By default, this value is chosen as (s - 1) / 2 where s is the down-scaling 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).shape
(51, 51)
>>> rescale(image, 0.5).shape
(256, 256)

 resize
skimage.transform.resize(image, output_shape, order=None, mode='reflect', 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 up-size or down-size N-dimensional images. Note that anti-aliasing should be enabled when down-sizing images to avoid aliasing artifacts. For down-sampling with an integer factor also see skimage.transform.downscale_local_mean.  Parameters

imagendarray

Input image.
output_shapetuple or ndarray

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 n-dimensional interpolation is applied.    Returns

resizedndarray

Resized version of the input.    Other Parameters

orderint, optional

The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See skimage.transform.warp for detail.
mode{‘constant’, ‘edge’, ‘symmetric’, ‘reflect’, ‘wrap’}, optional

Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad.
cvalfloat, optional

Used in conjunction with mode ‘constant’, the value outside the image boundaries.
clipbool, optional

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.
preserve_rangebool, 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
anti_aliasingbool, optional

Whether to apply a Gaussian filter to smooth the image prior to down-scaling. It is crucial to filter when down-sampling the image to avoid aliasing artifacts. If input image data type is bool, no anti-aliasing is applied.
anti_aliasing_sigma{float, tuple of floats}, optional

Standard deviation for Gaussian filtering to avoid aliasing artifacts. By default, this value is chosen as (s - 1) / 2 where s is the down-scaling factor, where s > 1. For the up-size case, s < 1, no anti-aliasing is performed prior to rescaling.     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)).shape
(100, 100)

 rotate
skimage.transform.rotate(image, angle, resize=False, center=None, order=None, mode='constant', cval=0, clip=True, preserve_range=False) [source]

Rotate image by a certain angle around its center.  Parameters

imagendarray

Input image.
anglefloat

Rotation angle in degrees in counter-clockwise direction.
resizebool, optional

Determine whether the shape of the output image will be automatically calculated, so the complete rotated image exactly fits. Default is False.
centeriterable of length 2

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.    Returns

rotatedndarray

Rotated version of the input.    Other Parameters

orderint, optional

The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See skimage.transform.warp for detail.
mode{‘constant’, ‘edge’, ‘symmetric’, ‘reflect’, ‘wrap’}, optional

Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad.
cvalfloat, optional

Used in conjunction with mode ‘constant’, the value outside the image boundaries.
clipbool, optional

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.
preserve_rangebool, 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     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)

 Examples using skimage.transform.rotate

  Different perimeters

  Measure region properties   swirl
skimage.transform.swirl(image, center=None, strength=1, radius=100, rotation=0, output_shape=None, order=None, mode='reflect', cval=0, clip=True, preserve_range=False) [source]

Perform a swirl transformation.  Parameters

imagendarray

Input image.
center(column, row) tuple or (2,) ndarray, optional

Center coordinate of transformation.
strengthfloat, optional

The amount of swirling applied.
radiusfloat, optional

The extent of the swirl in pixels. The effect dies out rapidly beyond radius.
rotationfloat, optional

Additional rotation applied to the image.    Returns

swirledndarray

Swirled version of the input.    Other Parameters

output_shapetuple (rows, cols), optional

Shape of the output image generated. By default the shape of the input image is preserved.
orderint, optional

The order of the spline interpolation, default is 0 if image.dtype is bool and 1 otherwise. The order has to be in the range 0-5. See skimage.transform.warp for detail.
mode{‘constant’, ‘edge’, ‘symmetric’, ‘reflect’, ‘wrap’}, optional

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.
cvalfloat, optional

Used in conjunction with mode ‘constant’, the value outside the image boundaries.
clipbool, optional

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.
preserve_rangebool, 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
 warp
skimage.transform.warp(image, inverse_map, map_args={}, output_shape=None, order=None, mode='constant', cval=0.0, clip=True, preserve_range=False) [source]

Warp an image according to a given coordinate transformation.  Parameters

imagendarray

Input image.
inverse_maptransformation object, callable cr = f(cr, **kwargs), or ndarray

Inverse 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 2-D image can have 2 dimensions for gray-scale images, or 3 dimensions with color information.  For 2-D images, you can directly pass a transformation object, e.g. skimage.transform.SimilarityTransform, or its inverse. For 2-D images, you can pass a (3, 3) homogeneous transformation matrix, e.g. skimage.transform.SimilarityTransform.params. For 2-D 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 N-D 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 2-D 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 3-D input, if the output is of shape (3,). See example section for usage.
map_argsdict, optional

Keyword arguments passed to inverse_map.
output_shapetuple (rows, cols), optional

Shape of the output image generated. By default the shape of the input image is preserved. Note that, even for multi-band images, only rows and columns need to be specified.
orderint, optional

 The order of interpolation. The order has to be in the range 0-5:

 0: Nearest-neighbor 1: Bi-linear (default) 2: Bi-quadratic 3: Bi-cubic 4: Bi-quartic 5: Bi-quintic  Default is 0 if image.dtype is bool and 1 otherwise.
mode{‘constant’, ‘edge’, ‘symmetric’, ‘reflect’, ‘wrap’}, optional

Points outside the boundaries of the input are filled according to the given mode. Modes match the behaviour of numpy.pad.
cvalfloat, optional

Used in conjunction with mode ‘constant’, the value outside the image boundaries.
clipbool, optional

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.
preserve_rangebool, 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    Returns

warpeddouble ndarray

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 N-D 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 3-D 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)

 Examples using skimage.transform.warp

  Registration using optical flow   warp_coords
skimage.transform.warp_coords(coord_map, shape, dtype=<class 'numpy.float64'>) [source]

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

coord_mapcallable like GeometricTransform.inverse

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.
shapetuple

Shape of output image (rows, cols[, bands]).
dtypenp.dtype or string

dtype for return value (sane choices: float32 or float64).    Returns

coords(ndim, rows, cols[, bands]) array of dtype dtype

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 lower-level routine that produces the source coordinates for 2-D images used by warp(). It is provided separately from warp to give additional flexibility to users who would like, for example, to re-use a particular coordinate mapping, to use specific dtypes at various points along the the image-warping process, or to implement different post-processing 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)

 warp_polar
skimage.transform.warp_polar(image, center=None, *, radius=None, output_shape=None, scaling='linear', multichannel=False, **kwargs) [source]

Remap image to polar or log-polar coordinates space.  Parameters

imagendarray

Input image. Only 2-D arrays are accepted by default. If multichannel=True, 3-D arrays are accepted and the last axis is interpreted as multiple channels.
centertuple (row, col), optional

Point in image that represents the center of the transformation (i.e., the origin in cartesian space). Values can be of type float. If no value is given, the center is assumed to be the center point of the image.
radiusfloat, optional

Radius of the circle that bounds the area to be transformed.
output_shapetuple (row, col), optional

scaling{‘linear’, ‘log’}, optional

Specify whether the image warp is polar or log-polar. Defaults to ‘linear’.
multichannelbool, optional

Whether the image is a 3-D array in which the third axis is to be interpreted as multiple channels. If set to False (default), only 2-D arrays are accepted.
**kwargskeyword arguments

Passed to transform.warp.    Returns

warpedndarray

The polar or log-polar warped image.     Examples Perform a basic polar warp on a grayscale image: >>> from skimage import data
>>> from skimage.transform import warp_polar
>>> image = data.checkerboard()
>>> warped = warp_polar(image)
 Perform a log-polar warp on a grayscale image: >>> warped = warp_polar(image, scaling='log')
 Perform a log-polar warp on a grayscale image while specifying center, radius, and output shape: >>> warped = warp_polar(image, (100,100), radius=100,
...                     output_shape=image.shape, scaling='log')
 Perform a log-polar warp on a color image: >>> image = data.astronaut()
>>> warped = warp_polar(image, scaling='log', multichannel=True)

 AffineTransform
class 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]]
  Parameters

matrix(3, 3) array, optional

Homogeneous transformation matrix.
scale{s as float or (sx, sy) as array, list or tuple}, optional

Scale factor(s). If a single value, it will be assigned to both sx and sy.  New in version 0.17: Added support for supplying a single scalar value.
rotationfloat, optional

Rotation angle in counter-clockwise direction as radians.
shearfloat, optional

Shear angle in counter-clockwise direction as radians.
translation(tx, ty) as array, list or tuple, optional

Translation parameters.    Attributes

params(3, 3) array

Homogeneous transformation matrix.
__init__(matrix=None, scale=None, rotation=None, shear=None, translation=None) [source]

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

property rotation

property scale

property shear

property translation

 EssentialMatrixTransform
class 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 non-planar 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).  Parameters

rotation(3, 3) array, optional

Rotation matrix of the relative camera motion.
translation(3, 1) array, optional

Translation vector of the relative camera motion. The vector must have unit length.
matrix(3, 3) array, optional

Essential matrix.     References
1
Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003.    Attributes

params(3, 3) array

Essential matrix.
__init__(rotation=None, translation=None, matrix=None) [source]

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

estimate(src, dst) [source]

Estimate essential matrix using 8-point algorithm. The 8-point algorithm requires at least 8 corresponding point pairs for a well-conditioned solution, otherwise the over-determined solution is estimated.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.

 EuclideanTransform
class 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.  Parameters

matrix(3, 3) array, optional

Homogeneous transformation matrix.
rotationfloat, optional

Rotation angle in counter-clockwise direction as radians.
translation(tx, ty) as array, list or tuple, optional

x, y translation parameters.    Attributes

params(3, 3) array

Homogeneous transformation matrix.
__init__(matrix=None, rotation=None, translation=None) [source]

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

estimate(src, dst) [source]

Estimate the transformation from a set of corresponding points. You can determine the over-, well- and under-determined parameters with the total least-squares method. Number of source and destination coordinates must match.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.

property rotation

property translation

 FundamentalMatrixTransform
class 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).  Parameters

matrix(3, 3) array, optional

Fundamental matrix.     References
1
Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003.    Attributes

params(3, 3) array

Fundamental matrix.
__init__(matrix=None) [source]

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

estimate(src, dst) [source]

Estimate fundamental matrix using 8-point algorithm. The 8-point algorithm requires at least 8 corresponding point pairs for a well-conditioned solution, otherwise the over-determined solution is estimated.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.

inverse(coords) [source]

Apply inverse transformation.  Parameters

coords(N, 2) array

Destination coordinates.    Returns

coords(N, 3) array

Epipolar lines in the source image.

residuals(src, dst) [source]

Compute the Sampson distance. The Sampson distance is the first approximation to the geometric error.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

residuals(N, ) array

Sampson distance.

 PiecewiseAffineTransform
class 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.  Attributes

affineslist of AffineTransform objects

Affine transformations for each triangle in the mesh.
inverse_affineslist of AffineTransform objects

Inverse affine transformations for each triangle in the mesh.
__init__() [source]

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

estimate(src, dst) [source]

Estimate the transformation from a set of corresponding points. Number of source and destination coordinates must match.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.

inverse(coords) [source]

Apply inverse transformation. Coordinates outside of the mesh will be set to - 1.  Parameters

coords(N, 2) array

Source coordinates.    Returns

coords(N, 2) array

Transformed coordinates.

 PolynomialTransform
class 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 ))
  Parameters

params(2, N) array, optional

Polynomial coefficients where N * 2 = (order + 1) * (order + 2). So, a_ji is defined in params[0, :] and b_ji in params[1, :].    Attributes

params(2, N) array

Polynomial coefficients where N * 2 = (order + 1) * (order + 2). So, a_ji is defined in params[0, :] and b_ji in params[1, :].
__init__(params=None) [source]

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

estimate(src, dst, order=2) [source]

Estimate the transformation from a set of corresponding points. You can determine the over-, well- and under-determined parameters with the total least-squares 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 least-squares 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.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.
orderint, optional

Polynomial order (number of coefficients is order + 1).    Returns

successbool

True, if model estimation succeeds.

inverse(coords) [source]

Apply inverse transformation.  Parameters

coords(N, 2) array

Destination coordinates.    Returns

coords(N, 2) array

Source coordinates.

 ProjectiveTransform
class 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 ]].
  Parameters

matrix(3, 3) array, optional

Homogeneous transformation matrix.    Attributes

params(3, 3) array

Homogeneous transformation matrix.
__init__(matrix=None) [source]

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

estimate(src, dst) [source]

Estimate the transformation from a set of corresponding points. You can determine the over-, well- and under-determined parameters with the total least-squares 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 least-squares 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]
  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.

inverse(coords) [source]

Apply inverse transformation.  Parameters

coords(N, 2) array

Destination coordinates.    Returns

coords(N, 2) array

Source coordinates.

 SimilarityTransform
class 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.  Parameters

matrix(3, 3) array, optional

Homogeneous transformation matrix.
scalefloat, optional

Scale factor.
rotationfloat, optional

Rotation angle in counter-clockwise direction as radians.
translation(tx, ty) as array, list or tuple, optional

x, y translation parameters.    Attributes

params(3, 3) array

Homogeneous transformation matrix.
__init__(matrix=None, scale=None, rotation=None, translation=None) [source]

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

estimate(src, dst) [source]

Estimate the transformation from a set of corresponding points. You can determine the over-, well- and under-determined parameters with the total least-squares method. Number of source and destination coordinates must match.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.

property scale


class 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]]
  Parameters

matrix(3, 3) array, optional

Homogeneous transformation matrix.
scale{s as float or (sx, sy) as array, list or tuple}, optional

Scale factor(s). If a single value, it will be assigned to both sx and sy.  New in version 0.17: Added support for supplying a single scalar value.
rotationfloat, optional

Rotation angle in counter-clockwise direction as radians.
shearfloat, optional

Shear angle in counter-clockwise direction as radians.
translation(tx, ty) as array, list or tuple, optional

Translation parameters.    Attributes

params(3, 3) array

Homogeneous transformation matrix.
__init__(matrix=None, scale=None, rotation=None, shear=None, translation=None) [source]

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

property rotation

property scale

property shear

property translation


__init__(matrix=None, scale=None, rotation=None, shear=None, translation=None) [source]

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


skimage.transform.downscale_local_mean(image, factors, cval=0, clip=True) [source]

Down-sample N-dimensional image by local averaging. The image is padded with cval if it is not perfectly divisible by the integer factors. In contrast to interpolation in skimage.transform.resize and skimage.transform.rescale this function calculates the local mean of elements in each block of size factors in the input image.  Parameters

imagendarray

N-dimensional input image.
factorsarray_like

Array containing down-sampling integer factor along each axis.
cvalfloat, optional

Constant padding value if image is not perfectly divisible by the integer factors.
clipbool, optional

Unused, but kept here for API consistency with the other transforms in this module. (The local mean will never fall outside the range of values in the input image, assuming the provided cval also falls within that range.)    Returns

imagendarray

Down-sampled image with same number of dimensions as input image. For integer inputs, the output dtype will be float64. See numpy.mean() for details.     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]])


class 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 non-planar 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).  Parameters

rotation(3, 3) array, optional

Rotation matrix of the relative camera motion.
translation(3, 1) array, optional

Translation vector of the relative camera motion. The vector must have unit length.
matrix(3, 3) array, optional

Essential matrix.     References
1
Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003.    Attributes

params(3, 3) array

Essential matrix.
__init__(rotation=None, translation=None, matrix=None) [source]

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

estimate(src, dst) [source]

Estimate essential matrix using 8-point algorithm. The 8-point algorithm requires at least 8 corresponding point pairs for a well-conditioned solution, otherwise the over-determined solution is estimated.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.


estimate(src, dst) [source]

Estimate essential matrix using 8-point algorithm. The 8-point algorithm requires at least 8 corresponding point pairs for a well-conditioned solution, otherwise the over-determined solution is estimated.  Parameters

src(N, 2) array

Source coordinates.
dst(N, 2) array

Destination coordinates.    Returns

successbool

True, if model estimation succeeds.


__init__(rotation=None, translation=None, matrix=None) [source]

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


skimage.transform.estimate_transform(ttype, src, dst, **kwargs) [source]

Estimate 2D geometric transformation parameters. You can determine the over-, well- and under-determined parameters with the total least-squares method. Number of source and destination coordinates must match.  Parameters

ttype{‘euclidean’, similarity’, ‘affine’, ‘piecewise-affine’, ‘projective’, ‘polynomial’}

Type of transform.
kwargsarray or int

Function parameters (src, dst, n, angle): NAME / TTYPE        FUNCTION PARAMETERS
'euclidean'         `src, `dst`
'similarity'        `src, `dst`
'affine'            `src, `dst`
'piecewise-affine'  `src, `dst`
'projective'        `src, `dst`
'polynomial'        `src, `dst`, `order` (polynomial order,
                                          default order is 2)
 Also see examples below.    Returns

tformGeometricTransform

Transform object containing the transformation parameters and providing access to forward and inverse transformation functions.     Examples >>> import numpy as np
>>> from skimage import transform
 >>> # estimate transformation parameters
>>> src = np.array([0, 0, 10, 10]).reshape((2, 2))
>>> dst = np.array([12, 14, 1, -20]).reshape((2, 2))
 >>> tform = transform.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)
 >>> # create transformation with explicit parameters
>>> tform2 = transform.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