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Examples

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

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

Compute Harris corner measure response image.

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

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

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

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

or:

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

Parameters:

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

Returns:

responsendarray: Harris response image.

References

[1]

Examples

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

Assemble images with simple image stitching

Corner detection

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

Compute Kitchen and Rosenfeld corner measure response image.

The corner measure is calculated as follows:

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

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

Parameters:

image(M, N) ndarray: Input image.
mode{‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional: How to handle values outside the image borders.
cvalfloat, optional: Used in conjunction with mode ‘constant’, the value outside the image boundaries.

Returns:

responsendarray: Kitchen and Rosenfeld response image.

References

[1]

Kitchen, L., & Rosenfeld, A. (1982). Gray-level corner detection. Pattern recognition letters, 1(2), 95-102. DOI:10.1016/0167-8655(82)90020-4

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

Compute Moravec corner measure response image.

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

Parameters:

image(M, N) ndarray: Input image.
window_sizeint, optional: Window size.

Returns:

responsendarray: Moravec response image.

References

[1]

Examples

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

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

Compute the orientation of corners.

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

Parameters:

image(M, N) array: Input grayscale image.
corners(K, 2) array: Corner coordinates as (row, col).
mask2D array: Mask defining the local neighborhood of the corner used for the calculation of the central moment.

Returns:

orientations(K, 1) array: Orientations of corners in the range [-pi, pi].

References

[1]

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

[2]

Paul L. Rosin, “Measuring Corner Properties” http://users.cs.cf.ac.uk/Paul.Rosin/corner2.pdf

Examples

>>> from skimage.morphology import octagon
>>> from skimage.feature import (corner_fast, corner_peaks,
...                              corner_orientations)
>>> square = np.zeros((12, 12))
>>> square[3:9, 3:9] = 1
>>> square.astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
>>> corners = corner_peaks(corner_fast(square, 9), min_distance=1)
>>> corners
array([[3, 3],
       [3, 8],
       [8, 3],
       [8, 8]])
>>> orientations = corner_orientations(square, corners, octagon(3, 2))
>>> np.rad2deg(orientations)
array([  45.,  135.,  -45., -135.])

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

Find peaks in corner measure response image.

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

Parameters:

image(M, N) ndarray: Input image.
min_distanceint, optional: The minimal allowed distance separating peaks.
**: See skimage.feature.peak_local_max().
p_normfloat: Which Minkowski p-norm to use. Should be in the range [1, inf]. A finite large p may cause a ValueError if overflow can occur. inf corresponds to the Chebyshev distance and 2 to the Euclidean distance.

Returns:

outputndarray or ndarray of bools

If indices = True : (row, column, …) coordinates of peaks.
If indices = False : Boolean array shaped like image, with peaks represented by True values.

See also

skimage.feature.peak_local_max

Notes

Changed in version 0.18: The default value of threshold_rel has changed to None, which corresponds to letting skimage.feature.peak_local_max decide on the default. This is equivalent to threshold_rel=0.

The num_peaks limit is applied before suppression of connected peaks. To limit the number of peaks after suppression, set num_peaks=np.inf and post-process the output of this function.

Examples

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

Assemble images with simple image stitching

Corner detection

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

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

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

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

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

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

Parameters:

image(M, N) ndarray: Input image.
sigmafloat, optional: Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix.

Returns:

responsendarray: Shi-Tomasi response image.

References

[1]

Examples

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

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

Determine subpixel position of corners.

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

Parameters:

image(M, N) ndarray: Input image.
corners(K, 2) ndarray: Corner coordinates (row, col).
window_sizeint, optional: Search window size for subpixel estimation.
alphafloat, optional: Significance level for corner classification.

Returns:

positions(K, 2) ndarray: Subpixel corner positions. NaN for “not classified” corners.

References

[1]

[2]

Examples

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

http://cvlab.epfl.ch/software/daisy

Corner detection

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

Extract DAISY feature descriptors densely for the given image.

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

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

Histogram bin contribution are smoothed with a circular Gaussian window over the tonal range (the angular range).
The sigma values of the spatial Gaussian smoothing in this code do not match the sigma values in the original code by Tola et al. [2]. In their code, spatial smoothing is applied to both the input image and the center histogram. However, this smoothing is not documented in [1] and, therefore, it is omitted.

Parameters:

image(M, N) array

Input image (grayscale).

stepint, optional

Distance between descriptor sampling points.

radiusint, optional

Radius (in pixels) of the outermost ring.

ringsint, optional

Number of rings.

histogramsint, optional

Number of histograms sampled per ring.

orientationsint, optional

Number of orientations (bins) per histogram.

normalization[ ‘l1’ | ‘l2’ | ‘daisy’ | ‘off’ ], optional

How to normalize the descriptors

‘l1’: L1-normalization of each descriptor.
‘l2’: L2-normalization of each descriptor.
‘daisy’: L2-normalization of individual histograms.
‘off’: Disable normalization.

sigmas1D array of float, optional

Standard deviation of spatial Gaussian smoothing for the center histogram and for each ring of histograms. The array of sigmas should be sorted from the center and out. I.e. the first sigma value defines the spatial smoothing of the center histogram and the last sigma value defines the spatial smoothing of the outermost ring. Specifying sigmas overrides the following parameter.

rings = len(sigmas) - 1

ring_radii1D array of int, optional

Radius (in pixels) for each ring. Specifying ring_radii overrides the following two parameters.

rings = len(ring_radii) radius = ring_radii[-1]

If both sigmas and ring_radii are given, they must satisfy the following predicate since no radius is needed for the center histogram.

len(ring_radii) == len(sigmas) + 1

visualizebool, optional

Generate a visualization of the DAISY descriptors

Returns:

descsarray

Grid of DAISY descriptors for the given image as an array dimensionality (P, Q, R) where

P = ceil((M - radius*2) / step) Q = ceil((N - radius*2) / step) R = (rings * histograms + 1) * orientations

descs_img(M, N, 3) array (only if visualize==True)

Visualization of the DAISY descriptors.

References

[1] (1,2)

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

[2]

Dense DAISY feature description

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

Visualization of Haar-like features.

Parameters:

image(M, N) ndarray

The region of an integral image for which the features need to be computed.

rint

Row-coordinate of top left corner of the detection window.

cint

Column-coordinate of top left corner of the detection window.

widthint

Width of the detection window.

heightint

Height of the detection window.

feature_coordndarray of list of tuples or None, optional

The array of coordinates to be extracted. This is useful when you want to recompute only a subset of features. In this case feature_type needs to be an array containing the type of each feature, as returned by haar_like_feature_coord(). By default, all coordinates are computed.

color_positive_blocktuple of 3 floats

Floats specifying the color for the positive block. Corresponding values define (R, G, B) values. Default value is red (1, 0, 0).

color_negative_blocktuple of 3 floats

Floats specifying the color for the negative block Corresponding values define (R, G, B) values. Default value is blue (0, 1, 0).

alphafloat

Value in the range [0, 1] that specifies opacity of visualization. 1 - fully transparent, 0 - opaque.

max_n_featuresint, default=None

The maximum number of features to be returned. By default, all features are returned.

rng{numpy.random.Generator, int}, optional

Pseudo-random number generator. By default, a PCG64 generator is used (see numpy.random.default_rng()). If rng is an int, it is used to seed the generator.

The rng is used when generating a set of features smaller than the total number of available features.

Returns:

features(M, N), ndarray: An image in which the different features will be added.

Examples

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

       [[0.5, 0. , 0. ],
        [0. , 0.5, 0. ]]])

Haar-like feature descriptor

Face classification using Haar-like feature descriptor

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

Multi-block local binary pattern visualization.

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

Parameters:

imagendarray of float or uint: Image on which to visualize the pattern.
rint: Row-coordinate of top left corner of a rectangle containing feature.
cint: Column-coordinate of top left corner of a rectangle containing feature.
widthint: Width of one of 9 equal rectangles that will be used to compute a feature.
heightint: Height of one of 9 equal rectangles that will be used to compute a feature.
lbp_codeint: The descriptor of feature to visualize. If not provided, the descriptor with 0 value will be used.
color_greater_blocktuple of 3 floats: Floats specifying the color for the block that has greater intensity value. They should be in the range [0, 1]. Corresponding values define (R, G, B) values. Default value is white (1, 1, 1).
color_greater_blocktuple of 3 floats: Floats specifying the color for the block that has greater intensity value. They should be in the range [0, 1]. Corresponding values define (R, G, B) values. Default value is cyan (0, 0.69, 0.96).
alphafloat: Value in the range [0, 1] that specifies opacity of visualization. 1 - fully transparent, 0 - opaque.

Returns:

outputndarray of float: Image with MB-LBP visualization.

References

[1]

L. Zhang, R. Chu, S. Xiang, S. Liao, S.Z. Li. “Face Detection Based on Multi-Block LBP Representation”, In Proceedings: Advances in Biometrics, International Conference, ICB 2007, Seoul, Korea. http://www.cbsr.ia.ac.cn/users/scliao/papers/Zhang-ICB07-MBLBP.pdf DOI:10.1007/978-3-540-74549-5_2

Multi-Block Local Binary Pattern for texture classification

skimage.feature.fisher_vector(descriptors, gmm, *, improved=False, alpha=0.5) [source]

Compute the Fisher vector given some descriptors/vectors, and an associated estimated GMM.

Parameters:

descriptorsnp.ndarray, shape=(n_descriptors, descriptor_length): NumPy array of the descriptors for which the Fisher vector representation is to be computed.
gmmsklearn.mixture.GaussianMixture: An estimated GMM object, which contains the necessary parameters needed to compute the Fisher vector.
improvedbool, default=False: Flag denoting whether to compute improved Fisher vectors or not. Improved Fisher vectors are L2 and power normalized. Power normalization is simply f(z) = sign(z) pow(abs(z), alpha) for some 0 <= alpha <= 1.
alphafloat, default=0.5: The parameter for the power normalization step. Ignored if improved=False.

Returns:

fisher_vectornp.ndarray: The computation Fisher vector, which is given by a concatenation of the gradients of a GMM with respect to its parameters (mixture weights, means, and covariance matrices). For D-dimensional input descriptors or vectors, and a K-mode GMM, the Fisher vector dimensionality will be 2KD + K. Thus, its dimensionality is invariant to the number of descriptors/vectors.

References

[1]

Perronnin, F. and Dance, C. Fisher kernels on Visual Vocabularies for Image Categorization, IEEE Conference on Computer Vision and Pattern Recognition, 2007

[2]

Perronnin, F. and Sanchez, J. and Mensink T. Improving the Fisher Kernel for Large-Scale Image Classification, ECCV, 2010

Examples

>>> from skimage.feature import fisher_vector, learn_gmm
>>> sift_for_images = [np.random.random((10, 128)) for _ in range(10)]
>>> num_modes = 16
>>> # Estimate 16-mode GMM with these synthetic SIFT vectors
>>> gmm = learn_gmm(sift_for_images, n_modes=num_modes)
>>> test_image_descriptors = np.random.random((25, 128))
>>> # Compute the Fisher vector
>>> fv = fisher_vector(test_image_descriptors, gmm)

Fisher vector feature encoding

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

Calculate the gray-level co-occurrence matrix.

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

Changed in version 0.19: greymatrix was renamed to graymatrix in 0.19.

Parameters:

imagearray_like: Integer typed input image. Only positive valued images are supported. If type is other than uint8, the argument levels needs to be set.
distancesarray_like: List of pixel pair distance offsets.
anglesarray_like: List of pixel pair angles in radians.
levelsint, optional: The input image should contain integers in [0, levels-1], where levels indicate the number of gray-levels counted (typically 256 for an 8-bit image). This argument is required for 16-bit images or higher and is typically the maximum of the image. As the output matrix is at least levels x levels, it might be preferable to use binning of the input image rather than large values for levels.
symmetricbool, optional: If True, the output matrix P[:, :, d, theta] is symmetric. This is accomplished by ignoring the order of value pairs, so both (i, j) and (j, i) are accumulated when (i, j) is encountered for a given offset. The default is False.
normedbool, optional: If True, normalize each matrix P[:, :, d, theta] by dividing by the total number of accumulated co-occurrences for the given offset. The elements of the resulting matrix sum to 1. The default is False.

Returns:

P4-D ndarray: The gray-level co-occurrence histogram. The value P[i,j,d,theta] is the number of times that gray-level j occurs at a distance d and at an angle theta from gray-level i. If normed is False, the output is of type uint32, otherwise it is float64. The dimensions are: levels x levels x number of distances x number of angles.

References

[1]

M. Hall-Beyer, 2007. GLCM Texture: A Tutorial https://prism.ucalgary.ca/handle/1880/51900 DOI:10.11575/PRISM/33280

[2]

R.M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification”, IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-3, no. 6, pp. 610-621, Nov. 1973. DOI:10.1109/TSMC.1973.4309314

[3]

M. Nadler and E.P. Smith, Pattern Recognition Engineering, Wiley-Interscience, 1993.

[4]

Wikipedia, https://en.wikipedia.org/wiki/Co-occurrence_matrix

Examples

Compute 4 GLCMs using 1-pixel distance and 4 different angles. For example, an angle of 0 radians refers to the neighboring pixel to the right; pi/4 radians to the top-right diagonal neighbor; pi/2 radians to the pixel above, and so forth.

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

GLCM Texture Features

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

Calculate texture properties of a GLCM.

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

‘contrast’: \(\sum_{i,j=0}^{levels-1} P_{i,j}(i-j)^2\)
‘dissimilarity’: \(\sum_{i,j=0}^{levels-1}P_{i,j}|i-j|\)
‘homogeneity’: \(\sum_{i,j=0}^{levels-1}\frac{P_{i,j}}{1+(i-j)^2}\)
‘ASM’: \(\sum_{i,j=0}^{levels-1} P_{i,j}^2\)
‘energy’: \(\sqrt{ASM}\)
‘correlation’:

\[\sum_{i,j=0}^{levels-1} P_{i,j}\left[\frac{(i-\mu_i) \ (j-\mu_j)}{\sqrt{(\sigma_i^2)(\sigma_j^2)}}\right]\]
‘mean’: \(\sum_{i=0}^{levels-1} i*P_{i}\)
‘variance’: \(\sum_{i=0}^{levels-1} P_{i}*(i-mean)^2\)
‘std’: \(\sqrt{variance}\)
‘entropy’: \(\sum_{i,j=0}^{levels-1} -P_{i,j}*log(P_{i,j})\)

Each GLCM is normalized to have a sum of 1 before the computation of texture properties.

Changed in version 0.19: greycoprops was renamed to graycoprops in 0.19.

Parameters:

Pndarray: Input array. P is the gray-level co-occurrence histogram for which to compute the specified property. The value P[i,j,d,theta] is the number of times that gray-level j occurs at a distance d and at an angle theta from gray-level i.
prop{‘contrast’, ‘dissimilarity’, ‘homogeneity’, ‘energy’, ‘correlation’, ‘ASM’, ‘mean’, ‘variance’, ‘std’, ‘entropy’}, optional: The property of the GLCM to compute. The default is ‘contrast’.

Returns:

results2-D ndarray: 2-dimensional array. results[d, a] is the property ‘prop’ for the d’th distance and the a’th angle.

References

[1]

M. Hall-Beyer, 2007. GLCM Texture: A Tutorial v. 1.0 through 3.0. The GLCM Tutorial Home Page, https://prism.ucalgary.ca/handle/1880/51900 DOI:10.11575/PRISM/33280

Examples

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

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

GLCM Texture Features

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

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

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

Parameters:

int_image(M, N) ndarray

Integral image for which the features need to be computed.

rint

Row-coordinate of top left corner of the detection window.

cint

Column-coordinate of top left corner of the detection window.

widthint

Width of the detection window.

heightint

Height of the detection window.

feature_typestr or list of str or None, optional

The type of feature to consider:

‘type-2-x’: 2 rectangles varying along the x axis;
‘type-2-y’: 2 rectangles varying along the y axis;
‘type-3-x’: 3 rectangles varying along the x axis;
‘type-3-y’: 3 rectangles varying along the y axis;
‘type-4’: 4 rectangles varying along x and y axis.

By default all features are extracted.

If using with feature_coord, it should correspond to the feature type of each associated coordinate feature.

feature_coordndarray of list of tuples or None, optional

Returns:

haar_features(n_features,) ndarray of int or float: Resulting Haar-like features. Each value is equal to the subtraction of sums of the positive and negative rectangles. The data type depends of the data type of int_image: int when the data type of int_image is uint or int and float when the data type of int_image is float.

Notes

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

References

[1]

https://en.wikipedia.org/wiki/Haar-like_feature

[2]

Oren, M., Papageorgiou, C., Sinha, P., Osuna, E., & Poggio, T. (1997, June). Pedestrian detection using wavelet templates. In Computer Vision and Pattern Recognition, 1997. Proceedings., 1997 IEEE Computer Society Conference on (pp. 193-199). IEEE. http://tinyurl.com/y6ulxfta DOI:10.1109/CVPR.1997.609319

[3]

Viola, Paul, and Michael J. Jones. “Robust real-time face detection.” International journal of computer vision 57.2 (2004): 137-154. https://www.merl.com/publications/docs/TR2004-043.pdf DOI:10.1109/CVPR.2001.990517

Examples

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

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

>>> from skimage.feature import haar_like_feature_coord
>>> feature_coord, feature_type = zip(
...     *[haar_like_feature_coord(5, 5, feat_t)
...       for feat_t in ('type-2-x', 'type-3-x')])
>>> # only select one feature over two
>>> feature_coord = np.concatenate([x[::2] for x in feature_coord])
>>> feature_type = np.concatenate([x[::2] for x in feature_type])
>>> feature = haar_like_feature(img_ii, 0, 0, 5, 5,
...                             feature_type=feature_type,
...                             feature_coord=feature_coord)
>>> feature
array([ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1, -3, -5, -2, -4, -1,
       -3, -5, -2, -4, -2, -4, -2, -4, -2, -1, -3, -2, -1, -1, -1, -1, -1])

Face classification using Haar-like feature descriptor

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

Compute the coordinates of Haar-like features.

Parameters:

widthint

Width of the detection window.

heightint

Height of the detection window.

feature_typestr or list of str or None, optional

The type of feature to consider:

‘type-2-x’: 2 rectangles varying along the x axis;
‘type-2-y’: 2 rectangles varying along the y axis;
‘type-3-x’: 3 rectangles varying along the x axis;
‘type-3-y’: 3 rectangles varying along the y axis;
‘type-4’: 4 rectangles varying along x and y axis.

By default all features are extracted.

Returns:

feature_coord(n_features, n_rectangles, 2, 2), ndarray of list of tuple coord: Coordinates of the rectangles for each feature.
feature_type(n_features,), ndarray of str: The corresponding type for each feature.

Examples

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

Haar-like feature descriptor

Face classification using Haar-like feature descriptor

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

Compute the Hessian matrix.

In 2D, the Hessian matrix is defined as:

H = [Hrr Hrc]
    [Hrc Hcc]

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

The implementation here also supports n-dimensional data.

Parameters:

imagendarray: Input image.
sigmafloat: Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix.
mode{‘constant’, ‘reflect’, ‘wrap’, ‘nearest’, ‘mirror’}, optional: How to handle values outside the image borders.
cvalfloat, optional: Used in conjunction with mode ‘constant’, the value outside the image boundaries.
order{‘rc’, ‘xy’}, optional: For 2D images, this parameter allows for the use of reverse or forward order of the image axes in gradient computation. ‘rc’ indicates the use of the first axis initially (Hrr, Hrc, Hcc), whilst ‘xy’ indicates the usage of the last axis initially (Hxx, Hxy, Hyy). Images with higher dimension must always use ‘rc’ order.
use_gaussian_derivativesboolean, optional: Indicates whether the Hessian is computed by convolving with Gaussian derivatives, or by a simple finite-difference operation.

Returns:

H_elemslist of ndarray: Upper-diagonal elements of the hessian matrix for each pixel in the input image. In 2D, this will be a three element list containing [Hrr, Hrc, Hcc]. In nD, the list will contain (n**2 + n) / 2 arrays.

Notes

The distributive property of derivatives and convolutions allows us to restate the derivative of an image, I, smoothed with a Gaussian kernel, G, as the convolution of the image with the derivative of G.

\[\frac{\partial }{\partial x_i}(I * G) = I * \left( \frac{\partial }{\partial x_i} G \right)\]

When use_gaussian_derivatives is True, this property is used to compute the second order derivatives that make up the Hessian matrix.

When use_gaussian_derivatives is False, simple finite differences on a Gaussian-smoothed image are used instead.

Examples

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

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

Compute the approximate Hessian Determinant over an image.

The 2D approximate method uses box filters over integral images to compute the approximate Hessian Determinant.

Parameters:

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

Returns:

outarray: The array of the Determinant of Hessians.

Notes

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

References

[1]

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

skimage.feature.hessian_matrix_eigvals(H_elems) [source]

Compute eigenvalues of Hessian matrix.

Parameters:

H_elemslist of ndarray: The upper-diagonal elements of the Hessian matrix, as returned by hessian_matrix.

Returns:

eigsndarray: The eigenvalues of the Hessian matrix, in decreasing order. The eigenvalues are the leading dimension. That is, eigs[i, j, k] contains the ith-largest eigenvalue at position (j, k).

Examples

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

skimage.feature.hog(image, orientations=9, pixels_per_cell=(8, 8), cells_per_block=(3, 3), block_norm='L2-Hys', visualize=False, transform_sqrt=False, feature_vector=True, *, channel_axis=None) [source]

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

Compute a Histogram of Oriented Gradients (HOG) by

(optional) global image normalization
computing the gradient image in row and col
computing gradient histograms
normalizing across blocks
flattening into a feature vector

Parameters:

image(M, N[, C]) ndarray

Input image.

orientationsint, optional

Number of orientation bins.

pixels_per_cell2-tuple (int, int), optional

Size (in pixels) of a cell.

cells_per_block2-tuple (int, int), optional

Number of cells in each block.

block_normstr {‘L1’, ‘L1-sqrt’, ‘L2’, ‘L2-Hys’}, optional

Block normalization method:

L1: Normalization using L1-norm.
L1-sqrt: Normalization using L1-norm, followed by square root.
L2: Normalization using L2-norm.
L2-Hys: Normalization using L2-norm, followed by limiting the maximum values to 0.2 (Hys stands for hysteresis) and renormalization using L2-norm. (default) For details, see [3], [4].

visualizebool, optional

Also return an image of the HOG. For each cell and orientation bin, the image contains a line segment that is centered at the cell center, is perpendicular to the midpoint of the range of angles spanned by the orientation bin, and has intensity proportional to the corresponding histogram value.

transform_sqrtbool, optional

Apply power law compression to normalize the image before processing. DO NOT use this if the image contains negative values. Also see notes section below.

feature_vectorbool, optional

Return the data as a feature vector by calling .ravel() on the result just before returning.

channel_axisint or None, optional

If None, the image is assumed to be a grayscale (single channel) image. Otherwise, this parameter indicates which axis of the array corresponds to channels.

Added in version 0.19: channel_axis was added in 0.19.

Returns:

out(n_blocks_row, n_blocks_col, n_cells_row, n_cells_col, n_orient) ndarray: HOG descriptor for the image. If feature_vector is True, a 1D (flattened) array is returned.
hog_image(M, N) ndarray, optional: A visualisation of the HOG image. Only provided if visualize is True.

Raises:

ValueError: If the image is too small given the values of pixels_per_cell and cells_per_block.

Notes

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

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

References

[1]

https://en.wikipedia.org/wiki/Histogram_of_oriented_gradients

[2]

Dalal, N and Triggs, B, Histograms of Oriented Gradients for Human Detection, IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2005 San Diego, CA, USA, https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf, DOI:10.1109/CVPR.2005.177

[3]

Lowe, D.G., Distinctive image features from scale-invatiant keypoints, International Journal of Computer Vision (2004) 60: 91, http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf, DOI:10.1023/B:VISI.0000029664.99615.94

[4]

Dalal, N, Finding People in Images and Videos, Human-Computer Interaction [cs.HC], Institut National Polytechnique de Grenoble - INPG, 2006, https://tel.archives-ouvertes.fr/tel-00390303/file/NavneetDalalThesis.pdf

Histogram of Oriented Gradients

skimage.feature.learn_gmm(descriptors, *, n_modes=32, gm_args=None) [source]

Estimate a Gaussian mixture model (GMM) given a set of descriptors and number of modes (i.e. Gaussians). This function is essentially a wrapper around the scikit-learn implementation of GMM, namely the sklearn.mixture.GaussianMixture class.

Due to the nature of the Fisher vector, the only enforced parameter of the underlying scikit-learn class is the covariance_type, which must be ‘diag’.

There is no simple way to know what value to use for n_modes a-priori. Typically, the value is usually one of {16, 32, 64, 128}. One may train a few GMMs and choose the one that maximises the log probability of the GMM, or choose n_modes such that the downstream classifier trained on the resultant Fisher vectors has maximal performance.

Parameters:

descriptorsnp.ndarray (N, M) or list [(N1, M), (N2, M), …]: List of NumPy arrays, or a single NumPy array, of the descriptors used to estimate the GMM. The reason a list of NumPy arrays is permissible is because often when using a Fisher vector encoding, descriptors/vectors are computed separately for each sample/image in the dataset, such as SIFT vectors for each image. If a list if passed in, then each element must be a NumPy array in which the number of rows may differ (e.g. different number of SIFT vector for each image), but the number of columns for each must be the same (i.e. the dimensionality must be the same).
n_modesint: The number of modes/Gaussians to estimate during the GMM estimate.
gm_argsdict: Keyword arguments that can be passed into the underlying scikit-learn sklearn.mixture.GaussianMixture class.

Returns:

gmmsklearn.mixture.GaussianMixture: The estimated GMM object, which contains the necessary parameters needed to compute the Fisher vector.

References

[1]

https://scikit-learn.org/stable/modules/generated/sklearn.mixture.GaussianMixture.html

Examples

>>> from skimage.feature import fisher_vector
>>> rng = np.random.Generator(np.random.PCG64())
>>> sift_for_images = [rng.standard_normal((10, 128)) for _ in range(10)]
>>> num_modes = 16
>>> # Estimate 16-mode GMM with these synthetic SIFT vectors
>>> gmm = learn_gmm(sift_for_images, n_modes=num_modes)

Fisher vector feature encoding

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

Compute the local binary patterns (LBP) of an image.

LBP is a visual descriptor often used in texture classification.

Parameters:

image(M, N) array

2D grayscale image.

Pint

Number of circularly symmetric neighbor set points (quantization of the angular space).

Rfloat

Radius of circle (spatial resolution of the operator).

methodstr {‘default’, ‘ror’, ‘uniform’, ‘nri_uniform’, ‘var’}, optional

Method to determine the pattern:

default: Original local binary pattern which is grayscale invariant but not rotation invariant.
ror: Extension of default pattern which is grayscale invariant and rotation invariant.
uniform: Uniform pattern which is grayscale invariant and rotation invariant, offering finer quantization of the angular space. For details, see [1].
nri_uniform: Variant of uniform pattern which is grayscale invariant but not rotation invariant. For details, see [2] and [3].
var: Variance of local image texture (related to contrast) which is rotation invariant but not grayscale invariant.

Returns:

output(M, N) array: LBP image.

References

[1]

T. Ojala, M. Pietikainen, T. Maenpaa, “Multiresolution gray-scale and rotation invariant texture classification with local binary patterns”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 7, pp. 971-987, July 2002 DOI:10.1109/TPAMI.2002.1017623

[2]

T. Ahonen, A. Hadid and M. Pietikainen. “Face recognition with local binary patterns”, in Proc. Eighth European Conf. Computer Vision, Prague, Czech Republic, May 11-14, 2004, pp. 469-481, 2004. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.6851 DOI:10.1007/978-3-540-24670-1_36

[3]

T. Ahonen, A. Hadid and M. Pietikainen, “Face Description with Local Binary Patterns: Application to Face Recognition”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 12, pp. 2037-2041, Dec. 2006 DOI:10.1109/TPAMI.2006.244

Local Binary Pattern for texture classification

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

Brute-force matching of descriptors.

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

Parameters:

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

Returns:

matches(Q, 2) array: Indices of corresponding matches in first and second set of descriptors, where matches[:, 0] denote the indices in the first and matches[:, 1] the indices in the second set of descriptors.

Fundamental matrix estimation

ORB feature detector and binary descriptor

SIFT feature detector and descriptor extractor

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

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

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

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

Parameters:

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

Returns:

outputarray: Response image with correlation coefficients.

Notes

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

References

[1]

J. P. Lewis, “Fast Normalized Cross-Correlation”, Industrial Light and Magic.

[2]

Briechle and Hanebeck, “Template Matching using Fast Normalized Cross Correlation”, Proceedings of the SPIE (2001). DOI:10.1117/12.421129

Examples

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

Template Matching

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

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

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

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

Parameters:

int_image(N, M) array: Integral image.
rint: Row-coordinate of top left corner of a rectangle containing feature.
cint: Column-coordinate of top left corner of a rectangle containing feature.
widthint: Width of one of the 9 equal rectangles that will be used to compute a feature.
heightint: Height of one of the 9 equal rectangles that will be used to compute a feature.

Returns:

outputint: 8-bit MB-LBP feature descriptor.

References

[1]

Multi-Block Local Binary Pattern for texture classification

skimage.feature.multiscale_basic_features(image, intensity=True, edges=True, texture=True, sigma_min=0.5, sigma_max=16, num_sigma=None, num_workers=None, *, channel_axis=None) [source]

Local features for a single- or multi-channel nd image.

Intensity, gradient intensity and local structure are computed at different scales thanks to Gaussian blurring.

Parameters:

imagendarray: Input image, which can be grayscale or multichannel.
intensitybool, default True: If True, pixel intensities averaged over the different scales are added to the feature set.
edgesbool, default True: If True, intensities of local gradients averaged over the different scales are added to the feature set.
texturebool, default True: If True, eigenvalues of the Hessian matrix after Gaussian blurring at different scales are added to the feature set.
sigma_minfloat, optional: Smallest value of the Gaussian kernel used to average local neighborhoods before extracting features.
sigma_maxfloat, optional: Largest value of the Gaussian kernel used to average local neighborhoods before extracting features.
num_sigmaint, optional: Number of values of the Gaussian kernel between sigma_min and sigma_max. If None, sigma_min multiplied by powers of 2 are used.
num_workersint or None, optional: The number of parallel threads to use. If set to None, the full set of available cores are used.
channel_axisint or None, optional: If None, the image is assumed to be a grayscale (single channel) image. Otherwise, this parameter indicates which axis of the array corresponds to channels.

Added in version 0.19: channel_axis was added in 0.19.

Returns:

featuresnp.ndarray: Array of shape image.shape + (n_features,). When channel_axis is not None, all channels are concatenated along the features dimension. (i.e. n_features == n_features_singlechannel * n_channels)

Trainable segmentation using local features and random forests

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

Find peaks in an image as coordinate list.

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

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

Changed in version 0.18: Prior to version 0.18, peaks of the same height within a radius of min_distance were all returned, but this could cause unexpected behaviour. From 0.18 onwards, an arbitrary peak within the region is returned. See issue gh-2592.

Parameters:

imagendarray: Input image.
min_distanceint, optional: The minimal allowed distance separating peaks. To find the maximum number of peaks, use min_distance=1.
threshold_absfloat or None, optional: Minimum intensity of peaks. By default, the absolute threshold is the minimum intensity of the image.
threshold_relfloat or None, optional: Minimum intensity of peaks, calculated as max(image) * threshold_rel.
exclude_borderint, tuple of ints, or bool, optional: If positive integer, exclude_border excludes peaks from within exclude_border-pixels of the border of the image. If tuple of non-negative ints, the length of the tuple must match the input array’s dimensionality. Each element of the tuple will exclude peaks from within exclude_border-pixels of the border of the image along that dimension. If True, takes the min_distance parameter as value. If zero or False, peaks are identified regardless of their distance from the border.
num_peaksint, optional: Maximum number of peaks. When the number of peaks exceeds num_peaks, return num_peaks peaks based on highest peak intensity.
footprintndarray of bools, optional: If provided, footprint == 1 represents the local region within which to search for peaks at every point in image.
labelsndarray of ints, optional: If provided, each unique region labels == value represents a unique region to search for peaks. Zero is reserved for background.
num_peaks_per_labelint, optional: Maximum number of peaks for each label.
p_normfloat: Which Minkowski p-norm to use. Should be in the range [1, inf]. A finite large p may cause a ValueError if overflow can occur. inf corresponds to the Chebyshev distance and 2 to the Euclidean distance.

Returns:

outputndarray: The coordinates of the peaks.

See also

skimage.feature.corner_peaks

Notes

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

Examples

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

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

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

>>> img2 = np.zeros((20, 20, 20))
>>> img2[10, 10, 10] = 1
>>> img2[15, 15, 15] = 1
>>> peak_idx = peak_local_max(img2, exclude_border=0)
>>> peak_idx
array([[10, 10, 10],
       [15, 15, 15]])

>>> peak_mask = np.zeros_like(img2, dtype=bool)
>>> peak_mask[tuple(peak_idx.T)] = True
>>> np.argwhere(peak_mask)
array([[10, 10, 10],
       [15, 15, 15]])

Finding local maxima

Watershed segmentation

Segment human cells (in mitosis)

skimage.feature.plot_matched_features(image0, image1, *, keypoints0, keypoints1, matches, ax, keypoints_color='k', matches_color=None, only_matches=False, alignment='horizontal') [source]

Plot matched features between two images.

Added in version 0.23.

Parameters:

image0(N, M [, 3]) array: First image.
image1(N, M [, 3]) array: Second image.
keypoints0(K1, 2) array: First keypoint coordinates as (row, col).
keypoints1(K2, 2) array: Second keypoint coordinates as (row, col).
matches(Q, 2) array: Indices of corresponding matches in first and second sets of descriptors, where matches[:, 0] (resp. matches[:, 1]) contains the indices in the first (resp. second) set of descriptors.
axmatplotlib.axes.Axes: The Axes object where the images and their matched features are drawn.
keypoints_colormatplotlib color, optional: Color for keypoint locations.
matches_colormatplotlib color or sequence thereof, optional: Single color or sequence of colors for each line defined by matches, which connect keypoint matches. See [1] for an overview of supported color formats. By default, colors are picked randomly.
only_matchesbool, optional: Set to True to plot matches only and not the keypoint locations.
alignment{‘horizontal’, ‘vertical’}, optional: Whether to show the two images side by side ('horizontal'), or one above the other ('vertical').

Notes

To make a sequence of colors passed to matches_color work for any number of matches, you can wrap that sequence in itertools.cycle().

References

[1]

https://matplotlib.org/stable/users/explain/colors/colors.html#specifying-colors

Fundamental matrix estimation

ORB feature detector and binary descriptor