mirror of
https://github.com/wassname/scikit-image.git
synced 2026-07-02 09:04:31 +08:00
Make structure tensor function public and add function to compute hessian matrix
This commit is contained in:
Johannes Schönberger
@@ -4,7 +4,8 @@ from .texture import greycomatrix, greycoprops, local_binary_pattern
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from .peak import peak_local_max
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from .corner import (corner_kitchen_rosenfeld, corner_harris,
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corner_shi_tomasi, corner_foerstner, corner_subpix,
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corner_peaks, corner_fast)
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corner_peaks, corner_fast, structure_tensor,
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hessian_matrix)
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from .corner_cy import corner_moravec, corner_orientations
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from .template import match_template
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from ._brief import brief, match_keypoints_brief
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@@ -2,7 +2,7 @@ import numpy as np
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from scipy.ndimage.filters import maximum_filter, minimum_filter, convolve
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from skimage.transform import integral_image
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from skimage.feature.corner import _compute_auto_correlation
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from skimage.feature import structure_tensor
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from skimage.util import img_as_float
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from skimage.morphology import octagon, star
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from skimage.feature.util import _mask_border_keypoints
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@@ -104,7 +104,7 @@ def _star_filter_kernel(m, n):
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def _suppress_lines(feature_mask, image, sigma, line_threshold):
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Axx, Axy, Ayy = _compute_auto_correlation(image, sigma)
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Axx, Axy, Ayy = structure_tensor(image, sigma)
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feature_mask[(Axx + Ayy) * (Axx + Ayy)
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> line_threshold * (Axx * Ayy - Axy * Axy)] = False
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+108
-26
@@ -8,13 +8,18 @@ from skimage.feature import peak_local_max
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from corner_cy import _corner_fast
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def _compute_derivatives(image):
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def _compute_derivatives(image, mode='constant', cval=0):
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"""Compute derivatives in x and y direction using the Sobel operator.
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Parameters
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----------
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image : ndarray
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Input image.
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mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional
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How to handle values outside the image borders.
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cval : float, optional
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Used in conjunction with mode 'constant', the value outside
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the image boundaries.
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Returns
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-------
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@@ -25,14 +30,71 @@ def _compute_derivatives(image):
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"""
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imy = ndimage.sobel(image, axis=0, mode='constant', cval=0)
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imx = ndimage.sobel(image, axis=1, mode='constant', cval=0)
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imy = ndimage.sobel(image, axis=0, mode=mode, cval=cval)
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imx = ndimage.sobel(image, axis=1, mode=mode, cval=cval)
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return imx, imy
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def _compute_auto_correlation(image, sigma):
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"""Compute auto-correlation matrix using sum of squared differences.
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def structure_tensor(image, sigma=1, mode='constant', cval=0):
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"""Compute structure tensor using sum of squared differences.
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The structure tensor A is defined as::
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A = [Axx Axy]
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[Axy Ayy]
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which is approximated by the weighted sum of squared differences in a local
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window around each pixel in the image.
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Parameters
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----------
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image : ndarray
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Input image.
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sigma : float
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Standard deviation used for the Gaussian kernel, which is used as a
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weighting function for the local summation of squared differences.
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mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional
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How to handle values outside the image borders.
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cval : float, optional
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Used in conjunction with mode 'constant', the value outside
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the image boundaries.
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Returns
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-------
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Axx : ndarray
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Element of the structure tensor for each pixel in the input image.
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Axy : ndarray
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Element of the structure tensor for each pixel in the input image.
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Ayy : ndarray
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Element of the structure tensor for each pixel in the input image.
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"""
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image = np.squeeze(image)
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if image.ndim != 2:
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raise ValueError("Only 2-D gray-scale images supported.")
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imx, imy = _compute_derivatives(image, mode=mode, cval=cval)
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# structure tensore
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Axx = ndimage.gaussian_filter(imx * imx, sigma, mode=mode, cval=cval)
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Axy = ndimage.gaussian_filter(imx * imy, sigma, mode=mode, cval=cval)
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Ayy = ndimage.gaussian_filter(imy * imy, sigma, mode=mode, cval=cval)
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return Axx, Axy, Ayy
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def hessian_matrix(image, sigma=1, mode='constant', cval=0):
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"""Compute Hessian matrix.
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The Hessian matrix is defined as::
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H = [Hxx Hxy]
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[Hxy Hyy]
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which is computed by convolving the image with the second derivatives
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of the Gaussian kernel in the respective x- and y-directions.
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Parameters
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----------
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@@ -41,15 +103,20 @@ def _compute_auto_correlation(image, sigma):
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sigma : float
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Standard deviation used for the Gaussian kernel, which is used as
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weighting function for the auto-correlation matrix.
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mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional
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How to handle values outside the image borders.
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cval : float, optional
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Used in conjunction with mode 'constant', the value outside
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the image boundaries.
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Returns
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-------
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Axx : ndarray
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Element of the auto-correlation matrix for each pixel in input image.
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Axy : ndarray
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Element of the auto-correlation matrix for each pixel in input image.
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Ayy : ndarray
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Element of the auto-correlation matrix for each pixel in input image.
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Hxx : ndarray
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Element of the Hessian matrix for each pixel in the input image.
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Hxy : ndarray
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Element of the Hessian matrix for each pixel in the input image.
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Hyy : ndarray
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Element of the Hessian matrix for each pixel in the input image.
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"""
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@@ -57,17 +124,28 @@ def _compute_auto_correlation(image, sigma):
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if image.ndim != 2:
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raise ValueError("Only 2-D gray-scale images supported.")
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imx, imy = _compute_derivatives(image)
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# window extent to the left and right, which covers > 99% of the normal
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# distribution
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window_ext = np.ceil(3 * sigma)
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# structure tensore
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Axx = ndimage.gaussian_filter(imx * imx, sigma, mode='constant', cval=0)
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Axy = ndimage.gaussian_filter(imx * imy, sigma, mode='constant', cval=0)
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Ayy = ndimage.gaussian_filter(imy * imy, sigma, mode='constant', cval=0)
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ky, kx = np.mgrid[-window_ext:window_ext + 1, -window_ext:window_ext + 1]
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return Axx, Axy, Ayy
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# second derivative Gaussian kernels
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gaussian_exp = np.exp(-(kx ** 2 + ky ** 2) / (2 * sigma ** 2))
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kernel_xx = 1 / (2 * np.pi * sigma ** 4) * (kx ** 2 / sigma ** 2 - 1)
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kernel_xx *= gaussian_exp
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kernel_xy = 1 / (2 * np.pi * sigma ** 6) * (kx * ky)
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kernel_xy *= gaussian_exp
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kernel_yy = kernel_xx.transpose()
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Hxx = ndimage.convolve(image, kernel_xx, mode=mode, cval=cval)
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Hxy = ndimage.convolve(image, kernel_xy, mode=mode, cval=cval)
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Hyy = ndimage.convolve(image, kernel_yy, mode=mode, cval=cval)
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return Hxx, Hxy, Hyy
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def corner_kitchen_rosenfeld(image):
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def corner_kitchen_rosenfeld(image, mode='constant', cval=0):
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"""Compute Kitchen and Rosenfeld corner measure response image.
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The corner measure is calculated as follows::
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@@ -82,6 +160,11 @@ def corner_kitchen_rosenfeld(image):
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----------
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image : ndarray
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Input image.
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mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional
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How to handle values outside the image borders.
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cval : float, optional
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Used in conjunction with mode 'constant', the value outside
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the image boundaries.
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Returns
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-------
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@@ -90,9 +173,9 @@ def corner_kitchen_rosenfeld(image):
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"""
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imx, imy = _compute_derivatives(image)
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imxx, imxy = _compute_derivatives(imx)
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imyx, imyy = _compute_derivatives(imy)
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imx, imy = _compute_derivatives(image, mode=mode, cval=cval)
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imxx, imxy = _compute_derivatives(imx, mode=mode, cval=cval)
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imyx, imyy = _compute_derivatives(imy, mode=mode, cval=cval)
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numerator = (imxx * imy**2 + imyy * imx**2 - 2 * imxy * imx * imy)
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denominator = (imx**2 + imy**2)
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@@ -171,7 +254,7 @@ def corner_harris(image, method='k', k=0.05, eps=1e-6, sigma=1):
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"""
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Axx, Axy, Ayy = _compute_auto_correlation(image, sigma)
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Axx, Axy, Ayy = structure_tensor(image, sigma)
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# determinant
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detA = Axx * Ayy - Axy**2
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@@ -241,7 +324,7 @@ def corner_shi_tomasi(image, sigma=1):
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"""
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Axx, Axy, Ayy = _compute_auto_correlation(image, sigma)
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Axx, Axy, Ayy = structure_tensor(image, sigma)
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# minimum eigenvalue of A
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response = ((Axx + Ayy) - np.sqrt((Axx - Ayy)**2 + 4 * Axy**2)) / 2
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@@ -311,7 +394,7 @@ def corner_foerstner(image, sigma=1):
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"""
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Axx, Axy, Ayy = _compute_auto_correlation(image, sigma)
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Axx, Axy, Ayy = structure_tensor(image, sigma)
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# determinant
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detA = Axx * Ayy - Axy**2
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@@ -330,7 +413,6 @@ def corner_foerstner(image, sigma=1):
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def corner_fast(image, n=12, threshold=0.15):
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"""Extract FAST corners for a given image.
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Parameters
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@@ -478,7 +560,7 @@ def corner_subpix(image, corners, window_size=11, alpha=0.99):
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maxx = x0 + wext + 2
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window = image[miny:maxy, minx:maxx]
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winx, winy = _compute_derivatives(window)
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winx, winy = _compute_derivatives(window, mode='constant', cval=0)
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# compute gradient suares and remove border
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winx_winx = (winx * winx)[1:-1, 1:-1]
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