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Use separated Gaussian/gradient filters as Hessian

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Juan Nunez-Iglesias
2016-07-16 18:38:00 -05:00
parent 418de7e4f0
commit 48d0973ab3
1 changed files with 11 additions and 26 deletions
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skimage/feature/corner.py
+11 -26
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@@ -136,41 +136,26 @@ def hessian_matrix(image, sigma=1, mode='constant', cval=0):
--------
>>> from skimage.feature import hessian_matrix
>>> square = np.zeros((5, 5))
>>> square[2, 2] = -1.0 / 1591.54943092
>>> square[2, 2] = 4
>>> Hxx, Hxy, Hyy = hessian_matrix(square, sigma=0.1)
>>> Hxx
>>> Hxy
array([[ 0., 0., 0., 0., 0.],
[ 0., 1., 0., -1., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., -1., 0., 1., 0.],
[ 0., 0., 0., 0., 0.]])
"""
image = _prepare_grayscale_input_2D(image)
# Window extent which covers > 99% of the normal distribution.
window_ext = max(1, np.ceil(3 * sigma))
gaussian_filtered = ndi.gaussian_filter(image, sigma=sigma,
mode=mode, cval=cval)
ky, kx = np.mgrid[-window_ext:window_ext + 1, -window_ext:window_ext + 1]
# Second derivative Gaussian kernels.
gaussian_exp = np.exp(-(kx ** 2 + ky ** 2) / (2 * sigma ** 2))
kernel_xx = 1 / (2 * np.pi * sigma ** 4) * (kx ** 2 / sigma ** 2 - 1)
kernel_xx *= gaussian_exp
kernel_xy = 1 / (2 * np.pi * sigma ** 6) * (kx * ky)
kernel_xy *= gaussian_exp
kernel_yy = kernel_xx.transpose()
# Remove small kernel values.
eps = np.finfo(kernel_xx.dtype).eps
kernel_xx[np.abs(kernel_xx) < eps * np.abs(kernel_xx).max()] = 0
kernel_xy[np.abs(kernel_xy) < eps * np.abs(kernel_xy).max()] = 0
kernel_yy[np.abs(kernel_yy) < eps * np.abs(kernel_yy).max()] = 0
Hxx = ndi.convolve(image, kernel_xx, mode=mode, cval=cval)
Hxy = ndi.convolve(image, kernel_xy, mode=mode, cval=cval)
Hyy = ndi.convolve(image, kernel_yy, mode=mode, cval=cval)
dy = np.gradient(gaussian_filtered, axis=0)
dx = np.gradient(gaussian_filtered, axis=1)
Hxx = np.gradient(dx, axis=1)
Hxy = np.gradient(dx, axis=0)
Hyy = np.gradient(dy, axis=0)
return Hxx, Hxy, Hyy