hessian-matrix

hessian_matrix

skimage.feature.hessian_matrix(image, sigma=1, mode='constant', cval=0) [source]

Compute Hessian matrix.

The Hessian matrix is defined as:

H = [Hxx Hxy]
    [Hxy Hyy]

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

Parameters:	image : ndarray Input image. sigma : float 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. cval : float, optional Used in conjunction with mode ‘constant’, the value outside the image boundaries.
Returns:	Hxx : ndarray Element of the Hessian matrix for each pixel in the input image. Hxy : ndarray Element of the Hessian matrix for each pixel in the input image. Hyy : ndarray Element of the Hessian matrix for each pixel in the input image.

Examples

>>> from skimage.feature import hessian_matrix
>>> square = np.zeros((5, 5))
>>> square[2, 2] = -1.0 / 1591.54943092
>>> Hxx, Hxy, Hyy = hessian_matrix(square, sigma=0.1)
>>> Hxx
array([[ 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.]])