807 lines
23 KiB
Python
807 lines
23 KiB
Python
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"""
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Sobel and Prewitt filters originally part of CellProfiler, code licensed under
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both GPL and BSD licenses.
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Website: http://www.cellprofiler.org
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Copyright (c) 2003-2009 Massachusetts Institute of Technology
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Copyright (c) 2009-2011 Broad Institute
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All rights reserved.
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Original author: Lee Kamentsky
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"""
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import numpy as np
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from .. import img_as_float
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from .._shared.utils import check_nD
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from scipy import ndimage as ndi
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from scipy.ndimage import convolve, binary_erosion
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from ..restoration.uft import laplacian
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# n-dimensional filter weights
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SOBEL_EDGE = np.array([1, 0, -1])
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SOBEL_SMOOTH = np.array([1, 2, 1]) / 4
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HSOBEL_WEIGHTS = SOBEL_EDGE.reshape((3, 1)) * SOBEL_SMOOTH.reshape((1, 3))
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VSOBEL_WEIGHTS = HSOBEL_WEIGHTS.T
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SCHARR_EDGE = np.array([1, 0, -1])
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SCHARR_SMOOTH = np.array([3, 10, 3]) / 16
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HSCHARR_WEIGHTS = SCHARR_EDGE.reshape((3, 1)) * SCHARR_SMOOTH.reshape((1, 3))
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VSCHARR_WEIGHTS = HSCHARR_WEIGHTS.T
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PREWITT_EDGE = np.array([1, 0, -1])
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PREWITT_SMOOTH = np.full((3,), 1/3)
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HPREWITT_WEIGHTS = (PREWITT_EDGE.reshape((3, 1))
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* PREWITT_SMOOTH.reshape((1, 3)))
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VPREWITT_WEIGHTS = HPREWITT_WEIGHTS.T
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# 2D-only filter weights
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ROBERTS_PD_WEIGHTS = np.array([[1, 0],
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[0, -1]], dtype=np.double)
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ROBERTS_ND_WEIGHTS = np.array([[0, 1],
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[-1, 0]], dtype=np.double)
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# These filter weights can be found in Farid & Simoncelli (2004),
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# Table 1 (3rd and 4th row). Additional decimal places were computed
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# using the code found at https://www.cs.dartmouth.edu/farid/
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p = np.array([[0.0376593171958126, 0.249153396177344, 0.426374573253687,
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0.249153396177344, 0.0376593171958126]])
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d1 = np.array([[0.109603762960254, 0.276690988455557, 0, -0.276690988455557,
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-0.109603762960254]])
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HFARID_WEIGHTS = d1.T * p
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VFARID_WEIGHTS = np.copy(HFARID_WEIGHTS.T)
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def _mask_filter_result(result, mask):
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"""Return result after masking.
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Input masks are eroded so that mask areas in the original image don't
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affect values in the result.
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"""
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if mask is not None:
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erosion_selem = ndi.generate_binary_structure(mask.ndim, mask.ndim)
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mask = binary_erosion(mask, erosion_selem, border_value=0)
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result *= mask
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return result
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def _kernel_shape(ndim, dim):
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"""Return list of `ndim` 1s except at position `dim`, where value is -1.
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Parameters
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----------
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ndim : int
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The number of dimensions of the kernel shape.
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dim : int
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The axis of the kernel to expand to shape -1.
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Returns
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-------
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shape : list of int
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The requested shape.
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Examples
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--------
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>>> _kernel_shape(2, 0)
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[-1, 1]
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>>> _kernel_shape(3, 1)
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[1, -1, 1]
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>>> _kernel_shape(4, -1)
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[1, 1, 1, -1]
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"""
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shape = [1, ] * ndim
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shape[dim] = -1
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return shape
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def _reshape_nd(arr, ndim, dim):
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"""Reshape a 1D array to have n dimensions, all singletons but one.
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Parameters
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----------
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arr : array, shape (N,)
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Input array
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ndim : int
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Number of desired dimensions of reshaped array.
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dim : int
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Which dimension/axis will not be singleton-sized.
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Returns
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-------
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arr_reshaped : array, shape ([1, ...], N, [1,...])
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View of `arr` reshaped to the desired shape.
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Examples
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--------
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>>> arr = np.random.random(7)
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>>> _reshape_nd(arr, 2, 0).shape
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(7, 1)
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>>> _reshape_nd(arr, 3, 1).shape
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(1, 7, 1)
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>>> _reshape_nd(arr, 4, -1).shape
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(1, 1, 1, 7)
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"""
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kernel_shape = _kernel_shape(ndim, dim)
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return np.reshape(arr, kernel_shape)
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def _generic_edge_filter(image, *, smooth_weights, edge_weights=[1, 0, -1],
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axis=None, mode='reflect', cval=0.0, mask=None):
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"""Apply a generic, n-dimensional edge filter.
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The filter is computed by applying the edge weights along one dimension
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and the smoothing weights along all other dimensions. If no axis is given,
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or a tuple of axes is given the filter is computed along all axes in turn,
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and the magnitude is computed as the square root of the average square
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magnitude of all the axes.
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Parameters
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----------
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image : array
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The input image.
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smooth_weights : array of float
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The smoothing weights for the filter. These are applied to dimensions
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orthogonal to the edge axis.
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edge_weights : 1D array of float, optional
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The weights to compute the edge along the chosen axes.
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axis : int or sequence of int, optional
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Compute the edge filter along this axis. If not provided, the edge
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magnitude is computed. This is defined as::
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edge_mag = np.sqrt(sum([_generic_edge_filter(image, ..., axis=i)**2
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for i in range(image.ndim)]) / image.ndim)
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The magnitude is also computed if axis is a sequence.
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mode : str or sequence of str, optional
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The boundary mode for the convolution. See `scipy.ndimage.convolve`
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for a description of the modes. This can be either a single boundary
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mode or one boundary mode per axis.
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cval : float, optional
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When `mode` is ``'constant'``, this is the constant used in values
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outside the boundary of the image data.
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"""
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ndim = image.ndim
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if axis is None:
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axes = list(range(ndim))
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elif np.isscalar(axis):
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axes = [axis]
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else:
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axes = axis
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return_magnitude = (len(axes) > 1)
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output = np.zeros(image.shape, dtype=float)
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for edge_dim in axes:
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kernel = _reshape_nd(edge_weights, ndim, edge_dim)
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smooth_axes = list(set(range(ndim)) - {edge_dim})
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for smooth_dim in smooth_axes:
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kernel = kernel * _reshape_nd(smooth_weights, ndim, smooth_dim)
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ax_output = ndi.convolve(image, kernel, mode=mode)
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if return_magnitude:
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ax_output *= ax_output
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output += ax_output
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if return_magnitude:
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output = np.sqrt(output) / np.sqrt(ndim)
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return output
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def sobel(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
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"""Find edges in an image using the Sobel filter.
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Parameters
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----------
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image : array
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The input image.
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mask : array of bool, optional
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Clip the output image to this mask. (Values where mask=0 will be set
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to 0.)
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axis : int or sequence of int, optional
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Compute the edge filter along this axis. If not provided, the edge
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magnitude is computed. This is defined as::
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sobel_mag = np.sqrt(sum([sobel(image, axis=i)**2
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for i in range(image.ndim)]) / image.ndim)
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The magnitude is also computed if axis is a sequence.
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mode : str or sequence of str, optional
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The boundary mode for the convolution. See `scipy.ndimage.convolve`
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for a description of the modes. This can be either a single boundary
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mode or one boundary mode per axis.
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cval : float, optional
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When `mode` is ``'constant'``, this is the constant used in values
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outside the boundary of the image data.
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Returns
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-------
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output : array of float
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The Sobel edge map.
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See also
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--------
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scharr, prewitt, canny
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References
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----------
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.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
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Optimization of Kernel Based Image Derivatives.
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.. [2] https://en.wikipedia.org/wiki/Sobel_operator
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Examples
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--------
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>>> from skimage import data
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>>> from skimage import filters
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>>> camera = data.camera()
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>>> edges = filters.sobel(camera)
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"""
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image = img_as_float(image)
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output = _generic_edge_filter(image, smooth_weights=SOBEL_SMOOTH,
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axis=axis, mode=mode, cval=cval)
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output = _mask_filter_result(output, mask)
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return output
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def sobel_h(image, mask=None):
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"""Find the horizontal edges of an image using the Sobel transform.
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Parameters
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----------
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image : 2-D array
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Image to process.
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mask : 2-D array, optional
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An optional mask to limit the application to a certain area.
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Note that pixels surrounding masked regions are also masked to
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prevent masked regions from affecting the result.
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Returns
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-------
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output : 2-D array
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The Sobel edge map.
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Notes
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-----
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We use the following kernel::
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1 2 1
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0 0 0
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-1 -2 -1
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"""
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check_nD(image, 2)
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return sobel(image, mask=mask, axis=0)
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def sobel_v(image, mask=None):
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"""Find the vertical edges of an image using the Sobel transform.
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Parameters
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----------
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image : 2-D array
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Image to process.
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mask : 2-D array, optional
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An optional mask to limit the application to a certain area.
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Note that pixels surrounding masked regions are also masked to
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prevent masked regions from affecting the result.
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Returns
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-------
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output : 2-D array
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The Sobel edge map.
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Notes
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-----
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We use the following kernel::
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1 0 -1
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2 0 -2
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1 0 -1
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"""
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check_nD(image, 2)
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return sobel(image, mask=mask, axis=1)
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def scharr(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
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"""Find the edge magnitude using the Scharr transform.
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Parameters
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----------
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image : array
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The input image.
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mask : array of bool, optional
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Clip the output image to this mask. (Values where mask=0 will be set
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to 0.)
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axis : int or sequence of int, optional
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Compute the edge filter along this axis. If not provided, the edge
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magnitude is computed. This is defined as::
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sch_mag = np.sqrt(sum([scharr(image, axis=i)**2
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for i in range(image.ndim)]) / image.ndim)
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The magnitude is also computed if axis is a sequence.
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mode : str or sequence of str, optional
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The boundary mode for the convolution. See `scipy.ndimage.convolve`
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for a description of the modes. This can be either a single boundary
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mode or one boundary mode per axis.
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cval : float, optional
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When `mode` is ``'constant'``, this is the constant used in values
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outside the boundary of the image data.
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Returns
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-------
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output : array of float
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The Scharr edge map.
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See also
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--------
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sobel, prewitt, canny
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Notes
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-----
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The Scharr operator has a better rotation invariance than
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other edge filters such as the Sobel or the Prewitt operators.
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References
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----------
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.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
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Optimization of Kernel Based Image Derivatives.
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.. [2] https://en.wikipedia.org/wiki/Sobel_operator#Alternative_operators
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Examples
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--------
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>>> from skimage import data
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>>> from skimage import filters
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>>> camera = data.camera()
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>>> edges = filters.scharr(camera)
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"""
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image = img_as_float(image)
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output = _generic_edge_filter(image, smooth_weights=SCHARR_SMOOTH,
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axis=axis, mode=mode, cval=cval)
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output = _mask_filter_result(output, mask)
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return output
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def scharr_h(image, mask=None):
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"""Find the horizontal edges of an image using the Scharr transform.
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Parameters
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----------
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image : 2-D array
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Image to process.
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mask : 2-D array, optional
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An optional mask to limit the application to a certain area.
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Note that pixels surrounding masked regions are also masked to
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prevent masked regions from affecting the result.
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Returns
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-------
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output : 2-D array
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The Scharr edge map.
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Notes
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-----
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We use the following kernel::
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3 10 3
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0 0 0
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-3 -10 -3
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References
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----------
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.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
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Optimization of Kernel Based Image Derivatives.
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"""
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check_nD(image, 2)
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return scharr(image, mask=mask, axis=0)
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def scharr_v(image, mask=None):
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"""Find the vertical edges of an image using the Scharr transform.
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Parameters
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----------
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image : 2-D array
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Image to process
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mask : 2-D array, optional
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An optional mask to limit the application to a certain area.
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Note that pixels surrounding masked regions are also masked to
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prevent masked regions from affecting the result.
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Returns
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-------
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output : 2-D array
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The Scharr edge map.
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Notes
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-----
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We use the following kernel::
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3 0 -3
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10 0 -10
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3 0 -3
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References
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----------
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.. [1] D. Kroon, 2009, Short Paper University Twente, Numerical
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Optimization of Kernel Based Image Derivatives.
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"""
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check_nD(image, 2)
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return scharr(image, mask=mask, axis=1)
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def prewitt(image, mask=None, *, axis=None, mode='reflect', cval=0.0):
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"""Find the edge magnitude using the Prewitt transform.
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Parameters
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----------
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image : array
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The input image.
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mask : array of bool, optional
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Clip the output image to this mask. (Values where mask=0 will be set
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to 0.)
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axis : int or sequence of int, optional
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Compute the edge filter along this axis. If not provided, the edge
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magnitude is computed. This is defined as::
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prw_mag = np.sqrt(sum([prewitt(image, axis=i)**2
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for i in range(image.ndim)]) / image.ndim)
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The magnitude is also computed if axis is a sequence.
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mode : str or sequence of str, optional
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The boundary mode for the convolution. See `scipy.ndimage.convolve`
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for a description of the modes. This can be either a single boundary
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||
|
mode or one boundary mode per axis.
|
||
|
cval : float, optional
|
||
|
When `mode` is ``'constant'``, this is the constant used in values
|
||
|
outside the boundary of the image data.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : array of float
|
||
|
The Prewitt edge map.
|
||
|
|
||
|
See also
|
||
|
--------
|
||
|
sobel, scharr
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
The edge magnitude depends slightly on edge directions, since the
|
||
|
approximation of the gradient operator by the Prewitt operator is not
|
||
|
completely rotation invariant. For a better rotation invariance, the Scharr
|
||
|
operator should be used. The Sobel operator has a better rotation
|
||
|
invariance than the Prewitt operator, but a worse rotation invariance than
|
||
|
the Scharr operator.
|
||
|
|
||
|
Examples
|
||
|
--------
|
||
|
>>> from skimage import data
|
||
|
>>> from skimage import filters
|
||
|
>>> camera = data.camera()
|
||
|
>>> edges = filters.prewitt(camera)
|
||
|
"""
|
||
|
image = img_as_float(image)
|
||
|
output = _generic_edge_filter(image, smooth_weights=PREWITT_SMOOTH,
|
||
|
axis=axis, mode=mode, cval=cval)
|
||
|
output = _mask_filter_result(output, mask)
|
||
|
return output
|
||
|
|
||
|
|
||
|
def prewitt_h(image, mask=None):
|
||
|
"""Find the horizontal edges of an image using the Prewitt transform.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Prewitt edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
We use the following kernel::
|
||
|
|
||
|
1/3 1/3 1/3
|
||
|
0 0 0
|
||
|
-1/3 -1/3 -1/3
|
||
|
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
return prewitt(image, mask=mask, axis=0)
|
||
|
|
||
|
|
||
|
def prewitt_v(image, mask=None):
|
||
|
"""Find the vertical edges of an image using the Prewitt transform.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Prewitt edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
We use the following kernel::
|
||
|
|
||
|
1/3 0 -1/3
|
||
|
1/3 0 -1/3
|
||
|
1/3 0 -1/3
|
||
|
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
return prewitt(image, mask=mask, axis=1)
|
||
|
|
||
|
|
||
|
def roberts(image, mask=None):
|
||
|
"""Find the edge magnitude using Roberts' cross operator.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Roberts' Cross edge map.
|
||
|
|
||
|
See also
|
||
|
--------
|
||
|
sobel, scharr, prewitt, feature.canny
|
||
|
|
||
|
Examples
|
||
|
--------
|
||
|
>>> from skimage import data
|
||
|
>>> camera = data.camera()
|
||
|
>>> from skimage import filters
|
||
|
>>> edges = filters.roberts(camera)
|
||
|
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
out = np.sqrt(roberts_pos_diag(image, mask) ** 2 +
|
||
|
roberts_neg_diag(image, mask) ** 2)
|
||
|
out /= np.sqrt(2)
|
||
|
return out
|
||
|
|
||
|
|
||
|
def roberts_pos_diag(image, mask=None):
|
||
|
"""Find the cross edges of an image using Roberts' cross operator.
|
||
|
|
||
|
The kernel is applied to the input image to produce separate measurements
|
||
|
of the gradient component one orientation.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Robert's edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
We use the following kernel::
|
||
|
|
||
|
1 0
|
||
|
0 -1
|
||
|
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
image = img_as_float(image)
|
||
|
result = convolve(image, ROBERTS_PD_WEIGHTS)
|
||
|
return _mask_filter_result(result, mask)
|
||
|
|
||
|
|
||
|
def roberts_neg_diag(image, mask=None):
|
||
|
"""Find the cross edges of an image using the Roberts' Cross operator.
|
||
|
|
||
|
The kernel is applied to the input image to produce separate measurements
|
||
|
of the gradient component one orientation.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Robert's edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
We use the following kernel::
|
||
|
|
||
|
0 1
|
||
|
-1 0
|
||
|
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
image = img_as_float(image)
|
||
|
result = convolve(image, ROBERTS_ND_WEIGHTS)
|
||
|
return _mask_filter_result(result, mask)
|
||
|
|
||
|
|
||
|
def laplace(image, ksize=3, mask=None):
|
||
|
"""Find the edges of an image using the Laplace operator.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : ndarray
|
||
|
Image to process.
|
||
|
ksize : int, optional
|
||
|
Define the size of the discrete Laplacian operator such that it
|
||
|
will have a size of (ksize,) * image.ndim.
|
||
|
mask : ndarray, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : ndarray
|
||
|
The Laplace edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
The Laplacian operator is generated using the function
|
||
|
skimage.restoration.uft.laplacian().
|
||
|
|
||
|
"""
|
||
|
image = img_as_float(image)
|
||
|
# Create the discrete Laplacian operator - We keep only the real part of
|
||
|
# the filter
|
||
|
_, laplace_op = laplacian(image.ndim, (ksize,) * image.ndim)
|
||
|
result = convolve(image, laplace_op)
|
||
|
return _mask_filter_result(result, mask)
|
||
|
|
||
|
|
||
|
def farid(image, *, mask=None):
|
||
|
"""Find the edge magnitude using the Farid transform.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Farid edge map.
|
||
|
|
||
|
See also
|
||
|
--------
|
||
|
sobel, prewitt, canny
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
Take the square root of the sum of the squares of the horizontal and
|
||
|
vertical derivatives to get a magnitude that is somewhat insensitive to
|
||
|
direction. Similar to the Scharr operator, this operator is designed with
|
||
|
a rotation invariance constraint.
|
||
|
|
||
|
References
|
||
|
----------
|
||
|
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
|
||
|
multidimensional signals", IEEE Transactions on Image Processing
|
||
|
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
|
||
|
.. [2] Wikipedia, "Farid and Simoncelli Derivatives." Available at:
|
||
|
<https://en.wikipedia.org/wiki/Image_derivatives#Farid_and_Simoncelli_Derivatives>
|
||
|
|
||
|
Examples
|
||
|
--------
|
||
|
>>> from skimage import data
|
||
|
>>> camera = data.camera()
|
||
|
>>> from skimage import filters
|
||
|
>>> edges = filters.farid(camera)
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
out = np.sqrt(farid_h(image, mask=mask) ** 2
|
||
|
+ farid_v(image, mask=mask) ** 2)
|
||
|
out /= np.sqrt(2)
|
||
|
return out
|
||
|
|
||
|
|
||
|
def farid_h(image, *, mask=None):
|
||
|
"""Find the horizontal edges of an image using the Farid transform.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Farid edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
The kernel was constructed using the 5-tap weights from [1].
|
||
|
|
||
|
References
|
||
|
----------
|
||
|
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
|
||
|
multidimensional signals", IEEE Transactions on Image Processing
|
||
|
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
|
||
|
.. [2] Farid, H. and Simoncelli, E. P. "Optimally rotation-equivariant
|
||
|
directional derivative kernels", In: 7th International Conference on
|
||
|
Computer Analysis of Images and Patterns, Kiel, Germany. Sep, 1997.
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
image = img_as_float(image)
|
||
|
result = convolve(image, HFARID_WEIGHTS)
|
||
|
return _mask_filter_result(result, mask)
|
||
|
|
||
|
|
||
|
def farid_v(image, *, mask=None):
|
||
|
"""Find the vertical edges of an image using the Farid transform.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
image : 2-D array
|
||
|
Image to process.
|
||
|
mask : 2-D array, optional
|
||
|
An optional mask to limit the application to a certain area.
|
||
|
Note that pixels surrounding masked regions are also masked to
|
||
|
prevent masked regions from affecting the result.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
output : 2-D array
|
||
|
The Farid edge map.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
The kernel was constructed using the 5-tap weights from [1].
|
||
|
|
||
|
References
|
||
|
----------
|
||
|
.. [1] Farid, H. and Simoncelli, E. P., "Differentiation of discrete
|
||
|
multidimensional signals", IEEE Transactions on Image Processing
|
||
|
13(4): 496-508, 2004. :DOI:`10.1109/TIP.2004.823819`
|
||
|
"""
|
||
|
check_nD(image, 2)
|
||
|
image = img_as_float(image)
|
||
|
result = convolve(image, VFARID_WEIGHTS)
|
||
|
return _mask_filter_result(result, mask)
|