""" Sobel and Prewitt filters originally part of CellProfiler, code licensed under both GPL and BSD licenses. Website: http://www.cellprofiler.org Copyright (c) 2003-2009 Massachusetts Institute of Technology Copyright (c) 2009-2011 Broad Institute All rights reserved. Original author: Lee Kamentsky """ import numpy as np from .. import img_as_float from .._shared.utils import check_nD from scipy import ndimage as ndi from scipy.ndimage import convolve, binary_erosion from ..restoration.uft import laplacian # n-dimensional filter weights SOBEL_EDGE = np.array([1, 0, -1]) SOBEL_SMOOTH = np.array([1, 2, 1]) / 4 HSOBEL_WEIGHTS = SOBEL_EDGE.reshape((3, 1)) * SOBEL_SMOOTH.reshape((1, 3)) VSOBEL_WEIGHTS = HSOBEL_WEIGHTS.T SCHARR_EDGE = np.array([1, 0, -1]) SCHARR_SMOOTH = np.array([3, 10, 3]) / 16 HSCHARR_WEIGHTS = SCHARR_EDGE.reshape((3, 1)) * SCHARR_SMOOTH.reshape((1, 3)) VSCHARR_WEIGHTS = HSCHARR_WEIGHTS.T PREWITT_EDGE = np.array([1, 0, -1]) PREWITT_SMOOTH = np.full((3,), 1/3) HPREWITT_WEIGHTS = (PREWITT_EDGE.reshape((3, 1)) * PREWITT_SMOOTH.reshape((1, 3))) VPREWITT_WEIGHTS = HPREWITT_WEIGHTS.T # 2D-only filter weights ROBERTS_PD_WEIGHTS = np.array([[1, 0], [0, -1]], dtype=np.double) ROBERTS_ND_WEIGHTS = np.array([[0, 1], [-1, 0]], dtype=np.double) # These filter weights can be found in Farid & Simoncelli (2004), # Table 1 (3rd and 4th row). Additional decimal places were computed # using the code found at https://www.cs.dartmouth.edu/farid/ p = np.array([[0.0376593171958126, 0.249153396177344, 0.426374573253687, 0.249153396177344, 0.0376593171958126]]) d1 = np.array([[0.109603762960254, 0.276690988455557, 0, -0.276690988455557, -0.109603762960254]]) HFARID_WEIGHTS = d1.T * p VFARID_WEIGHTS = np.copy(HFARID_WEIGHTS.T) def _mask_filter_result(result, mask): """Return result after masking. Input masks are eroded so that mask areas in the original image don't affect values in the result. """ if mask is not None: erosion_selem = ndi.generate_binary_structure(mask.ndim, mask.ndim) mask = binary_erosion(mask, erosion_selem, border_value=0) result *= mask return result def _kernel_shape(ndim, dim): """Return list of `ndim` 1s except at position `dim`, where value is -1. Parameters ---------- ndim : int The number of dimensions of the kernel shape. dim : int The axis of the kernel to expand to shape -1. Returns ------- shape : list of int The requested shape. Examples -------- >>> _kernel_shape(2, 0) [-1, 1] >>> _kernel_shape(3, 1) [1, -1, 1] >>> _kernel_shape(4, -1) [1, 1, 1, -1] """ shape = [1, ] * ndim shape[dim] = -1 return shape def _reshape_nd(arr, ndim, dim): """Reshape a 1D array to have n dimensions, all singletons but one. Parameters ---------- arr : array, shape (N,) Input array ndim : int Number of desired dimensions of reshaped array. dim : int Which dimension/axis will not be singleton-sized. Returns ------- arr_reshaped : array, shape ([1, ...], N, [1,...]) View of `arr` reshaped to the desired shape. Examples -------- >>> arr = np.random.random(7) >>> _reshape_nd(arr, 2, 0).shape (7, 1) >>> _reshape_nd(arr, 3, 1).shape (1, 7, 1) >>> _reshape_nd(arr, 4, -1).shape (1, 1, 1, 7) """ kernel_shape = _kernel_shape(ndim, dim) return np.reshape(arr, kernel_shape) def _generic_edge_filter(image, *, smooth_weights, edge_weights=[1, 0, -1], axis=None, mode='reflect', cval=0.0, mask=None): """Apply a generic, n-dimensional edge filter. The filter is computed by applying the edge weights along one dimension and the smoothing weights along all other dimensions. If no axis is given, or a tuple of axes is given the filter is computed along all axes in turn, and the magnitude is computed as the square root of the average square magnitude of all the axes. Parameters ---------- image : array The input image. smooth_weights : array of float The smoothing weights for the filter. These are applied to dimensions orthogonal to the edge axis. edge_weights : 1D array of float, optional The weights to compute the edge along the chosen axes. axis : int or sequence of int, optional Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as:: edge_mag = np.sqrt(sum([_generic_edge_filter(image, ..., axis=i)**2 for i in range(image.ndim)]) / image.ndim) The magnitude is also computed if axis is a sequence. mode : str or sequence of str, optional The boundary mode for the convolution. See `scipy.ndimage.convolve` for a description of the modes. This can be either a single boundary 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. """ ndim = image.ndim if axis is None: axes = list(range(ndim)) elif np.isscalar(axis): axes = [axis] else: axes = axis return_magnitude = (len(axes) > 1) output = np.zeros(image.shape, dtype=float) for edge_dim in axes: kernel = _reshape_nd(edge_weights, ndim, edge_dim) smooth_axes = list(set(range(ndim)) - {edge_dim}) for smooth_dim in smooth_axes: kernel = kernel * _reshape_nd(smooth_weights, ndim, smooth_dim) ax_output = ndi.convolve(image, kernel, mode=mode) if return_magnitude: ax_output *= ax_output output += ax_output if return_magnitude: output = np.sqrt(output) / np.sqrt(ndim) return output def sobel(image, mask=None, *, axis=None, mode='reflect', cval=0.0): """Find edges in an image using the Sobel filter. Parameters ---------- image : array The input image. mask : array of bool, optional Clip the output image to this mask. (Values where mask=0 will be set to 0.) axis : int or sequence of int, optional Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as:: sobel_mag = np.sqrt(sum([sobel(image, axis=i)**2 for i in range(image.ndim)]) / image.ndim) The magnitude is also computed if axis is a sequence. mode : str or sequence of str, optional The boundary mode for the convolution. See `scipy.ndimage.convolve` for a description of the modes. This can be either a single boundary 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 Sobel edge map. See also -------- scharr, prewitt, canny References ---------- .. [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. .. [2] https://en.wikipedia.org/wiki/Sobel_operator Examples -------- >>> from skimage import data >>> from skimage import filters >>> camera = data.camera() >>> edges = filters.sobel(camera) """ image = img_as_float(image) output = _generic_edge_filter(image, smooth_weights=SOBEL_SMOOTH, axis=axis, mode=mode, cval=cval) output = _mask_filter_result(output, mask) return output def sobel_h(image, mask=None): """Find the horizontal edges of an image using the Sobel 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 Sobel edge map. Notes ----- We use the following kernel:: 1 2 1 0 0 0 -1 -2 -1 """ check_nD(image, 2) return sobel(image, mask=mask, axis=0) def sobel_v(image, mask=None): """Find the vertical edges of an image using the Sobel 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 Sobel edge map. Notes ----- We use the following kernel:: 1 0 -1 2 0 -2 1 0 -1 """ check_nD(image, 2) return sobel(image, mask=mask, axis=1) def scharr(image, mask=None, *, axis=None, mode='reflect', cval=0.0): """Find the edge magnitude using the Scharr transform. Parameters ---------- image : array The input image. mask : array of bool, optional Clip the output image to this mask. (Values where mask=0 will be set to 0.) axis : int or sequence of int, optional Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as:: sch_mag = np.sqrt(sum([scharr(image, axis=i)**2 for i in range(image.ndim)]) / image.ndim) The magnitude is also computed if axis is a sequence. mode : str or sequence of str, optional The boundary mode for the convolution. See `scipy.ndimage.convolve` for a description of the modes. This can be either a single boundary 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 Scharr edge map. See also -------- sobel, prewitt, canny Notes ----- The Scharr operator has a better rotation invariance than other edge filters such as the Sobel or the Prewitt operators. References ---------- .. [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. .. [2] https://en.wikipedia.org/wiki/Sobel_operator#Alternative_operators Examples -------- >>> from skimage import data >>> from skimage import filters >>> camera = data.camera() >>> edges = filters.scharr(camera) """ image = img_as_float(image) output = _generic_edge_filter(image, smooth_weights=SCHARR_SMOOTH, axis=axis, mode=mode, cval=cval) output = _mask_filter_result(output, mask) return output def scharr_h(image, mask=None): """Find the horizontal edges of an image using the Scharr 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 Scharr edge map. Notes ----- We use the following kernel:: 3 10 3 0 0 0 -3 -10 -3 References ---------- .. [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. """ check_nD(image, 2) return scharr(image, mask=mask, axis=0) def scharr_v(image, mask=None): """Find the vertical edges of an image using the Scharr 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 Scharr edge map. Notes ----- We use the following kernel:: 3 0 -3 10 0 -10 3 0 -3 References ---------- .. [1] D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. """ check_nD(image, 2) return scharr(image, mask=mask, axis=1) def prewitt(image, mask=None, *, axis=None, mode='reflect', cval=0.0): """Find the edge magnitude using the Prewitt transform. Parameters ---------- image : array The input image. mask : array of bool, optional Clip the output image to this mask. (Values where mask=0 will be set to 0.) axis : int or sequence of int, optional Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as:: prw_mag = np.sqrt(sum([prewitt(image, axis=i)**2 for i in range(image.ndim)]) / image.ndim) The magnitude is also computed if axis is a sequence. mode : str or sequence of str, optional The boundary mode for the convolution. See `scipy.ndimage.convolve` for a description of the modes. This can be either a single boundary 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: 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)