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 """ 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 assert_nD from scipy.ndimage import convolve, binary_erosion, generate_binary_structure from ..restoration.uft import laplacian EROSION_SELEM = generate_binary_structure(2, 2) HSOBEL_WEIGHTS = np.array([[ 1, 2, 1], [ 0, 0, 0], [-1,-2,-1]]) / 4.0 VSOBEL_WEIGHTS = HSOBEL_WEIGHTS.T HSCHARR_WEIGHTS = np.array([[ 3, 10, 3], [ 0, 0, 0], [-3, -10, -3]]) / 16.0 VSCHARR_WEIGHTS = HSCHARR_WEIGHTS.T HPREWITT_WEIGHTS = np.array([[ 1, 1, 1], [ 0, 0, 0], [-1,-1,-1]]) / 3.0 VPREWITT_WEIGHTS = HPREWITT_WEIGHTS.T ROBERTS_PD_WEIGHTS = np.array([[1, 0], [0, -1]], dtype=np.double) ROBERTS_ND_WEIGHTS = np.array([[0, 1], [-1, 0]], dtype=np.double) 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 None: result[0, :] = 0 result[-1, :] = 0 result[:, 0] = 0 result[:, -1] = 0 return result else: mask = binary_erosion(mask, EROSION_SELEM, border_value=0) return result * mask def sobel(image, mask=None): """Find the edge magnitude 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. See also -------- scharr, prewitt, roberts, feature.canny Notes ----- Take the square root of the sum of the squares of the horizontal and vertical Sobels to get a magnitude that's somewhat insensitive to direction. The 3x3 convolution kernel used in the horizontal and vertical Sobels is an approximation of the gradient of the image (with some slight blurring since 9 pixels are used to compute the gradient at a given pixel). As an approximation of the gradient, the Sobel operator is not completely rotation-invariant. The Scharr operator should be used for a better rotation invariance. Note that ``scipy.ndimage.sobel`` returns a directional Sobel which has to be further processed to perform edge detection. Examples -------- >>> from skimage import data >>> camera = data.camera() >>> from skimage import filters >>> edges = filters.sobel(camera) """ assert_nD(image, 2) out = np.sqrt(sobel_h(image, mask)**2 + sobel_v(image, mask)**2) out /= np.sqrt(2) return out 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 """ assert_nD(image, 2) image = img_as_float(image) result = convolve(image, HSOBEL_WEIGHTS) return _mask_filter_result(result, mask) 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 """ assert_nD(image, 2) image = img_as_float(image) result = convolve(image, VSOBEL_WEIGHTS) return _mask_filter_result(result, mask) def scharr(image, mask=None): """Find the edge magnitude 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. See also -------- sobel, prewitt, canny Notes ----- Take the square root of the sum of the squares of the horizontal and vertical Scharrs to get a magnitude that is somewhat insensitive to direction. The Scharr operator has a better rotation invariance than other edge filters such as the Sobel or the Prewitt operators. References ---------- ..  D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. ..  https://en.wikipedia.org/wiki/Sobel_operator#Alternative_operators Examples -------- >>> from skimage import data >>> camera = data.camera() >>> from skimage import filters >>> edges = filters.scharr(camera) """ out = np.sqrt(scharr_h(image, mask)**2 + scharr_v(image, mask)**2) out /= np.sqrt(2) return out 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 ---------- ..  D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. """ assert_nD(image, 2) image = img_as_float(image) result = convolve(image, HSCHARR_WEIGHTS) return _mask_filter_result(result, mask) 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 ---------- ..  D. Kroon, 2009, Short Paper University Twente, Numerical Optimization of Kernel Based Image Derivatives. """ assert_nD(image, 2) image = img_as_float(image) result = convolve(image, VSCHARR_WEIGHTS) return _mask_filter_result(result, mask) def prewitt(image, mask=None): """Find the edge magnitude 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. See also -------- sobel, scharr Notes ----- Return the square root of the sum of squares of the horizontal and vertical Prewitt transforms. 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 >>> camera = data.camera() >>> from skimage import filters >>> edges = filters.prewitt(camera) """ assert_nD(image, 2) out = np.sqrt(prewitt_h(image, mask)**2 + prewitt_v(image, mask)**2) out /= np.sqrt(2) return out 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 1 1 0 0 0 -1 -1 -1 """ assert_nD(image, 2) image = img_as_float(image) result = convolve(image, HPREWITT_WEIGHTS) return _mask_filter_result(result, mask) 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 0 -1 1 0 -1 1 0 -1 """ assert_nD(image, 2) image = img_as_float(image) result = convolve(image, VPREWITT_WEIGHTS) return _mask_filter_result(result, mask) 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) """ assert_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 """ assert_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 """ assert_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)
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