diff options
Diffstat (limited to 'silx/image/bilinear.pyx')
| -rw-r--r-- | silx/image/bilinear.pyx | 335 |
1 files changed, 335 insertions, 0 deletions
diff --git a/silx/image/bilinear.pyx b/silx/image/bilinear.pyx new file mode 100644 index 0000000..ce440b4 --- /dev/null +++ b/silx/image/bilinear.pyx @@ -0,0 +1,335 @@ +# -*- coding: utf-8 -*- +# +# Project: silx (originally pyFAI) +# https://github.com/silx-kit/silx +# +# Copyright (C) 2012-2017 European Synchrotron Radiation Facility, Grenoble, France +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to deal +# in the Software without restriction, including without limitation the rights +# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +# copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +# THE SOFTWARE. + +__authors__ = ["J. Kieffer"] +__license__ = "MIT" +__date__ = "15/09/2016" +__doc__ = "Bilinear interpolator, peak finder, line-profile for images" + +import cython +from cython.view cimport array as cvarray +import numpy +from libc.math cimport floor, ceil, sin, cos, sqrt, atan2 +import logging +logger = logging.getLogger("silx.image.bilinear") + + +cdef class BilinearImage: + """Bilinear interpolator for images ... or any data on a regular grid + """ + cdef: + readonly float[:, ::1] data + readonly float maxi, mini + readonly size_t width, height + + cpdef size_t coarse_local_maxi(self, size_t) + cdef size_t c_local_maxi(self, size_t) nogil + cdef float c_funct(self, float, float) nogil + + def __cinit__(self, data not None): + """Constructor + + :param data: image as a 2D array + """ + assert data.ndim == 2 + self.height = data.shape[0] + self.width = data.shape[1] + self.maxi = data.max() + self.mini = data.min() + self.data = numpy.ascontiguousarray(data, dtype=numpy.float32) + + def __dealloc__(self): + self.data = None + + def __call__(self, coord): + """Function f((y, x)) where f is a continuous function + made from the image and (y,x)=(row, column) is the pixel coordinates + in natural C-order + + :param x: 2-tuple of float (row, column) + :return: Interpolated signal from the image + """ + return self.c_funct(coord[1], coord[0]) + + @cython.boundscheck(False) + @cython.wraparound(False) + cdef float c_funct(self, float x, float y) nogil: + """Function f(x, y) where f is a continuous function + made from the image. + + :param x (float): column coordinate + :param y (float): row coordinate + :return: Interpolated signal from the image (nearest for outside) + + Cython only function due to NOGIL + """ + cdef: + float d0 = min(max(y, 0.0), (self.height - 1.0)) + float d1 = min(max(x, 0.0), (self.width - 1.0)) + int i0, i1, j0, j1 + float x0, x1, y0, y1, res + + x0 = floor(d0) + x1 = ceil(d0) + y0 = floor(d1) + y1 = ceil(d1) + i0 = < int > x0 + i1 = < int > x1 + j0 = < int > y0 + j1 = < int > y1 + if (i0 == i1) and (j0 == j1): + res = self.data[i0, j0] + elif i0 == i1: + res = (self.data[i0, j0] * (y1 - d1)) + (self.data[i0, j1] * (d1 - y0)) + elif j0 == j1: + res = (self.data[i0, j0] * (x1 - d0)) + (self.data[i1, j0] * (d0 - x0)) + else: + res = (self.data[i0, j0] * (x1 - d0) * (y1 - d1)) \ + + (self.data[i1, j0] * (d0 - x0) * (y1 - d1)) \ + + (self.data[i0, j1] * (x1 - d0) * (d1 - y0)) \ + + (self.data[i1, j1] * (d0 - x0) * (d1 - y0)) + return res + + @cython.boundscheck(False) + @cython.wraparound(False) + def opp_f(self, coord): + """Function -f((y,x)) for peak finding via minimizer. + + Gives large number outside the boundaries to return into the image + + :param x: 2-tuple of float in natural C order, i.e (row, column) + :return: Negative interpolated signal from the image + """ + cdef: + float d0, d1, res + d0, d1 = coord + if d0 < 0: + res = self.mini + d0 + elif d1 < 0: + res = self.mini + d1 + elif d0 > (self.height - 1): + res = self.mini - d0 + self.height - 1 + elif d1 > self.width - 1: + res = self.mini - d1 + self.width - 1 + else: + res = self.c_funct(d1, d0) + return - res + + @cython.boundscheck(False) + @cython.wraparound(False) + @cython.cdivision(True) + def local_maxi(self, coord): + """Return the nearest local maximum ... with sub-pixel refinement + + Nearest maximum search: + steepest ascent + + Sub-pixel refinement: + Second order Taylor expansion of the function; + At the maximum, the first derivative is null + delta = x-i = -Inverse[Hessian].gradient + if Hessian is singular or \|delta\|>1: use a center of mass. + + :param coord: 2-tuple of scalar (row, column) + :return: 2-tuple of float with the nearest local maximum + """ + cdef: + int res, current0, current1 + int i0, i1 + float tmp, sum0 = 0, sum1 = 0, sum = 0 + float a00, a01, a02, a10, a11, a12, a20, a21, a22 + float d00, d11, d01, denom, delta0, delta1 + res = self.c_local_maxi(round(coord[0]) * self.width + round(coord[1])) + + current0 = res // self.width + current1 = res % self.width + if (current0 > 0) and (current0 < self.height - 1) and (current1 > 0) and (current1 < self.width - 1): + # Use second order polynomial Taylor expansion + a00 = self.data[current0 - 1, current1 - 1] + a01 = self.data[current0 - 1, current1 ] + a02 = self.data[current0 - 1, current1 + 1] + a10 = self.data[current0 , current1 - 1] + a11 = self.data[current0 , current1 ] + a12 = self.data[current0 , current1 + 1] + a20 = self.data[current0 + 1, current1 - 1] + a21 = self.data[current0 + 1, current1 ] + a22 = self.data[current0 + 1, current1 - 1] + d00 = a12 - 2.0 * a11 + a10 + d11 = a21 - 2.0 * a11 + a01 + d01 = (a00 - a02 - a20 + a22) / 4.0 + denom = 2.0 * (d00 * d11 - d01 * d01) + if abs(denom) < 1e-10: + logger.debug("Singular determinant, Hessian undefined") + else: + delta0 = ((a12 - a10) * d01 + (a01 - a21) * d11) / denom + delta1 = ((a10 - a12) * d00 + (a21 - a01) * d01) / denom + if abs(delta0) <= 1.0 and abs(delta1) <= 1.0: + # Result is OK if lower than 0.5. + return (delta0 + float(current0), delta1 + float(current1)) + else: + logger.debug("Failed to find root using second order expansion") + # refinement of the position by a simple center of mass of the last valid region used + for i0 in range(current0 - 1, current0 + 2): + for i1 in range(current1 - 1, current1 + 2): + tmp = self.data[i0, i1] + sum0 += tmp * i0 + sum1 += tmp * i1 + sum += tmp + if sum > 0: + return (sum0 / sum, sum1 / sum) + + return (float(current0), float(current1)) + + cpdef size_t coarse_local_maxi(self, size_t x): + """Return the nearest local maximum ... without sub-pixel refinement + + :param idx: start index (=row*width+column) + :return: local maximum index + """ + return self.c_local_maxi(x) + + @cython.boundscheck(False) + @cython.wraparound(False) + @cython.cdivision(True) + cdef size_t c_local_maxi(self, size_t idx) nogil: + """Return the nearest local maximum without sub-pixel refinement + + :param idx: start index (=row*width+column) + :return: local maximum index + + This method is Cython only due to the NOGIL + """ + cdef: + int current0 = idx // self.width + int current1 = idx % self.width + int i0, i1, start0, stop0, start1, stop1, new0, new1 + float tmp, value, old_value + + value = self.data[current0, current1] + old_value = value - 1.0 + new0, new1 = current0, current1 + + while value > old_value: + old_value = value + start0 = max(0, current0 - 1) + stop0 = min(self.height, current0 + 2) + start1 = max(0, current1 - 1) + stop1 = min(self.width, current1 + 2) + for i0 in range(start0, stop0): + for i1 in range(start1, stop1): + tmp = self.data[i0, i1] + if tmp > value: + new0, new1 = i0, i1 + value = tmp + current0, current1 = new0, new1 + return self.width * current0 + current1 + + @cython.boundscheck(False) + def map_coordinates(self, coordinates): + """Map coordinates of the array on the image + + :param coordinates: 2-tuple of array of the same size (row_array, column_array) + :return: array of values at given coordinates + """ + cdef: + float[:] d0, d1, res + size_t size, i + shape = coordinates[0].shape + size = coordinates[0].size + d0 = numpy.ascontiguousarray(coordinates[0].ravel(), dtype=numpy.float32) + d1 = numpy.ascontiguousarray(coordinates[1].ravel(), dtype=numpy.float32) + assert size == d1.size + res = numpy.empty(size, dtype=numpy.float32) + with nogil: + for i in range(size): + res[i] = self.c_funct(d1[i], d0[i]) + return numpy.asarray(res).reshape(shape) + + @cython.boundscheck(False) + def profile_line(self, src, dst, int linewidth=1): + """Return the intensity profile of an image measured along a scan line. + + :param src: The start point of the scan line. + :type src: 2-tuple of numeric scalar + :param dst: The end point of the scan line. + The destination point is included in the profile, + in contrast to standard numpy indexing. + :type dst: 2-tuple of numeric scalar + :param int linewidth: Width of the scanline (unit image pixel). + :return: The intensity profile along the scan line. + The length of the profile is the ceil of the computed length + of the scan line. + :rtype: 1d array + + Inspired from skimage + """ + cdef: + float src_row, src_col, dst_row, dst_col, d_row, d_col + float length, col_width, row_width, sum, row, col, new_row, new_col + int lengt, i, j, cnt + float[::1] result + src_row, src_col = src + dst_row, dst_col = dst + if (src_row == dst_row) and (src_col == dst_col): + logger.warning("Source and destination points are the same") + return numpy.array([self.c_funct(src_col, src_row)]) + d_row = dst_row - src_row + d_col = dst_col - src_col + + # Offsets to deal with linewidth + length = sqrt(d_row * d_row + d_col * d_col) + row_width = d_col / length + col_width = - d_row / length + + lengt = <int> ceil(length + 1) + d_row /= <float> (lengt -1) + d_col /= <float> (lengt -1) + + result = numpy.zeros(lengt, dtype=numpy.float32) + + # Offset position to the center of the bottom pixels of the profile + src_row -= row_width * (linewidth - 1) / 2. + src_col -= col_width * (linewidth - 1) / 2. + + with nogil: + for i in range(lengt): + sum = 0 + cnt = 0 + + row = src_row + i * d_row + col = src_col + i * d_col + + for j in range(linewidth): + new_row = row + j * row_width + new_col = col + j * col_width + if ((new_col >= 0) and (new_col < self.width) and + (new_row >= 0) and (new_row < self.height)): + cnt = cnt + 1 + sum = sum + self.c_funct(new_col, new_row) + if cnt: + result[i] += sum / cnt + + # Ensures the result is exported as numpy array and not memory view. + return numpy.asarray(result) |