# Copyright (C) 2003, 2004 Peter J. Verveer # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above # copyright notice, this list of conditions and the following # disclaimer in the documentation and/or other materials provided # with the distribution. # # 3. The name of the author may not be used to endorse or promote # products derived from this software without specific prior # written permission. # # THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS # OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED # WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE # ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY # DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE # GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS # INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, # WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING # NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS # SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. import types import math import numarray import _ni_support import _nd_image def spline_filter1d(input, order = 3, axis = -1, output = None, output_type = numarray.Float64): """Calculates a one-dimensional spline filter along the given axis. The lines of the array along the given axis are filtered by a spline filter. The type of the output can be forced by the type parameter. If equal to None, the output array type is equal to the input array type. An output array can optionally be provided. The order of the spline must be >= 2 and <= 5. """ inplace = isinstance(output, numarray.NumArray) if order in [0, 1]: if inplace: output[...] = numarray.array(input).astype(output_type)[...] else: output = numarray.array(input).copy().astype(output_type) else: output = _nd_image.spline_filter1d(input, order, axis, output, output_type) if not inplace: return output def spline_filter(input, order = 3, output = None, output_type = numarray.Float64): """Multi-dimensional spline filter. The data type of the output array can be specified. The data type of the output is equal to the input type if the output_type argument is equal to None. Optionally an output array can be provided. Note: The multi-dimensional filter is implemented as a sequence of one-dimensional spline filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision. """ inplace = isinstance(output, numarray.NumArray) input = numarray.asarray(input) if output_type == None: output_type = input.type() if isinstance(output_type, numarray.ComplexType): raise RuntimeError, "complex array types not supported" done = False # loop over the dimensions for axis in range(input.rank): if order in [0, 1]: continue # zero filter sizes are skipped: if done: # if one or more axes are already processed, work in-place: spline_filter1d(output, order, axis, output_type = None, output = output) else: if inplace: spline_filter1d(input, order, axis, output_type = output_type, output = output) else: output = spline_filter1d(input, order, axis, output_type = output_type) done = True if not done: # if no filter was applied, make a copy: if inplace: output[...] = numarray.array(input).astype(output_type)[...] else: output = numarray.array(input).copy().astype(output_type) if not inplace: return output def geometric_transform(input, mapping, output_shape = None, output_type = None, output = None, order = 3, mode = 'constant', cval = 0.0, prefilter = True): """Apply an arbritrary geometric transform. The given mapping function is used to find for each point in the output the corresponding coordinates in the input. The value of the input at those coordinates is determined by spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode. The output shape and output type can optionally be given. If not given they are equal to the input shape and type. Optionally an output array can be provided that must match the requested output shape and type. The parameter prefilter determines if the input is pre-filtered before interpolation, if False it is assumed that the input is already filtered. """ input = numarray.asarray(input) if output_type == None: output_type = input.type() if isinstance(output_type, numarray.ComplexType): raise RuntimeError, "complex array types not supported" if output_shape == None: output_shape = input.shape mode = _ni_support._extend_mode_to_code(mode) if prefilter: filtered = spline_filter(input, order, output_type = numarray.Float64) else: filtered = input return _nd_image.geometric_transform(filtered, mapping, output_shape, output_type, output, order, mode, cval) def map_coordinates(input, coordinates, output_type = None, output = None, order = 3, mode = 'constant', cval = 0.0, prefilter = True): """Apply an arbritrary coordinate transformation. The array of coordinates is used to find for each point in the output the corresponding coordinates in the input. The value of the input at that coordinates is determined by spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode. The output type can optionally be given. If not given it is equal to the input type. Optionally an output array can be provided that must match the array of coordinates and the requested type. The parameter prefilter determines if the input is pre-filtered before interpolation, if False it is assumed that the input is already filtered. """ input = numarray.asarray(input) coordinates = numarray.asarray(coordinates) if output_type == None: output_type = input.type() if isinstance(output_type, numarray.ComplexType): raise RuntimeError, "complex array types not supported" output_shape = coordinates.shape[1:] mode = _ni_support._extend_mode_to_code(mode) if prefilter: filtered = spline_filter(input, order, output_type = numarray.Float64) else: filtered = input return _nd_image.map_coordinates(filtered, coordinates, output_shape, output_type, output, order, mode, cval) def affine_transform(input, matrix, offset = 0.0, output_shape = None, output_type = None, output = None, order = 3, mode = 'constant', cval = 0.0, prefilter = True): """Apply an affine transformation. The given matrix and offset are used to find for each point in the output the corresponding coordinates in the input by an affine transformation. The value of the input at those coordinates is determined by spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode. The output shape and output type can optionally be given. If not given they are equal to the input shape and type. Optionally an output array can be provided that must match the requested output shape and type. The parameter prefilter determines if the input is pre-filtered before interpolation, if False it is assumed that the input is already filtered. The matrix must be two-dimensional or can also be given as a one-dimensional sequence or array. In the latter case, it is assumed that the matrix is diagonal. A more efficient algorithms is then applied that exploits the separability of the problem. """ input = numarray.asarray(input) if output_type == None: output_type = input.type() if isinstance(output_type, numarray.ComplexType): raise RuntimeError, "complex array types not supported" if output_shape == None: output_shape = input.shape mode = _ni_support._extend_mode_to_code(mode) offset = _ni_support._normalize_sequence(offset, input) if prefilter: filtered = spline_filter(input, order, output_type = numarray.Float64) else: filtered = input return _nd_image.affine_transform(filtered, matrix, offset, output_shape, output_type, output, order, mode, cval) def shift(input, shift, output_type = None, output = None, order = 3, mode = 'constant', cval = 0.0, prefilter = True): """Shift an array. The array is shifted using spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode. The output type can optionally be given. If not given it is equal to the input type. Optionally an output array can be provided that must match the requested output shape and type. The parameter prefilter determines if the input is pre-filtered before interpolation, if False it is assumed that the input is already filtered. """ input = numarray.asarray(input) if output_type == None: output_type = input.type() if isinstance(output_type, numarray.ComplexType): raise RuntimeError, "complex array types not supported" mode = _ni_support._extend_mode_to_code(mode) shift = _ni_support._normalize_sequence(shift, input) shift = [-ii for ii in shift] if prefilter: filtered = spline_filter(input, order, output_type = numarray.Float64) else: filtered = input return _nd_image.shift(filtered, shift, input.shape, output_type, output, order, mode, cval) def zoom(input, zoom, output_type = None, output = None, order = 3, mode = 'constant', cval = 0.0, prefilter = True): """Zoom an array. The array is zoomed using spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode. The output type can optionally be given. If not given it is equal to the input type. Optionally an output array can be provided that must match the requested output shape and type. The parameter prefilter determines if the input is pre-filtered before interpolation, if False it is assumed that the input is already filtered. """ input = numarray.asarray(input) if output_type == None: output_type = input.type() if isinstance(output_type, numarray.ComplexType): raise RuntimeError, "complex array types not supported" mode = _ni_support._extend_mode_to_code(mode) zoom = _ni_support._normalize_sequence(zoom, input) output_shape = [ii[0] * ii[1] for ii in zip(input.shape, zoom)] zoom = [1.0 / ii for ii in zoom] if prefilter: filtered = spline_filter(input, order, output_type = numarray.Float64) else: filtered = input return _nd_image.zoom(filtered, zoom, output_shape, output_type, output, order, mode, cval) def rotate(input, angle, axes = (-1, -2), reshape = True, output_type = None, output = None, order = 3, mode = 'constant', cval = 0.0, prefilter = True): """Rotate an array. The array is rotated in the plane definde by the two axes given by the axes parameter using spline interpolation of the requested order. The angle is given in degrees. Points outside the boundaries of the input are filled according to the given mode. The output type can optionally be given. If not given it is equal to the input type. If reshape is true, the output shape is adapted so that the input array is contained completely in the output. Optionally an output array can be provided that must match the requested output shape and type. The parameter prefilter determines if the input is pre-filtered before interpolation, if False it is assumed that the input is already filtered. """ input = numarray.asarray(input) angle = numarray.pi / 180 * angle if axes[0] < axes[1]: a1 = axes[0] a2 = axes[1] else: a1 = axes[1] a2 = axes[0] oshape = list(input.shape) ix = input.shape[a1] iy = input.shape[a2] if reshape: ox = int(ix * math.cos(angle) + iy * math.sin(angle) + 0.5) oy = int(iy * math.cos(angle) + ix * math.sin(angle) + 0.5) oshape[a1] = ox oshape[a2] = oy else: ox = oshape[a1] oy = oshape[a2] m11 = math.cos(angle) m12 = math.sin(angle) m21 = -math.sin(angle) m22 = math.cos(angle) matrix = numarray.identity(input.rank, type = numarray.Float64) matrix[a1, a1] = m11 matrix[a1, a2] = m12 matrix[a2, a1] = m21 matrix[a2, a2] = m22 offset = numarray.zeros((input.rank,), type = numarray.Float64) offset[a1] = float(ox) / 2.0 - 0.5 offset[a2] = float(oy) / 2.0 - 0.5 offset = numarray.matrixmultiply(matrix, offset) tmp = numarray.zeros((input.rank,), type = numarray.Float64) tmp[a1] = float(ix) / 2.0 - 0.5 tmp[a2] = float(iy) / 2.0 - 0.5 offset = tmp - offset return affine_transform(input, matrix, offset, oshape, output_type, output, order, mode, cval, prefilter)