# Copyright (C) 2003-2005 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 = numarray.Float64,
output_type = None):
"""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 order of the spline must be >= 2 and <= 5.
"""
if order < 0 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
output, return_value = _ni_support._get_output(output, input,
output_type)
if order in [0, 1]:
output[...] = numarray.array(input)
else:
axis = _ni_support._check_axis(axis, input.rank)
_nd_image.spline_filter1d(input, order, axis, output)
return return_value
def spline_filter(input, order = 3, output = numarray.Float64,
output_type = None):
"""Multi-dimensional spline filter.
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.
"""
if order < 2 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
output, return_value = _ni_support._get_output(output, input,
output_type)
if order not in [0, 1] and input.rank > 0:
for axis in range(input.rank):
spline_filter1d(input, order, axis, output = output)
input = output
else:
output[...] = input[...]
return return_value
def geometric_transform(input, mapping, output_shape = None,
output_type = None, output = None, order = 3,
mode = 'constant', cval = 0.0, prefilter = True,
extra_arguments = (), extra_keywords = {}):
"""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 can optionally be
given. If not given, it is equal to the input shape. The parameter
prefilter determines if the input is pre-filtered before
interpolation, if False it is assumed that the input is already
filtered. The extra_arguments and extra_keywords arguments can be
used to provide extra arguments and keywords that are passed to the
mapping function at each call.
"""
if order < 0 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
if output_shape == None:
output_shape = input.shape
if input.rank < 1 or len(output_shape) < 1:
raise RuntimeError, 'input and output rank must be > 0'
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output = numarray.Float64)
else:
filtered = input
output, return_value = _ni_support._get_output(output, input,
output_type, shape = output_shape)
_nd_image.geometric_transform(filtered, mapping, None, None, None,
output, order, mode, cval, extra_arguments, extra_keywords)
return return_value
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 parameter prefilter determines if the
input is pre-filtered before interpolation, if False it is assumed
that the input is already filtered.
"""
if order < 0 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
coordinates = numarray.asarray(coordinates)
if isinstance(coordinates.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
output_shape = coordinates.shape[1:]
if input.rank < 1 or len(output_shape) < 1:
raise RuntimeError, 'input and output rank must be > 0'
if coordinates.shape[0] != input.rank:
raise RuntimeError, 'invalid shape for coordinate array'
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output = numarray.Float64)
else:
filtered = input
output, return_value = _ni_support._get_output(output, input,
output_type, shape = output_shape)
_nd_image.geometric_transform(filtered, None, coordinates, None, None,
output, order, mode, cval, None, None)
return return_value
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 can optionally be given. If not given it is
equal to the input shape. 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.
"""
if order < 0 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
if output_shape == None:
output_shape = input.shape
if input.rank < 1 or len(output_shape) < 1:
raise RuntimeError, 'input and output rank must be > 0'
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output = numarray.Float64)
else:
filtered = input
output, return_value = _ni_support._get_output(output, input,
output_type, shape = output_shape)
matrix = numarray.asarray(matrix, type = numarray.Float64)
if matrix.rank not in [1, 2] or matrix.shape[0] < 1:
raise RuntimeError, 'no proper affine matrix provided'
if matrix.shape[0] != input.rank:
raise RuntimeError, 'affine matrix has wrong number of rows'
if matrix.rank == 2 and matrix.shape[1] != output.rank:
raise RuntimeError, 'affine matrix has wrong number of columns'
if not matrix.iscontiguous():
matrix = matrix.copy()
offset = _ni_support._normalize_sequence(offset, input.rank)
offset = numarray.asarray(offset, type = numarray.Float64)
if offset.rank != 1 or offset.shape[0] < 1:
raise RuntimeError, 'no proper offset provided'
if not offset.iscontiguous():
offset = offset.copy()
if matrix.rank == 1:
_nd_image.zoom_shift(filtered, matrix, offset, output, order,
mode, cval)
else:
_nd_image.geometric_transform(filtered, None, None, matrix, offset,
output, order, mode, cval, None, None)
return return_value
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 parameter prefilter determines if the input is
pre-filtered before interpolation, if False it is assumed that the
input is already filtered.
"""
if order < 0 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
if input.rank < 1:
raise RuntimeError, 'input and output rank must be > 0'
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output = numarray.Float64)
else:
filtered = input
output, return_value = _ni_support._get_output(output, input,
output_type)
shift = _ni_support._normalize_sequence(shift, input.rank)
shift = [-ii for ii in shift]
shift = numarray.asarray(shift, type = numarray.Float64)
if not shift.iscontiguous():
shift = shift.copy()
_nd_image.zoom_shift(filtered, None, shift, output, order, mode, cval)
return return_value
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 parameter prefilter determines if the input is pre-
filtered before interpolation, if False it is assumed that the input
is already filtered.
"""
if order < 0 or order > 5:
raise RuntimeError, 'spline order not supported'
input = numarray.asarray(input)
if isinstance(input.type(), numarray.ComplexType):
raise TypeError, 'Complex type not supported'
if input.rank < 1:
raise RuntimeError, 'input and output rank must be > 0'
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output = numarray.Float64)
else:
filtered = input
zoom = _ni_support._normalize_sequence(zoom, input.rank)
output_shape = [int(ii * jj) for ii, jj in zip(input.shape, zoom)]
zoom = [1.0 / ii for ii in zoom]
output, return_value = _ni_support._get_output(output, input,
output_type, shape = output_shape)
zoom = numarray.asarray(zoom, type = numarray.Float64)
if not zoom.iscontiguous():
zoom = shift.copy()
_nd_image.zoom_shift(filtered, zoom, None, output, order, mode, cval)
return return_value
def _minmax(coor, minc, maxc):
if coor[0] < minc[0]:
minc[0] = coor[0]
if coor[0] > maxc[0]:
maxc[0] = coor[0]
if coor[1] < minc[1]:
minc[1] = coor[1]
if coor[1] > maxc[1]:
maxc[1] = coor[1]
return minc, maxc
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 defined 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. If reshape is true, the output
shape is adapted so that the input array is contained completely in
the output. 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)
axes = list(axes)
rank = input.rank
if axes[0] < 0:
axes[0] += rank
if axes[1] < 0:
axes[1] += rank
if axes[0] < 0 or axes[1] < 0 or axes[0] > rank or axes[1] > rank:
raise RuntimeError, 'invalid rotation plane specified'
if axes[0] > axes[1]:
axes = axes[1], axes[0]
angle = numarray.pi / 180 * angle
m11 = math.cos(angle)
m12 = math.sin(angle)
m21 = -math.sin(angle)
m22 = math.cos(angle)
matrix = numarray.array([[m11, m12],
[m21, m22]], type = numarray.Float64)
iy = input.shape[axes[0]]
ix = input.shape[axes[1]]
if reshape:
mtrx = numarray.array([[ m11, -m21],
[-m12, m22]], type = numarray.Float64)
minc = [0, 0]
maxc = [0, 0]
coor = numarray.matrixmultiply(mtrx, [0, ix])
minc, maxc = _minmax(coor, minc, maxc)
coor = numarray.matrixmultiply(mtrx, [iy, 0])
minc, maxc = _minmax(coor, minc, maxc)
coor = numarray.matrixmultiply(mtrx, [iy, ix])
minc, maxc = _minmax(coor, minc, maxc)
oy = int(maxc[0] - minc[0] + 0.5)
ox = int(maxc[1] - minc[1] + 0.5)
else:
oy = input.shape[axes[0]]
ox = input.shape[axes[1]]
offset = numarray.zeros((2,), type = numarray.Float64)
offset[0] = float(oy) / 2.0 - 0.5
offset[1] = float(ox) / 2.0 - 0.5
offset = numarray.matrixmultiply(matrix, offset)
tmp = numarray.zeros((2,), type = numarray.Float64)
tmp[0] = float(iy) / 2.0 - 0.5
tmp[1] = float(ix) / 2.0 - 0.5
offset = tmp - offset
output_shape = list(input.shape)
output_shape[axes[0]] = oy
output_shape[axes[1]] = ox
output_shape = tuple(output_shape)
output, return_value = _ni_support._get_output(output, input,
output_type, shape = output_shape)
if input.rank <= 2:
affine_transform(input, matrix, offset, output_shape, None, output,
order, mode, cval, prefilter)
else:
coordinates = []
size = input.nelements()
size /= input.shape[axes[0]]
size /= input.shape[axes[1]]
for ii in range(input.rank):
if ii not in axes:
coordinates.append(0)
else:
coordinates.append(slice(None, None, None))
iter_axes = range(input.rank)
iter_axes.reverse()
iter_axes.remove(axes[0])
iter_axes.remove(axes[1])
os = (output_shape[axes[0]], output_shape[axes[1]])
for ii in range(size):
ia = input[tuple(coordinates)]
oa = output[tuple(coordinates)]
affine_transform(ia, matrix, offset, os, None, oa, order, mode,
cval, prefilter)
for jj in iter_axes:
if coordinates[jj] < input.shape[jj] - 1:
coordinates[jj] += 1
break
else:
coordinates[jj] = 0
return return_value
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