Apply an arbitrary 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.
Parameters ---------- input : array_like The input array. mapping : callable, scipy.LowLevelCallable A callable object that accepts a tuple of length equal to the output array rank, and returns the corresponding input coordinates as a tuple of length equal to the input array rank. output_shape : tuple of ints, optional Shape tuple. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:
'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.
'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.
'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.
'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.
'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input. extra_arguments : tuple, optional Extra arguments passed to `mapping`. extra_keywords : dict, optional Extra keywords passed to `mapping`.
Returns ------- output : ndarray The filtered input.
See Also -------- map_coordinates, affine_transform, spline_filter1d
Notes ----- This function also accepts low-level callback functions with one the following signatures and wrapped in `scipy.LowLevelCallable`:
.. code:: c
int mapping(npy_intp *output_coordinates, double *input_coordinates, int output_rank, int input_rank, void *user_data) int mapping(intptr_t *output_coordinates, double *input_coordinates, int output_rank, int input_rank, void *user_data)
The calling function iterates over the elements of the output array, calling the callback function at each element. The coordinates of the current output element are passed through ``output_coordinates``. The callback function must return the coordinates at which the input must be interpolated in ``input_coordinates``. The rank of the input and output arrays are given by ``input_rank`` and ``output_rank`` respectively. ``user_data`` is the data pointer provided to `scipy.LowLevelCallable` as-is.
The callback function must return an integer error status that is zero if something went wrong and one otherwise. If an error occurs, you should normally set the Python error status with an informative message before returning, otherwise a default error message is set by the calling function.
In addition, some other low-level function pointer specifications are accepted, but these are for backward compatibility only and should not be used in new code.
Examples -------- >>> import numpy as np >>> from scipy.ndimage import geometric_transform >>> a = np.arange(12.).reshape((4, 3)) >>> def shift_func(output_coords): ... return (output_coords0 - 0.5, output_coords1 - 0.5) ... >>> geometric_transform(a, shift_func) array([ 0. , 0. , 0. ],
[ 0. , 1.362, 2.738],
[ 0. , 4.812, 6.187],
[ 0. , 8.263, 9.637])
>>> b = 1, 2, 3, 4, 5 >>> def shift_func(output_coords): ... return (output_coords0 - 3,) ... >>> geometric_transform(b, shift_func, mode='constant') array(0, 0, 0, 1, 2) >>> geometric_transform(b, shift_func, mode='nearest') array(1, 1, 1, 1, 2) >>> geometric_transform(b, shift_func, mode='reflect') array(3, 2, 1, 1, 2) >>> geometric_transform(b, shift_func, mode='wrap') array(2, 3, 4, 1, 2)