mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-28 01:46:21 +08:00
Gregory R. Lee
366 lines
10 KiB
Cython
366 lines
10 KiB
Cython
#cython: cdivision=True
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#cython: boundscheck=False
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#cython: nonecheck=False
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#cython: wraparound=False
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"""
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Note: All edge modes implemented here follow the corresponding numpy.pad
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conventions.
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The table below illustrates the behavior for the array [1, 2, 3, 4], if padded
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by 4 values on each side:
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pad original pad
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constant (with c=0) : 0 0 0 0 | 1 2 3 4 | 0 0 0 0
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wrap : 1 2 3 4 | 1 2 3 4 | 1 2 3 4
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symmetric : 4 3 2 1 | 1 2 3 4 | 4 3 2 1
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edge : 1 1 1 1 | 1 2 3 4 | 4 4 4 4
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reflect : 3 4 3 2 | 1 2 3 4 | 3 2 1 2
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"""
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from libc.math cimport ceil, floor
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cdef inline Py_ssize_t round(double r) nogil:
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return <Py_ssize_t>((r + 0.5) if (r > 0.0) else (r - 0.5))
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cdef inline double nearest_neighbour_interpolation(double* image,
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Py_ssize_t rows,
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Py_ssize_t cols, double r,
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double c, char mode,
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double cval) nogil:
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"""Nearest neighbour interpolation at a given position in the image.
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Parameters
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----------
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image : double array
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Input image.
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rows, cols : int
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Shape of image.
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r, c : double
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Position at which to interpolate.
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mode : {'C', 'W', 'S', 'E', 'R'}
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Wrapping mode. Constant, Wrap, Symmetric, Edge or Reflect.
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cval : double
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Constant value to use for constant mode.
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Returns
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-------
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value : double
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Interpolated value.
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"""
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return get_pixel2d(image, rows, cols, round(r), round(c), mode, cval)
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cdef inline double bilinear_interpolation(double* image, Py_ssize_t rows,
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Py_ssize_t cols, double r, double c,
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char mode, double cval) nogil:
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"""Bilinear interpolation at a given position in the image.
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Parameters
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----------
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image : double array
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Input image.
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rows, cols : int
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Shape of image.
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r, c : double
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Position at which to interpolate.
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mode : {'C', 'W', 'S', 'E', 'R'}
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Wrapping mode. Constant, Wrap, Symmetric, Edge or Reflect.
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cval : double
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Constant value to use for constant mode.
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Returns
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-------
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value : double
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Interpolated value.
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"""
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cdef double dr, dc
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cdef long minr, minc, maxr, maxc
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minr = <long>floor(r)
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minc = <long>floor(c)
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maxr = <long>ceil(r)
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maxc = <long>ceil(c)
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dr = r - minr
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dc = c - minc
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top = (1 - dc) * get_pixel2d(image, rows, cols, minr, minc, mode, cval) \
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+ dc * get_pixel2d(image, rows, cols, minr, maxc, mode, cval)
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bottom = (1 - dc) * get_pixel2d(image, rows, cols, maxr, minc, mode,
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cval) \
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+ dc * get_pixel2d(image, rows, cols, maxr, maxc, mode, cval)
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return (1 - dr) * top + dr * bottom
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cdef inline double quadratic_interpolation(double x, double[3] f) nogil:
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"""WARNING: Do not use, not implemented correctly.
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Quadratic interpolation.
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Parameters
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----------
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x : double
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Position in the interval [0, 2].
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f : double[3]
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Function values at positions [0, 2].
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Returns
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-------
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value : double
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Interpolated value.
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"""
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return (x * f[2] * (x - 1)) / 2 - \
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x * f[1] * (x - 2) + \
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(f[0] * (x - 1) * (x - 2)) / 2
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cdef inline double biquadratic_interpolation(double* image, Py_ssize_t rows,
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Py_ssize_t cols, double r,
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double c, char mode,
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double cval) nogil:
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"""WARNING: Do not use, not implemented correctly.
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Biquadratic interpolation at a given position in the image.
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Parameters
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----------
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image : double array
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Input image.
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rows, cols : int
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Shape of image.
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r, c : double
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Position at which to interpolate.
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mode : {'C', 'W', 'S', 'E', 'R'}
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Wrapping mode. Constant, Wrap, Symmetric, Edge or Reflect.
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cval : double
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Constant value to use for constant mode.
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Returns
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-------
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value : double
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Interpolated value.
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"""
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cdef long r0 = <long>round(r) - 1
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cdef long c0 = <long>round(c) - 1
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cdef double xr = r - r0
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cdef double xc = c - c0
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cdef double fc[3]
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cdef double fr[3]
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cdef long pr, pc
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# row-wise cubic interpolation
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for pr in range(3):
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for pc in range(3):
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fc[pc] = get_pixel2d(image, rows, cols,
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r0 + pr, c0 + pc, mode, cval)
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fr[pr] = quadratic_interpolation(xc, fc)
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# cubic interpolation for interpolated values of each row
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return quadratic_interpolation(xr, fr)
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cdef inline double cubic_interpolation(double x, double[4] f) nogil:
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"""Cubic interpolation.
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Parameters
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----------
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x : double
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Position in the interval [0, 1].
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f : double[4]
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Function values at positions [-1, 0, 1, 2].
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Returns
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-------
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value : double
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Interpolated value.
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"""
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return \
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f[1] + 0.5 * x * \
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(f[2] - f[0] + x * \
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(2.0 * f[0] - 5.0 * f[1] + 4.0 * f[2] - f[3] + x * \
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(3.0 * (f[1] - f[2]) + f[3] - f[0])))
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cdef inline double bicubic_interpolation(double* image, Py_ssize_t rows,
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Py_ssize_t cols, double r, double c,
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char mode, double cval) nogil:
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"""Bicubic interpolation at a given position in the image.
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Interpolation using Catmull-Rom splines, based on the bicubic convolution
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algorithm described in [1]_.
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Parameters
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----------
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image : double array
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Input image.
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rows, cols : int
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Shape of image.
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r, c : double
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Position at which to interpolate.
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mode : {'C', 'W', 'S', 'E', 'R'}
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Wrapping mode. Constant, Wrap, Symmetric, Edge or Reflect.
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cval : double
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Constant value to use for constant mode.
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Returns
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-------
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value : double
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Interpolated value.
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References
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----------
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.. [1] R. Keys, (1981). "Cubic convolution interpolation for digital image
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processing". IEEE Transactions on Signal Processing, Acoustics,
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Speech, and Signal Processing 29 (6): 1153–1160.
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"""
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cdef long r0 = <long>floor(r)
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cdef long c0 = <long>floor(c)
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# scale position to range [0, 1]
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cdef double xr = r - r0
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cdef double xc = c - c0
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r0 -= 1
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c0 -= 1
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cdef double fc[4]
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cdef double fr[4]
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cdef long pr, pc
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# row-wise cubic interpolation
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for pr in range(4):
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for pc in range(4):
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fc[pc] = get_pixel2d(image, rows, cols, pr + r0, pc + c0, mode, cval)
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fr[pr] = cubic_interpolation(xc, fc)
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# cubic interpolation for interpolated values of each row
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return cubic_interpolation(xr, fr)
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cdef inline double get_pixel2d(double* image, Py_ssize_t rows, Py_ssize_t cols,
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long r, long c, char mode,
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double cval) nogil:
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"""Get a pixel from the image, taking wrapping mode into consideration.
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Parameters
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----------
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image : double array
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Input image.
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rows, cols : int
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Shape of image.
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r, c : int
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Position at which to get the pixel.
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mode : {'C', 'W', 'S', 'E', 'R'}
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Wrapping mode. Constant, Wrap, Symmetric, Edge or Reflect.
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cval : double
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Constant value to use for constant mode.
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Returns
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-------
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value : double
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Pixel value at given position.
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"""
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if mode == 'C':
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if (r < 0) or (r >= rows) or (c < 0) or (c >= cols):
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return cval
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else:
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return image[r * cols + c]
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else:
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return image[coord_map(rows, r, mode) * cols + coord_map(cols, c, mode)]
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cdef inline double get_pixel3d(double* image, Py_ssize_t rows, Py_ssize_t cols,
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Py_ssize_t dims, long r, long c,
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long d, char mode, double cval) nogil:
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"""Get a pixel from the image, taking wrapping mode into consideration.
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Parameters
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----------
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image : double array
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Input image.
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rows, cols, dims : int
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Shape of image.
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r, c, d : int
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Position at which to get the pixel.
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mode : {'C', 'W', 'S', 'E', 'R'}
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Wrapping mode. Constant, Wrap, Symmetric, Edge or Reflect.
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cval : double
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Constant value to use for constant mode.
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Returns
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-------
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value : double
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Pixel value at given position.
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"""
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if mode == 'C':
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if (r < 0) or (r >= rows) or (c < 0) or (c >= cols):
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return cval
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else:
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return image[r * cols * dims + c * dims + d]
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else:
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return image[coord_map(rows, r, mode) * cols * dims
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+ coord_map(cols, c, mode) * dims
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+ coord_map(dims, d, mode)]
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cdef inline Py_ssize_t coord_map(Py_ssize_t dim, long coord, char mode) nogil:
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"""Wrap a coordinate, according to a given mode.
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Parameters
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----------
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dim : int
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Maximum coordinate.
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coord : int
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Coord provided by user. May be < 0 or > dim.
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mode : {'W', 'S', 'R', 'E'}
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Whether to wrap, symmetric reflect, reflect or use the nearest
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coordinate if `coord` falls outside [0, dim).
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"""
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cdef Py_ssize_t cmax
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cmax = dim - 1
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if mode == 'S': # symmetric
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if coord < 0:
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coord = -coord - 1
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if coord > cmax:
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if <Py_ssize_t>(coord / dim) % 2 != 0:
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return <Py_ssize_t>(cmax - (coord % dim))
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else:
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return <Py_ssize_t>(coord % dim)
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elif mode == 'W': # wrap
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if coord < 0:
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return <Py_ssize_t>(cmax - ((-coord - 1) % dim))
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elif coord > cmax:
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return <Py_ssize_t>(coord % dim)
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elif mode == 'E': # edge
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if coord < 0:
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return 0
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elif coord > cmax:
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return cmax
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elif mode == 'R': # reflect (mirror)
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if coord < 0:
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# How many times times does the coordinate wrap?
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if <Py_ssize_t>(-coord / cmax) % 2 != 0:
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return cmax - <Py_ssize_t>(-coord % cmax)
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else:
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return <Py_ssize_t>(-coord % cmax)
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elif coord > cmax:
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if <Py_ssize_t>(coord / cmax) % 2 != 0:
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return <Py_ssize_t>(cmax - (coord % cmax))
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else:
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return <Py_ssize_t>(coord % cmax)
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return coord
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