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Merge pull request #1051 from ahojnnes/bicubic-interp

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Bicubic interpolation fix and reference
This commit is contained in:
Stefan van der Walt
2014-12-15 23:15:13 +02:00
parent ea95835017 00c3a978aa
commit a2a8696ee9
3 changed files with 97 additions and 111 deletions
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skimage/_shared/interpolation.pxd
+66 -56
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@@ -9,7 +9,8 @@ cdef inline Py_ssize_t round(double r):
return <Py_ssize_t>((r + 0.5) if (r > 0.0) else (r - 0.5))
cdef inline double nearest_neighbour_interpolation(double* image, Py_ssize_t rows,
cdef inline double nearest_neighbour_interpolation(double* image,
Py_ssize_t rows,
Py_ssize_t cols, double r,
double c, char mode,
double cval):
@@ -63,30 +64,33 @@ cdef inline double bilinear_interpolation(double* image, Py_ssize_t rows,
"""
cdef double dr, dc
cdef Py_ssize_t minr, minc, maxr, maxc
cdef long minr, minc, maxr, maxc
minr = <Py_ssize_t>floor(r)
minc = <Py_ssize_t>floor(c)
maxr = <Py_ssize_t>ceil(r)
maxc = <Py_ssize_t>ceil(c)
minr = <long>floor(r)
minc = <long>floor(c)
maxr = <long>ceil(r)
maxc = <long>ceil(c)
dr = r - minr
dc = c - minc
top = (1 - dc) * get_pixel2d(image, rows, cols, minr, minc, mode, cval) \
+ dc * get_pixel2d(image, rows, cols, minr, maxc, mode, cval)
bottom = (1 - dc) * get_pixel2d(image, rows, cols, maxr, minc, mode, cval) \
bottom = (1 - dc) * get_pixel2d(image, rows, cols, maxr, minc, mode,
cval) \
+ dc * get_pixel2d(image, rows, cols, maxr, maxc, mode, cval)
return (1 - dr) * top + dr * bottom
cdef inline double quadratic_interpolation(double x, double[3] f):
"""Quadratic interpolation.
"""WARNING: Do not use, not implemented correctly.
Quadratic interpolation.
Parameters
----------
x : double
Position in the interval [-1, 1].
f : double[4]
Function values at positions [-1, 0, 1].
Position in the interval [0, 2].
f : double[3]
Function values at positions [0, 2].
Returns
-------
@@ -94,13 +98,17 @@ cdef inline double quadratic_interpolation(double x, double[3] f):
Interpolated value.
"""
return f[1] - 0.25 * (f[0] - f[2]) * x
return (x * f[2] * (x - 1)) / 2 - \
x * f[1] * (x - 2) + \
(f[0] * (x - 1) * (x - 2)) / 2
cdef inline double biquadratic_interpolation(double* image, Py_ssize_t rows,
Py_ssize_t cols, double r, double c,
char mode, double cval):
"""Biquadratic interpolation at a given position in the image.
Py_ssize_t cols, double r,
double c, char mode, double cval):
"""WARNING: Do not use, not implemented correctly.
Biquadratic interpolation at a given position in the image.
Parameters
----------
@@ -122,30 +130,23 @@ cdef inline double biquadratic_interpolation(double* image, Py_ssize_t rows,
"""
cdef Py_ssize_t r0 = round(r)
cdef Py_ssize_t c0 = round(c)
if r < 0:
r0 -= 1
if c < 0:
c0 -= 1
# scale position to range [-1, 1]
cdef double xr = (r - r0) - 1
cdef double xc = (c - c0) - 1
if r == r0:
xr += 1
if c == c0:
xc += 1
cdef long r0 = <long>round(r) - 1
cdef long c0 = <long>round(c) - 1
cdef double xr = r - r0
cdef double xc = c - c0
cdef double fc[3]
cdef double fr[3]
cdef Py_ssize_t pr, pc
cdef long pr, pc
# row-wise cubic interpolation
for pr in range(r0, r0 + 3):
for pc in range(c0, c0 + 3):
fc[pc - c0] = get_pixel2d(image, rows, cols, pr, pc, mode, cval)
fr[pr - r0] = quadratic_interpolation(xc, fc)
for pr in range(3):
for pc in range(3):
fc[pc] = get_pixel2d(image, rows, cols,
r0 + pr, c0 + pc, mode, cval)
fr[pr] = quadratic_interpolation(xc, fc)
# cubic interpolation for interpolated values of each row
return quadratic_interpolation(xr, fr)
@@ -159,7 +160,7 @@ cdef inline double cubic_interpolation(double x, double[4] f):
x : double
Position in the interval [0, 1].
f : double[4]
Function values at positions [0, 1/3, 2/3, 1].
Function values at positions [-1, 0, 1, 2].
Returns
-------
@@ -179,6 +180,9 @@ cdef inline double bicubic_interpolation(double* image, Py_ssize_t rows,
char mode, double cval):
"""Bicubic interpolation at a given position in the image.
Interpolation using Catmull-Rom splines, based on the bicubic convolution
algorithm described in [1]_.
Parameters
----------
image : double array
@@ -197,35 +201,42 @@ cdef inline double bicubic_interpolation(double* image, Py_ssize_t rows,
value : double
Interpolated value.
References
----------
.. [1] R. Keys, (1981). "Cubic convolution interpolation for digital image
processing". IEEE Transactions on Signal Processing, Acoustics,
Speech, and Signal Processing 29 (6): 1153–1160.
"""
cdef Py_ssize_t r0 = <Py_ssize_t>r - 1
cdef Py_ssize_t c0 = <Py_ssize_t>c - 1
if r < 0:
r0 -= 1
if c < 0:
c0 -= 1
cdef long r0 = <long>floor(r)
cdef long c0 = <long>floor(c)
# scale position to range [0, 1]
cdef double xr = (r - r0) / 3
cdef double xc = (c - c0) / 3
cdef double xr = r - r0
cdef double xc = c - c0
r0 -= 1
c0 -= 1
cdef double fc[4]
cdef double fr[4]
cdef Py_ssize_t pr, pc
cdef long pr, pc
# row-wise cubic interpolation
for pr in range(r0, r0 + 4):
for pc in range(c0, c0 + 4):
fc[pc - c0] = get_pixel2d(image, rows, cols, pr, pc, mode, cval)
fr[pr - r0] = cubic_interpolation(xc, fc)
for pr in range(4):
for pc in range(4):
fc[pc] = get_pixel2d(image, rows, cols, pr + r0, pc + c0, mode, cval)
fr[pr] = cubic_interpolation(xc, fc)
# cubic interpolation for interpolated values of each row
return cubic_interpolation(xr, fr)
cdef inline double get_pixel2d(double* image, Py_ssize_t rows, Py_ssize_t cols,
Py_ssize_t r, Py_ssize_t c, char mode, double cval):
long r, long c, char mode,
double cval):
"""Get a pixel from the image, taking wrapping mode into consideration.
Parameters
@@ -248,7 +259,7 @@ cdef inline double get_pixel2d(double* image, Py_ssize_t rows, Py_ssize_t cols,
"""
if mode == 'C':
if (r < 0) or (r > rows - 1) or (c < 0) or (c > cols - 1):
if (r < 0) or (r >= rows) or (c < 0) or (c >= cols):
return cval
else:
return image[r * cols + c]
@@ -257,8 +268,8 @@ cdef inline double get_pixel2d(double* image, Py_ssize_t rows, Py_ssize_t cols,
cdef inline double get_pixel3d(double* image, Py_ssize_t rows, Py_ssize_t cols,
Py_ssize_t dims, Py_ssize_t r, Py_ssize_t c, Py_ssize_t d,
char mode, double cval):
Py_ssize_t dims, long r, long c,
long d, char mode, double cval):
"""Get a pixel from the image, taking wrapping mode into consideration.
Parameters
@@ -281,19 +292,18 @@ cdef inline double get_pixel3d(double* image, Py_ssize_t rows, Py_ssize_t cols,
"""
if mode == 'C':
if (r < 0) or (r > rows - 1) or (c < 0) or (c > cols - 1):
if (r < 0) or (r >= rows) or (c < 0) or (c >= cols):
return cval
else:
return image[r * cols * dims + c * dims + d]
else:
return image[coord_map(rows, r, mode) * cols * dims
+ coord_map(cols, c, mode) * dims
+ d]
+ coord_map(dims, d, mode)]
cdef inline Py_ssize_t coord_map(Py_ssize_t dim, Py_ssize_t coord, char mode):
"""
Wrap a coordinate, according to a given mode.
cdef inline Py_ssize_t coord_map(Py_ssize_t dim, long coord, char mode):
"""Wrap a coordinate, according to a given mode.
Parameters
----------