/**
SamplesToCoefficients.<br>
Implement the algorithm that converts the image samples into B-spline coefficients.
This efficient procedure essentially relies on the three papers cited above;
data are processed in-place.
Even though this algorithm is robust with respect to quantization,
we advocate the use of a floating-point format for the data.
@param Image Input / Output image (in-place processing)
@param Width Width of the image
@param Height Height of the image
@param spline_degree Degree of the spline model
@return Returns true if success, false otherwise
*/
static bool
SamplesToCoefficients(double *Image, long Width, long Height, long spline_degree) {
double *Line;
double Pole[2];
long NbPoles;
long x, y;
// recover the poles from a lookup table
switch (spline_degree) {
case 2L:
NbPoles = 1L;
Pole[0] = sqrt(8.0) - 3.0;
break;
case 3L:
NbPoles = 1L;
Pole[0] = sqrt(3.0) - 2.0;
break;
case 4L:
NbPoles = 2L;
Pole[0] = sqrt(664.0 - sqrt(438976.0)) + sqrt(304.0) - 19.0;
Pole[1] = sqrt(664.0 + sqrt(438976.0)) - sqrt(304.0) - 19.0;
break;
case 5L:
NbPoles = 2L;
Pole[0] = sqrt(135.0 / 2.0 - sqrt(17745.0 / 4.0)) + sqrt(105.0 / 4.0)
- 13.0 / 2.0;
Pole[1] = sqrt(135.0 / 2.0 + sqrt(17745.0 / 4.0)) - sqrt(105.0 / 4.0)
- 13.0 / 2.0;
break;
default:
// Invalid spline degree
return false;
}
// convert the image samples into interpolation coefficients
// in-place separable process, along x
Line = (double *)malloc(Width * sizeof(double));
if (Line == NULL) {
// Row allocation failed
return false;
}
for (y = 0L; y < Height; y++) {
GetRow(Image, y, Line, Width);
ConvertToInterpolationCoefficients(Line, Width, Pole, NbPoles, DBL_EPSILON);
PutRow(Image, y, Line, Width);
}
free(Line);
// in-place separable process, along y
Line = (double *)malloc(Height * sizeof(double));
if (Line == NULL) {
// Column allocation failed
return false;
}
for (x = 0L; x < Width; x++) {
GetColumn(Image, Width, x, Line, Height);
ConvertToInterpolationCoefficients(Line, Height, Pole, NbPoles, DBL_EPSILON);
PutColumn(Image, Width, x, Line, Height);
}
free(Line);
return true;
}
/*--------------------------------------------------------------------------*/
int SamplesToCoefficients
(
MRI *mri_vol, /* in-place processing */
long SplineDegree /* degree of the spline model */
)
{ /* begin SamplesToCoefficients */
double *Line;
double Pole[2];
long NbPoles;
long x, y, z;
long Width, Height, Depth;
/* recover the poles from a lookup table */
switch (SplineDegree)
{
case 2L:
NbPoles = 1L;
Pole[0] = sqrt(8.0) - 3.0;
break;
case 3L:
NbPoles = 1L;
Pole[0] = sqrt(3.0) - 2.0;
break;
case 4L:
NbPoles = 2L;
Pole[0] = sqrt(664.0 - sqrt(438976.0)) + sqrt(304.0) - 19.0;
Pole[1] = sqrt(664.0 + sqrt(438976.0)) - sqrt(304.0) - 19.0;
break;
case 5L:
NbPoles = 2L;
Pole[0] = sqrt(135.0 / 2.0 - sqrt(17745.0 / 4.0)) + sqrt(105.0 / 4.0)
- 13.0 / 2.0;
Pole[1] = sqrt(135.0 / 2.0 + sqrt(17745.0 / 4.0)) - sqrt(105.0 / 4.0)
- 13.0 / 2.0;
break;
default:
printf("Invalid spline degree\n");
return(1);
}
Width = mri_vol->width;
Height = mri_vol->height;
Depth = mri_vol->depth;
/* convert the image samples into interpolation coefficients */
/* in-place separable process, along x */
Line = (double *)malloc((size_t)(Width * (long)sizeof(double)));
if (Line == (double *)NULL)
{
printf("Row allocation failed\n");
return(1);
}
for (z = 0L; z < Depth; z++)
{
for (y = 0L; y < Height; y++)
{
GetRow(mri_vol, y, z, Line);
ConvertToInterpolationCoefficients(Line, Width, Pole, NbPoles, DBL_EPSILON);
PutRow(mri_vol, y, z, Line);
}
}
free(Line);
/* in-place separable process, along y */
Line = (double *)malloc((size_t)(Height * (long)sizeof(double)));
if (Line == (double *)NULL)
{
printf("Column allocation failed\n");
return(1);
}
for (z = 0L; z < Depth; z++)
{
for (x = 0L; x < Width; x++)
{
GetColumn(mri_vol, x, z, Line);
ConvertToInterpolationCoefficients(Line, Height, Pole, NbPoles, DBL_EPSILON);
PutColumn(mri_vol, x, z, Line);
}
}
free(Line);
/* in-place separable process, along z */
Line = (double *)malloc((size_t)(Depth * (long)sizeof(double)));
if (Line == (double *)NULL)
{
printf("Column allocation failed\n");
return(1);
}
for (y = 0L; y < Height; y++)
{
for (x = 0L; x < Width; x++)
{
GetVertical(mri_vol, x, y, Line);
ConvertToInterpolationCoefficients(Line, Depth, Pole, NbPoles, DBL_EPSILON);
PutVertical(mri_vol, x, y, Line);
}
}
free(Line);
return(0);
} /* end SamplesToCoefficients */
