/*****************************************************************************
Major portions of this software are copyrighted by the Medical College
of Wisconsin, 1994-2000, and are released under the Gnu General Public
License, Version 2. See the file README.Copyright for details.
******************************************************************************/
#include "mrilib.h"
/*** NOT 7D SAFE ***/
#define FINS(i,j) ( ( (i)<0 || (j)<0 || (i)>=nx || (j)>=ny ) \
? 0.0 : far[(i)+(j)*nx] )
/** option to precompute cubic interpolation weights **/
#undef USE_CGRID
#ifdef USE_CGRID
# define CGRID 8192
static int p_first = 1 ;
static float p_m1[CGRID+1], p_00[CGRID+1],
p_p1[CGRID+1], p_p2[CGRID+1] ;
#endif
/* cubic interpolation polynomials */
#define P_M1(x) ((x)*(1.0-(x))*((x)-2.0))
#define P_00(x) (3.0*((x)+1.0)*((x)-1.0)*((x)-2.0))
#define P_P1(x) (3.0*(x)*((x)+1.0)*(2.0-(x)))
#define P_P2(x) ((x)*((x)+1.0)*((x)-1.0))
/**-------------------------------------------------------------------
Rotate and shift an image, using bicubic interpolation:
aa = shift in x
bb = shift in y
phi = angle in radians
Sort of a replacement for mri_rotate in mri_warp.c; supposed
to be faster. If the input image is MRI_complex, the output
will be also; otherwise, the output will be MRI_float.
----------------------------------------------------------------------**/
MRI_IMAGE *mri_rota( MRI_IMAGE *im, float aa, float bb, float phi )
{
float rot_dx , rot_dy , rot_cph , rot_sph , top,bot,val ;
MRI_IMAGE *imfl , *newImg ;
MRI_IMARR *impair ;
float *far , *nar ;
float xx,yy , fx,fy ;
int ii,jj, nx,ny , ix,jy , ifx,jfy ;
float f_jm1,f_j00,f_jp1,f_jp2 , wt_m1,wt_00,wt_p1,wt_p2 ;
#ifdef USE_CGRID
if( p_first ){
p_first = 0 ;
xx = 1.0 / CGRID ;
for( ii=0 ; ii <= CGRID ; ii++ ){
yy = ii * xx ;
p_m1[ii] = P_M1(yy) ;
p_00[ii] = P_00(yy) ;
p_p1[ii] = P_P1(yy) ;
p_p2[ii] = P_P2(yy) ;
}
}
#endif
if( im == NULL || ! MRI_IS_2D(im) ){
fprintf(stderr,"*** mri_rota only works on 2D images!\n") ; EXIT(1) ;
}
/** if complex image, break into pairs, do each separately, put back together **/
if( im->kind == MRI_complex ){
MRI_IMARR *impair ;
MRI_IMAGE * rim , * iim , * tim ;
impair = mri_complex_to_pair( im ) ;
if( impair == NULL ){
fprintf(stderr,"*** mri_complex_to_pair fails in mri_rota!\n") ; EXIT(1) ;
}
rim = IMAGE_IN_IMARR(impair,0) ;
iim = IMAGE_IN_IMARR(impair,1) ; FREE_IMARR(impair) ;
tim = mri_rota( rim , aa,bb,phi ) ; mri_free( rim ) ; rim = tim ;
tim = mri_rota( iim , aa,bb,phi ) ; mri_free( iim ) ; iim = tim ;
newImg = mri_pair_to_complex( rim , iim ) ;
mri_free( rim ) ; mri_free( iim ) ;
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
/** rotation params **/
rot_cph = cos(phi) ; rot_sph = sin(phi) ;
rot_dx = (0.5 * im->nx) * (1.0-rot_cph) - aa*rot_cph - bb*rot_sph
-(0.5 * im->ny) * rot_sph ;
rot_dy = (0.5 * im->nx) * rot_sph + aa*rot_sph - bb*rot_cph
+(0.5 * im->ny) * (1.0-rot_cph) ;
/** other initialization **/
nx = im->nx ; /* image dimensions */
ny = im->ny ;
if( im->kind == MRI_float ) imfl = im ;
else imfl = mri_to_float( im ) ;
far = MRI_FLOAT_PTR(imfl) ; /* access to float data */
newImg = mri_new( nx , nx , MRI_float ) ; /* output image */
nar = MRI_FLOAT_PTR(newImg) ; /* output image data */
bot = top = far[0] ;
for( ii=0 ; ii < nx*ny ; ii++ )
if( far[ii] < bot ) bot = far[ii] ;
else if( far[ii] > top ) top = far[ii] ;
/*** loop over output points and warp to them ***/
for( jj=0 ; jj < nx ; jj++ ){
xx = rot_sph * jj + rot_dx - rot_cph ;
yy = rot_cph * jj + rot_dy + rot_sph ;
for( ii=0 ; ii < nx ; ii++ ){
xx += rot_cph ; /* get x,y in original image */
yy -= rot_sph ;
ix = (xx >= 0.0) ? ((int) xx) : ((int) xx)-1 ; /* floor */
jy = (yy >= 0.0) ? ((int) yy) : ((int) yy)-1 ;
#ifdef USE_CGRID
ifx = (xx-ix)*CGRID + 0.499 ;
wt_m1 = p_m1[ifx] ; wt_00 = p_00[ifx] ;
wt_p1 = p_p1[ifx] ; wt_p2 = p_p2[ifx] ;
#else
fx = xx-ix ;
wt_m1 = P_M1(fx) ; wt_00 = P_00(fx) ;
wt_p1 = P_P1(fx) ; wt_p2 = P_P2(fx) ;
#endif
if( ix > 0 && ix < nx-2 && jy > 0 && jy < ny-2 ){
float * fym1, *fy00 , *fyp1 , *fyp2 ;
fym1 = far + (ix-1 + (jy-1)*nx) ;
fy00 = fym1 + nx ;
fyp1 = fy00 + nx ;
fyp2 = fyp1 + nx ;
f_jm1 = wt_m1 * fym1[0] + wt_00 * fym1[1]
+ wt_p1 * fym1[2] + wt_p2 * fym1[3] ;
f_j00 = wt_m1 * fy00[0] + wt_00 * fy00[1]
+ wt_p1 * fy00[2] + wt_p2 * fy00[3] ;
f_jp1 = wt_m1 * fyp1[0] + wt_00 * fyp1[1]
+ wt_p1 * fyp1[2] + wt_p2 * fyp1[3] ;
f_jp2 = wt_m1 * fyp2[0] + wt_00 * fyp2[1]
+ wt_p1 * fyp2[2] + wt_p2 * fyp2[3] ;
} else {
f_jm1 = wt_m1 * FINS(ix-1,jy-1)
+ wt_00 * FINS(ix ,jy-1)
+ wt_p1 * FINS(ix+1,jy-1)
+ wt_p2 * FINS(ix+2,jy-1) ;
f_j00 = wt_m1 * FINS(ix-1,jy)
+ wt_00 * FINS(ix ,jy)
+ wt_p1 * FINS(ix+1,jy)
+ wt_p2 * FINS(ix+2,jy) ;
f_jp1 = wt_m1 * FINS(ix-1,jy+1)
+ wt_00 * FINS(ix ,jy+1)
+ wt_p1 * FINS(ix+1,jy+1)
+ wt_p2 * FINS(ix+2,jy+1) ;
f_jp2 = wt_m1 * FINS(ix-1,jy+2)
+ wt_00 * FINS(ix ,jy+2)
+ wt_p1 * FINS(ix+1,jy+2)
+ wt_p2 * FINS(ix+2,jy+2) ;
}
#define THIRTYSIX 2.7777778e-2 /* 1./36.0, actually */
#ifdef USE_CGRID
jfy = (yy-jy)*CGRID + 0.499 ;
val = ( p_m1[jfy] * f_jm1 + p_00[jfy] * f_j00
+ p_p1[jfy] * f_jp1 + p_p2[jfy] * f_jp2 ) * THIRTYSIX ;
#else
fy = yy-jy ;
val = ( P_M1(fy) * f_jm1 + P_00(fy) * f_j00
+ P_P1(fy) * f_jp1 + P_P2(fy) * f_jp2 ) * THIRTYSIX ;
#endif
if( val < bot ) nar[ii+jj*nx] = bot ; /* too small! */
else if( val > top ) nar[ii+jj*nx] = top ; /* too big! */
else nar[ii+jj*nx] = val ; /* just right */
}
}
/*** cleanup and return ***/
if( im != imfl ) mri_free(imfl) ; /* throw away unneeded workspace */
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
/**-------------------------------------------------------------------
Rotate and shift an image, using bilinear interpolation:
aa = shift in x
bb = shift in y
phi = angle in radians
Sort of a replacement for mri_rotate in mri_warp.c; supposed
to be faster. If the input image is MRI_complex, the output
will be also; otherwise, the output will be MRI_float.
----------------------------------------------------------------------**/
MRI_IMAGE *mri_rota_bilinear( MRI_IMAGE *im, float aa, float bb, float phi )
{
float rot_dx , rot_dy , rot_cph , rot_sph ;
MRI_IMAGE *imfl , *newImg ;
MRI_IMARR *impair ;
float *far , *nar ;
float xx,yy , fx,fy ;
int ii,jj, nx,ny , ix,jy ;
float f_j00,f_jp1 , wt_00,wt_p1 ;
if( im == NULL || ! MRI_IS_2D(im) ){
fprintf(stderr,"*** mri_rota_bilinear only works on 2D images!\n") ; EXIT(1) ;
}
/** if complex image, break into pairs, do each separately, put back together **/
if( im->kind == MRI_complex ){
MRI_IMARR *impair ;
MRI_IMAGE * rim , * iim , * tim ;
impair = mri_complex_to_pair( im ) ;
if( impair == NULL ){
fprintf(stderr,"*** mri_complex_to_pair fails in mri_rota!\n") ; EXIT(1) ;
}
rim = IMAGE_IN_IMARR(impair,0) ;
iim = IMAGE_IN_IMARR(impair,1) ; FREE_IMARR(impair) ;
tim = mri_rota_bilinear( rim , aa,bb,phi ) ; mri_free( rim ) ; rim = tim ;
tim = mri_rota_bilinear( iim , aa,bb,phi ) ; mri_free( iim ) ; iim = tim ;
newImg = mri_pair_to_complex( rim , iim ) ;
mri_free( rim ) ; mri_free( iim ) ;
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
/** rotation params **/
rot_cph = cos(phi) ; rot_sph = sin(phi) ;
rot_dx = (0.5 * im->nx) * (1.0-rot_cph) - aa*rot_cph - bb*rot_sph
-(0.5 * im->ny) * rot_sph ;
rot_dy = (0.5 * im->nx) * rot_sph + aa*rot_sph - bb*rot_cph
+(0.5 * im->ny) * (1.0-rot_cph) ;
/** other initialization **/
nx = im->nx ; /* image dimensions */
ny = im->ny ;
if( im->kind == MRI_float ) imfl = im ;
else imfl = mri_to_float( im ) ;
far = MRI_FLOAT_PTR(imfl) ; /* access to float data */
newImg = mri_new( nx , nx , MRI_float ) ; /* output image */
nar = MRI_FLOAT_PTR(newImg) ; /* output image data */
/*** loop over output points and warp to them ***/
for( jj=0 ; jj < nx ; jj++ ){
xx = rot_sph * jj + rot_dx - rot_cph ;
yy = rot_cph * jj + rot_dy + rot_sph ;
for( ii=0 ; ii < nx ; ii++ ){
xx += rot_cph ; /* get x,y in original image */
yy -= rot_sph ;
ix = (xx >= 0.0) ? ((int) xx) : ((int) xx)-1 ; /* floor */
jy = (yy >= 0.0) ? ((int) yy) : ((int) yy)-1 ;
fx = xx-ix ; wt_00 = 1.0 - fx ; wt_p1 = fx ;
if( ix >= 0 && ix < nx-1 && jy >= 0 && jy < ny-1 ){
float *fy00 , *fyp1 ;
fy00 = far + (ix + jy*nx) ; fyp1 = fy00 + nx ;
f_j00 = wt_00 * fy00[0] + wt_p1 * fy00[1] ;
f_jp1 = wt_00 * fyp1[0] + wt_p1 * fyp1[1] ;
} else {
f_j00 = wt_00 * FINS(ix,jy ) + wt_p1 * FINS(ix+1,jy ) ;
f_jp1 = wt_00 * FINS(ix,jy+1) + wt_p1 * FINS(ix+1,jy+1) ;
}
fy = yy-jy ; nar[ii+jj*nx] = (1.0-fy) * f_j00 + fy * f_jp1 ;
}
}
/*** cleanup and return ***/
if( im != imfl ) mri_free(imfl) ; /* throw away unneeded workspace */
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
/*--------------------------------------------------------------------------
Routines to rotate using FFTs and the shearing transformation
----------------------------------------------------------------------------*/
/*** Shift 2 rows at a time with the FFT ***/
void ft_shift2( int n, int nup, float af, float * f, float ag, float * g )
{
static int nupold=0 ;
static complex * row=NULL , * cf=NULL , * cg=NULL ;
int ii , nby2=nup/2 , n21=nby2+1 ;
complex fac , gac ;
float sf , sg , dk ;
/* make new memory for row storage? */
if( nup > nupold ){
if( row != NULL ){ free(row) ; free(cf) ; free(cg) ; }
row = (complex *) malloc( sizeof(complex) * nup ) ;
cf = (complex *) malloc( sizeof(complex) * n21 ) ;
cg = (complex *) malloc( sizeof(complex) * n21 ) ;
nupold = nup ;
}
/* FFT the pair of rows */
for( ii=0 ; ii < n ; ii++ ){ row[ii].r = f[ii] ; row[ii].i = g[ii] ; }
for( ; ii < nup ; ii++ ){ row[ii].r = row[ii].i = 0.0 ; }
csfft_cox( -1 , nup , row ) ;
/* untangle FFT coefficients from row into cf,cg */
cf[0].r = 2.0 * row[0].r ; cf[0].i = 0.0 ; /* twice too big */
cg[0].r = 2.0 * row[0].i ; cg[0].i = 0.0 ;
for( ii=1 ; ii < nby2 ; ii++ ){
cf[ii].r = row[ii].r + row[nup-ii].r ;
cf[ii].i = row[ii].i - row[nup-ii].i ;
cg[ii].r = row[ii].i + row[nup-ii].i ;
cg[ii].i = -row[ii].r + row[nup-ii].r ;
}
cf[nby2].r = 2.0 * row[nby2].r ; cf[nby2].i = 0.0 ;
cg[nby2].r = 2.0 * row[nby2].i ; cg[nby2].i = 0.0 ;
/* phase shift both rows (cf,cg) */
dk = (2.0*PI) / nup ;
sf = -af * dk ; sg = -ag * dk ;
for( ii=1 ; ii <= nby2 ; ii++ ){
fac = CEXPIT(ii*sf) ; cf[ii] = CMULT( fac , cf[ii] ) ;
gac = CEXPIT(ii*sg) ; cg[ii] = CMULT( gac , cg[ii] ) ;
}
cf[nby2].i = 0.0 ; cg[nby2].i = 0.0 ;
/* retangle the coefficients from 2 rows */
row[0].r = cf[0].r ; row[0].i = cg[0].r ;
for( ii=1 ; ii < nby2 ; ii++ ){
row[ii].r = cf[ii].r - cg[ii].i ;
row[ii].i = cf[ii].i + cg[ii].r ;
row[nup-ii].r = cf[ii].r + cg[ii].i ;
row[nup-ii].i = -cf[ii].i + cg[ii].r ;
}
row[nby2].r = cf[nby2].r ;
row[nby2].i = cg[nby2].r ;
/* inverse FFT and store back in output arrays */
csfft_cox( 1 , nup , row ) ;
sf = 0.5 / nup ; /* 0.5 to allow for twice too big above */
for( ii=0 ; ii < n ; ii++ ){
f[ii] = sf * row[ii].r ; g[ii] = sf * row[ii].i ;
}
return ;
}
/*** Shear in the x-direction ***/
void ft_xshear( float a , float b , int nx , int ny , float * f )
{
int jj , nxup ;
float * fj0 , * fj1 , * zz=NULL ;
float a0 , a1 ;
if( a == 0.0 && b == 0.0 ) return ; /* nothing to do */
if( nx < 2 || ny < 1 || f == NULL ) return ; /* nothing to operate on */
if( ny%2 == 1 ){ /* we work in pairs, so */
zz = (float *) malloc( sizeof(float)*nx ) ; /* if not an even number */
for( jj=0 ; jj < nx ; jj++ ) zz[jj] = 0.0 ; /* of rows, make an extra */
}
nxup = nx ; /* min FFT length */
jj = 2 ; while( jj < nxup ){ jj *= 2 ; } /* next power of 2 larger */
nxup = jj ;
for( jj=0 ; jj < ny ; jj+=2 ){ /* shear rows in pairs */
fj0 = f + (jj*nx) ; /* row 0 */
fj1 = (jj < ny-1) ? (fj0 + nx) : zz ; /* row 1 */
a0 = a*(jj-0.5*ny) + b ; /* phase ramp for row 0 */
a1 = a0 + a ; /* phase ramp for row 1 */
ft_shift2( nx , nxup , a0 , fj0 , a1 , fj1 ) ;
}
if( zz != NULL ) free(zz) ; /* toss the trash */
return ;
}
/*** Shear in the y direction ***/
void ft_yshear( float a , float b , int nx , int ny , float * f )
{
int jj , nyup , ii ;
float * fj0 , * fj1 ;
float a0 , a1 ;
if( a == 0.0 && b == 0.0 ) return ; /* nothing to do */
if( ny < 2 || nx < 1 || f == NULL ) return ; /* nothing to operate on */
/* make memory for a pair of columns */
fj0 = (float *) malloc( sizeof(float) * 2*ny ) ; fj1 = fj0 + ny ;
nyup = ny ; /* min FFT length */
jj = 2 ; while( jj < nyup ){ jj *= 2 ; } /* next power of 2 larger */
nyup = jj ;
for( jj=0 ; jj < nx ; jj+=2 ){ /* shear rows in pairs */
if( jj < nx-1 ){
for( ii=0; ii < ny; ii++ ){ fj0[ii] = f[jj+ii*nx]; fj1[ii] = f[jj+1+ii*nx]; }
} else {
for( ii=0; ii < ny; ii++ ){ fj0[ii] = f[jj+ii*nx]; fj1[ii] = 0.0; }
}
a0 = a*(jj-0.5*nx) + b ; /* phase ramp for row 0 */
a1 = a0 + a ; /* phase ramp for row 1 */
ft_shift2( ny , nyup , a0 , fj0 , a1 , fj1 ) ;
if( jj < nx-1 ){
for( ii=0; ii < ny; ii++ ){ f[jj+ii*nx] = fj0[ii]; f[jj+1+ii*nx] = fj1[ii]; }
} else {
for( ii=0; ii < ny; ii++ ){ f[jj+ii*nx] = fj0[ii]; }
}
}
free(fj0) ; return ;
}
/*** Image rotation using 3 shears ***/
MRI_IMAGE * mri_rota_shear( MRI_IMAGE *im, float aa, float bb, float phi )
{
double cph , sph ;
float a , b , bot,top ;
MRI_IMAGE *flim ;
float *flar ;
int ii , nxy ;
if( im == NULL || ! MRI_IS_2D(im) ){
fprintf(stderr,"*** mri_rota_shear only works on 2D images!\n") ; EXIT(1) ;
}
/** if complex image, break into pairs, do each separately, put back together **/
if( im->kind == MRI_complex ){
MRI_IMARR *impair ;
MRI_IMAGE * rim , * iim , * tim ;
impair = mri_complex_to_pair( im ) ;
if( impair == NULL ){
fprintf(stderr,"*** mri_complex_to_pair fails in mri_rota!\n") ; EXIT(1) ;
}
rim = IMAGE_IN_IMARR(impair,0) ;
iim = IMAGE_IN_IMARR(impair,1) ; FREE_IMARR(impair) ;
tim = mri_rota_shear( rim , aa,bb,phi ) ; mri_free( rim ) ; rim = tim ;
tim = mri_rota_shear( iim , aa,bb,phi ) ; mri_free( iim ) ; iim = tim ;
flim = mri_pair_to_complex( rim , iim ) ;
mri_free( rim ) ; mri_free( iim ) ;
MRI_COPY_AUX(flim,im) ;
return flim ;
}
/** copy input to output **/
flim = mri_to_float( im ) ;
flar = MRI_FLOAT_PTR( flim ) ;
/* find range of image data */
bot = top = flar[0] ; nxy = im->nx * im->ny ;
for( ii=1 ; ii < nxy ; ii++ )
if( flar[ii] < bot ) bot = flar[ii] ;
else if( flar[ii] > top ) top = flar[ii] ;
/** rotation params **/
cph = cos(phi) ; sph = sin(phi) ;
/* More than 90 degrees?
Must be reduced to less than 90 degrees by a 180 degree flip. */
if( cph < 0.0 ){
int ii , jj , top , nx=flim->nx , ny=flim->ny ;
float val ;
top = (nx+1)/2 ;
for( jj=0 ; jj < ny ; jj++ ){
for( ii=1 ; ii < top ; ii++ ){
val = flar[jj*nx+ii] ;
flar[jj*nx+ii] = flar[jj*nx+nx-ii] ;
flar[jj*nx+nx-ii] = val ;
}
}
top = (ny+1)/2 ;
for( ii=0 ; ii < nx ; ii++ ){
for( jj=1 ; jj < top ; jj++ ){
val = flar[ii+jj*nx] ;
flar[ii+jj*nx] = flar[ii+(ny-jj)*nx] ;
flar[ii+(ny-jj)*nx] = val ;
}
}
cph = -cph ; sph = -sph ;
}
/* compute shear factors for each direction */
b = sph ;
a = (b != 0.0 ) ? ((cph - 1.0) / b) : (0.0) ;
/* shear thrice */
ft_xshear( a , 0.0 , im->nx , im->ny , flar ) ;
ft_yshear( b , bb , im->nx , im->ny , flar ) ;
ft_xshear( a , aa - a*bb , im->nx , im->ny , flar ) ;
/* make sure data does not go out of original range */
for( ii=0 ; ii < nxy ; ii++ )
if( flar[ii] < bot ) flar[ii] = bot ;
else if( flar[ii] > top ) flar[ii] = top ;
return flim ;
}
MRI_IMAGE * mri_rota_variable( int mode, MRI_IMAGE *im, float aa, float bb, float phi )
{
switch(mode){
default:
case MRI_BICUBIC: return mri_rota( im,aa,bb,phi ) ;
case MRI_BILINEAR: return mri_rota_bilinear( im,aa,bb,phi ) ;
case MRI_FOURIER: return mri_rota_shear( im,aa,bb,phi ) ;
}
}
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