V1 Readme + rangement
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1339 changed files with 248781 additions and 4282 deletions
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// Authors: Unknown. Please, if you are the author of this file, or if you
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// know who are the authors of this file, let us know, so we can give the
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// adequate credits and/or get the adequate authorizations.
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#include "splines.h"
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double initcausal(double *c,int n,double z)
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{
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double zk,z2k,iz,sum;
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int k;
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zk = z; iz = 1./z;
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z2k = pow(z,(double)n-1.);
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sum = c[0] + z2k * c[n-1];
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z2k = z2k*z2k*iz;
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for (k=1;k<=n-2;k++) {
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sum += (zk+z2k)*c[k];
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zk *= z;
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z2k *= iz;
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}
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return (sum/(1.-zk*zk));
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}
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double initanticausal(double *c,int n,double z)
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{
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return((z/(z*z-1.))*(z*c[n-2]+c[n-1]));
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}
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void invspline1D(double *c,int size,double *z,int npoles)
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{
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double lambda;
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int n,k;
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/* normalization */
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for (k=npoles,lambda=1.;k--;) lambda *= (1.-z[k])*(1.-1./z[k]);
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for (n=size;n--;) c[n] *= lambda;
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/*----- Loop on poles -----*/
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for (k=0;k<npoles;k++) {
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/* forward recursion */
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c[0] = initcausal(c,size,z[k]);
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for (n=1;n<size;n++)
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c[n] += z[k]*c[n-1];
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/* backwards recursion */
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c[size-1] = initanticausal(c,size,z[k]);
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for (n=size-1;n--;)
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c[n] = z[k]*(c[n+1]-c[n]);
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}
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}
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/*------------------------------ MAIN MODULE ------------------------------*/
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// void finvspline(float *in,int order,float *out, int width, int height)
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// Guoshen Yu, 2010.09.21, Windows version
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void finvspline(vector<float> &in,int order,vector<float>& out, int width, int height)
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// void finvspline(float *in,int order,float *out, int width, int height)
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{
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double *c,*d,z[5];
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int npoles,nx,ny,x,y;
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ny = height; nx = width;
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/* initialize poles of associated z-filter */
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switch (order)
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{
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case 2: z[0]=-0.17157288; /* sqrt(8)-3 */
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break;
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case 3: z[0]=-0.26794919; /* sqrt(3)-2 */
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break;
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case 4: z[0]=-0.361341; z[1]=-0.0137254;
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break;
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case 5: z[0]=-0.430575; z[1]=-0.0430963;
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break;
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case 6: z[0]=-0.488295; z[1]=-0.0816793; z[2]=-0.00141415;
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break;
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case 7: z[0]=-0.53528; z[1]=-0.122555; z[2]=-0.00914869;
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break;
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case 8: z[0]=-0.574687; z[1]=-0.163035; z[2]=-0.0236323; z[3]=-0.000153821;
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break;
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case 9: z[0]=-0.607997; z[1]=-0.201751; z[2]=-0.0432226; z[3]=-0.00212131;
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break;
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case 10: z[0]=-0.636551; z[1]=-0.238183; z[2]=-0.065727; z[3]=-0.00752819;
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z[4]=-0.0000169828;
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break;
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case 11: z[0]=-0.661266; z[1]=-0.27218; z[2]=-0.0897596; z[3]=-0.0166696;
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z[4]=-0.000510558;
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break;
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default:
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printf("finvspline: order should be in 2..11.\n");
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exit(-1);
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}
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npoles = order/2;
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/* initialize double array containing image */
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c = (double *)malloc(nx*ny*sizeof(double));
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d = (double *)malloc(nx*ny*sizeof(double));
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for (x=nx*ny;x--;)
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c[x] = (double)in[x];
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/* apply filter on lines */
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for (y=0;y<ny;y++)
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invspline1D(c+y*nx,nx,z,npoles);
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/* transpose */
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for (x=0;x<nx;x++)
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for (y=0;y<ny;y++)
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d[x*ny+y] = c[y*nx+x];
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/* apply filter on columns */
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for (x=0;x<nx;x++)
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invspline1D(d+x*ny,ny,z,npoles);
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/* transpose directy into image */
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for (x=0;x<nx;x++)
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for (y=0;y<ny;y++)
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out[y*nx+x] = (float)(d[x*ny+y]);
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/* free array */
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free(d);
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free(c);
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}
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/* extract image value (even outside image domain) */
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//float v(float *in,int x,int y,float bg, int width, int height)
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// Guoshen Yu, 2010.09.21, Windows version
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float v(vector<float>& in,int x,int y,float bg, int width, int height)
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// float v(float *in, int x,int y,float bg, int width, int height)
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{
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if (x<0 || x>=width || y<0 || y>=height)
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return(bg); else return(in[y*width+x]);
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}
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/* c[] = values of interpolation function at ...,t-2,t-1,t,t+1,... */
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/* coefficients for cubic interpolant (Keys' function) */
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void keys(float *c,float t,float a)
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{
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float t2,at;
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t2 = t*t;
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at = a*t;
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c[0] = a*t2*(1.0-t);
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c[1] = (2.0*a+3.0 - (a+2.0)*t)*t2 - at;
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c[2] = ((a+2.0)*t - a-3.0)*t2 + 1.0;
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c[3] = a*(t-2.0)*t2 + at;
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}
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/* coefficients for cubic spline */
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void spline3(float *c,float t)
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{
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float tmp;
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tmp = 1.-t;
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c[0] = 0.1666666666*t*t*t;
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c[1] = 0.6666666666-0.5*tmp*tmp*(1.+t);
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c[2] = 0.6666666666-0.5*t*t*(2.-t);
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c[3] = 0.1666666666*tmp*tmp*tmp;
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}
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/* pre-computation for spline of order >3 */
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void init_splinen(float *a,int n)
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{
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int k;
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a[0] = 1.;
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for (k=2;k<=n;k++) a[0]/=(float)k;
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for (k=1;k<=n+1;k++)
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a[k] = - a[k-1] *(float)(n+2-k)/(float)k;
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}
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/* fast integral power function */
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float ipow(float x,int n)
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{
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float res;
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for (res=1.;n;n>>=1) {
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if (n&1) res*=x;
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x*=x;
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}
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return(res);
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}
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/* coefficients for spline of order >3 */
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void splinen(float *c,float t,float *a,int n)
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{
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int i,k;
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float xn;
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memset((void *)c,0,(n+1)*sizeof(float));
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for (k=0;k<=n+1;k++) {
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xn = ipow(t+(float)k,n);
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for (i=k;i<=n;i++)
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c[i] += a[i-k]*xn;
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}
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}
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