diff options
Diffstat (limited to 'Source/FreeImageToolkit/MultigridPoissonSolver.cpp')
| -rw-r--r-- | Source/FreeImageToolkit/MultigridPoissonSolver.cpp | 502 |
1 files changed, 502 insertions, 0 deletions
diff --git a/Source/FreeImageToolkit/MultigridPoissonSolver.cpp b/Source/FreeImageToolkit/MultigridPoissonSolver.cpp new file mode 100644 index 0000000..6f661b8 --- /dev/null +++ b/Source/FreeImageToolkit/MultigridPoissonSolver.cpp @@ -0,0 +1,502 @@ +// ========================================================== +// Poisson solver based on a full multigrid algorithm +// +// Design and implementation by +// - Hervé Drolon (drolon@infonie.fr) +// Reference: +// PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T., AND FLANNERY, B. P. +// 1992. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. Cambridge University Press. +// +// This file is part of FreeImage 3 +// +// COVERED CODE IS PROVIDED UNDER THIS LICENSE ON AN "AS IS" BASIS, WITHOUT WARRANTY +// OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, WARRANTIES +// THAT THE COVERED CODE IS FREE OF DEFECTS, MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE +// OR NON-INFRINGING. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE COVERED +// CODE IS WITH YOU. SHOULD ANY COVERED CODE PROVE DEFECTIVE IN ANY RESPECT, YOU (NOT +// THE INITIAL DEVELOPER OR ANY OTHER CONTRIBUTOR) ASSUME THE COST OF ANY NECESSARY +// SERVICING, REPAIR OR CORRECTION. THIS DISCLAIMER OF WARRANTY CONSTITUTES AN ESSENTIAL +// PART OF THIS LICENSE. NO USE OF ANY COVERED CODE IS AUTHORIZED HEREUNDER EXCEPT UNDER +// THIS DISCLAIMER. +// +// Use at your own risk! +// ========================================================== + +#include "FreeImage.h" +#include "Utilities.h" +#include "ToneMapping.h" + +static const int NPRE = 1; // Number of relaxation sweeps before ... +static const int NPOST = 1; // ... and after the coarse-grid correction is computed +static const int NGMAX = 15; // Maximum number of grids + +/** +Copy src into dst +*/ +static inline void fmg_copyArray(FIBITMAP *dst, FIBITMAP *src) { + memcpy(FreeImage_GetBits(dst), FreeImage_GetBits(src), FreeImage_GetHeight(dst) * FreeImage_GetPitch(dst)); +} + +/** +Fills src with zeros +*/ +static inline void fmg_fillArrayWithZeros(FIBITMAP *src) { + memset(FreeImage_GetBits(src), 0, FreeImage_GetHeight(src) * FreeImage_GetPitch(src)); +} + +/** +Half-weighting restriction. nc is the coarse-grid dimension. The fine-grid solution is input in +uf[0..2*nc-2][0..2*nc-2], the coarse-grid solution is returned in uc[0..nc-1][0..nc-1]. +*/ +static void fmg_restrict(FIBITMAP *UC, FIBITMAP *UF, int nc) { + int row_uc, row_uf, col_uc, col_uf; + + const int uc_pitch = FreeImage_GetPitch(UC) / sizeof(float); + const int uf_pitch = FreeImage_GetPitch(UF) / sizeof(float); + + float *uc_bits = (float*)FreeImage_GetBits(UC); + const float *uf_bits = (float*)FreeImage_GetBits(UF); + + // interior points + { + float *uc_scan = uc_bits + uc_pitch; + for (row_uc = 1, row_uf = 2; row_uc < nc-1; row_uc++, row_uf += 2) { + const float *uf_scan = uf_bits + row_uf * uf_pitch; + for (col_uc = 1, col_uf = 2; col_uc < nc-1; col_uc++, col_uf += 2) { + // calculate + // UC(row_uc, col_uc) = + // 0.5 * UF(row_uf, col_uf) + 0.125 * [ UF(row_uf+1, col_uf) + UF(row_uf-1, col_uf) + UF(row_uf, col_uf+1) + UF(row_uf, col_uf-1) ] + float *uc_pixel = uc_scan + col_uc; + const float *uf_center = uf_scan + col_uf; + *uc_pixel = 0.5F * *uf_center + 0.125F * ( *(uf_center + uf_pitch) + *(uf_center - uf_pitch) + *(uf_center + 1) + *(uf_center - 1) ); + } + uc_scan += uc_pitch; + } + } + // boundary points + const int ncc = 2*nc-1; + { + /* + calculate the following: + for (row_uc = 0, row_uf = 0; row_uc < nc; row_uc++, row_uf += 2) { + UC(row_uc, 0) = UF(row_uf, 0); + UC(row_uc, nc-1) = UF(row_uf, ncc-1); + } + */ + float *uc_scan = uc_bits; + for (row_uc = 0, row_uf = 0; row_uc < nc; row_uc++, row_uf += 2) { + const float *uf_scan = uf_bits + row_uf * uf_pitch; + uc_scan[0] = uf_scan[0]; + uc_scan[nc-1] = uf_scan[ncc-1]; + uc_scan += uc_pitch; + } + } + { + /* + calculate the following: + for (col_uc = 0, col_uf = 0; col_uc < nc; col_uc++, col_uf += 2) { + UC(0, col_uc) = UF(0, col_uf); + UC(nc-1, col_uc) = UF(ncc-1, col_uf); + } + */ + float *uc_scan_top = uc_bits; + float *uc_scan_bottom = uc_bits + (nc-1)*uc_pitch; + const float *uf_scan_top = uf_bits + (ncc-1)*uf_pitch; + const float *uf_scan_bottom = uf_bits; + for (col_uc = 0, col_uf = 0; col_uc < nc; col_uc++, col_uf += 2) { + uc_scan_top[col_uc] = uf_scan_top[col_uf]; + uc_scan_bottom[col_uc] = uf_scan_bottom[col_uf]; + } + } +} + +/** +Solution of the model problem on the coarsest grid, where h = 1/2 . +The right-hand side is input +in rhs[0..2][0..2] and the solution is returned in u[0..2][0..2]. +*/ +static void fmg_solve(FIBITMAP *U, FIBITMAP *RHS) { + // fill U with zeros + fmg_fillArrayWithZeros(U); + // calculate U(1, 1) = -h*h*RHS(1, 1)/4.0 where h = 1/2 + float *u_scan = (float*)FreeImage_GetScanLine(U, 1); + const float *rhs_scan = (float*)FreeImage_GetScanLine(RHS, 1); + u_scan[1] = -rhs_scan[1] / 16; +} + +/** +Coarse-to-fine prolongation by bilinear interpolation. nf is the fine-grid dimension. The coarsegrid +solution is input as uc[0..nc-1][0..nc-1], where nc = nf/2 + 1. The fine-grid solution is +returned in uf[0..nf-1][0..nf-1]. +*/ +static void fmg_prolongate(FIBITMAP *UF, FIBITMAP *UC, int nf) { + int row_uc, row_uf, col_uc, col_uf; + + const int uf_pitch = FreeImage_GetPitch(UF) / sizeof(float); + const int uc_pitch = FreeImage_GetPitch(UC) / sizeof(float); + + float *uf_bits = (float*)FreeImage_GetBits(UF); + const float *uc_bits = (float*)FreeImage_GetBits(UC); + + // do elements that are copies + { + const int nc = nf/2 + 1; + + float *uf_scan = uf_bits; + const float *uc_scan = uc_bits; + for (row_uc = 0; row_uc < nc; row_uc++) { + for (col_uc = 0, col_uf = 0; col_uc < nc; col_uc++, col_uf += 2) { + // calculate UF(2*row_uc, col_uf) = UC(row_uc, col_uc); + uf_scan[col_uf] = uc_scan[col_uc]; + } + uc_scan += uc_pitch; + uf_scan += 2 * uf_pitch; + } + } + // do odd-numbered columns, interpolating vertically + { + for(row_uf = 1; row_uf < nf-1; row_uf += 2) { + float *uf_scan = uf_bits + row_uf * uf_pitch; + for (col_uf = 0; col_uf < nf; col_uf += 2) { + // calculate UF(row_uf, col_uf) = 0.5 * ( UF(row_uf+1, col_uf) + UF(row_uf-1, col_uf) ) + uf_scan[col_uf] = 0.5F * ( *(uf_scan + uf_pitch + col_uf) + *(uf_scan - uf_pitch + col_uf) ); + } + } + } + // do even-numbered columns, interpolating horizontally + { + float *uf_scan = uf_bits; + for(row_uf = 0; row_uf < nf; row_uf++) { + for (col_uf = 1; col_uf < nf-1; col_uf += 2) { + // calculate UF(row_uf, col_uf) = 0.5 * ( UF(row_uf, col_uf+1) + UF(row_uf, col_uf-1) ) + uf_scan[col_uf] = 0.5F * ( uf_scan[col_uf + 1] + uf_scan[col_uf - 1] ); + } + uf_scan += uf_pitch; + } + } +} + +/** +Red-black Gauss-Seidel relaxation for model problem. Updates the current value of the solution +u[0..n-1][0..n-1], using the right-hand side function rhs[0..n-1][0..n-1]. +*/ +static void fmg_relaxation(FIBITMAP *U, FIBITMAP *RHS, int n) { + int row, col, ipass, isw, jsw; + const float h = 1.0F / (n - 1); + const float h2 = h*h; + + const int u_pitch = FreeImage_GetPitch(U) / sizeof(float); + const int rhs_pitch = FreeImage_GetPitch(RHS) / sizeof(float); + + float *u_bits = (float*)FreeImage_GetBits(U); + const float *rhs_bits = (float*)FreeImage_GetBits(RHS); + + for (ipass = 0, jsw = 1; ipass < 2; ipass++, jsw = 3-jsw) { // Red and black sweeps + float *u_scan = u_bits + u_pitch; + const float *rhs_scan = rhs_bits + rhs_pitch; + for (row = 1, isw = jsw; row < n-1; row++, isw = 3-isw) { + for (col = isw; col < n-1; col += 2) { + // Gauss-Seidel formula + // calculate U(row, col) = + // 0.25 * [ U(row+1, col) + U(row-1, col) + U(row, col+1) + U(row, col-1) - h2 * RHS(row, col) ] + float *u_center = u_scan + col; + const float *rhs_center = rhs_scan + col; + *u_center = *(u_center + u_pitch) + *(u_center - u_pitch) + *(u_center + 1) + *(u_center - 1); + *u_center -= h2 * *rhs_center; + *u_center *= 0.25F; + } + u_scan += u_pitch; + rhs_scan += rhs_pitch; + } + } +} + +/** +Returns minus the residual for the model problem. Input quantities are u[0..n-1][0..n-1] and +rhs[0..n-1][0..n-1], while res[0..n-1][0..n-1] is returned. +*/ +static void fmg_residual(FIBITMAP *RES, FIBITMAP *U, FIBITMAP *RHS, int n) { + int row, col; + + const float h = 1.0F / (n-1); + const float h2i = 1.0F / (h*h); + + const int res_pitch = FreeImage_GetPitch(RES) / sizeof(float); + const int u_pitch = FreeImage_GetPitch(U) / sizeof(float); + const int rhs_pitch = FreeImage_GetPitch(RHS) / sizeof(float); + + float *res_bits = (float*)FreeImage_GetBits(RES); + const float *u_bits = (float*)FreeImage_GetBits(U); + const float *rhs_bits = (float*)FreeImage_GetBits(RHS); + + // interior points + { + float *res_scan = res_bits + res_pitch; + const float *u_scan = u_bits + u_pitch; + const float *rhs_scan = rhs_bits + rhs_pitch; + for (row = 1; row < n-1; row++) { + for (col = 1; col < n-1; col++) { + // calculate RES(row, col) = + // -h2i * [ U(row+1, col) + U(row-1, col) + U(row, col+1) + U(row, col-1) - 4 * U(row, col) ] + RHS(row, col); + float *res_center = res_scan + col; + const float *u_center = u_scan + col; + const float *rhs_center = rhs_scan + col; + *res_center = *(u_center + u_pitch) + *(u_center - u_pitch) + *(u_center + 1) + *(u_center - 1) - 4 * *u_center; + *res_center *= -h2i; + *res_center += *rhs_center; + } + res_scan += res_pitch; + u_scan += u_pitch; + rhs_scan += rhs_pitch; + } + } + + // boundary points + { + memset(FreeImage_GetScanLine(RES, 0), 0, FreeImage_GetPitch(RES)); + memset(FreeImage_GetScanLine(RES, n-1), 0, FreeImage_GetPitch(RES)); + float *left = res_bits; + float *right = res_bits + (n-1); + for(int k = 0; k < n; k++) { + *left = 0; + *right = 0; + left += res_pitch; + right += res_pitch; + } + } +} + +/** +Does coarse-to-fine interpolation and adds result to uf. nf is the fine-grid dimension. The +coarse-grid solution is input as uc[0..nc-1][0..nc-1], where nc = nf/2+1. The fine-grid solution +is returned in uf[0..nf-1][0..nf-1]. res[0..nf-1][0..nf-1] is used for temporary storage. +*/ +static void fmg_addint(FIBITMAP *UF, FIBITMAP *UC, FIBITMAP *RES, int nf) { + fmg_prolongate(RES, UC, nf); + + const int uf_pitch = FreeImage_GetPitch(UF) / sizeof(float); + const int res_pitch = FreeImage_GetPitch(RES) / sizeof(float); + + float *uf_bits = (float*)FreeImage_GetBits(UF); + const float *res_bits = (float*)FreeImage_GetBits(RES); + + for(int row = 0; row < nf; row++) { + for(int col = 0; col < nf; col++) { + // calculate UF(row, col) = UF(row, col) + RES(row, col); + uf_bits[col] += res_bits[col]; + } + uf_bits += uf_pitch; + res_bits += res_pitch; + } +} + +/** +Full Multigrid Algorithm for solution of linear elliptic equation, here the model problem (19.0.6). +On input u[0..n-1][0..n-1] contains the right-hand side ñ, while on output it returns the solution. +The dimension n must be of the form 2^j + 1 for some integer j. (j is actually the number of +grid levels used in the solution, called ng below.) ncycle is the number of V-cycles to be +used at each level. +*/ +static BOOL fmg_mglin(FIBITMAP *U, int n, int ncycle) { + int j, jcycle, jj, jpost, jpre, nf, ngrid; + + FIBITMAP **IRHO = NULL; + FIBITMAP **IU = NULL; + FIBITMAP **IRHS = NULL; + FIBITMAP **IRES = NULL; + + int ng = 0; // number of allocated grids + +// -------------------------------------------------------------------------- + +#define _CREATE_ARRAY_GRID_(array, array_size) \ + array = (FIBITMAP**)malloc(array_size * sizeof(FIBITMAP*));\ + if(!array) throw(1);\ + memset(array, 0, array_size * sizeof(FIBITMAP*)) + +#define _FREE_ARRAY_GRID_(array, array_size) \ + if(NULL != array) {\ + for(int k = 0; k < array_size; k++) {\ + if(NULL != array[k]) {\ + FreeImage_Unload(array[k]); array[k] = NULL;\ + }\ + }\ + free(array);\ + } + +// -------------------------------------------------------------------------- + + try { + int nn = n; + // check grid size and grid levels + while (nn >>= 1) ng++; + if (n != 1 + (1L << ng)) { + FreeImage_OutputMessageProc(FIF_UNKNOWN, "Multigrid algorithm: n = %d, while n-1 must be a power of 2.", n); + throw(1); + } + if (ng > NGMAX) { + FreeImage_OutputMessageProc(FIF_UNKNOWN, "Multigrid algorithm: ng = %d while NGMAX = %d, increase NGMAX.", ng, NGMAX); + throw(1); + } + // allocate grid arrays + { + _CREATE_ARRAY_GRID_(IRHO, ng); + _CREATE_ARRAY_GRID_(IU, ng); + _CREATE_ARRAY_GRID_(IRHS, ng); + _CREATE_ARRAY_GRID_(IRES, ng); + } + + nn = n/2 + 1; + ngrid = ng - 2; + + // allocate storage for r.h.s. on grid (ng - 2) ... + IRHO[ngrid] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IRHO[ngrid]) throw(1); + + // ... and fill it by restricting from the fine grid + fmg_restrict(IRHO[ngrid], U, nn); + + // similarly allocate storage and fill r.h.s. on all coarse grids. + while (nn > 3) { + nn = nn/2 + 1; + ngrid--; + IRHO[ngrid] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IRHO[ngrid]) throw(1); + fmg_restrict(IRHO[ngrid], IRHO[ngrid+1], nn); + } + + nn = 3; + + IU[0] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IU[0]) throw(1); + IRHS[0] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IRHS[0]) throw(1); + + // initial solution on coarsest grid + fmg_solve(IU[0], IRHO[0]); + // irho[0] no longer needed ... + FreeImage_Unload(IRHO[0]); IRHO[0] = NULL; + + ngrid = ng; + + // nested iteration loop + for (j = 1; j < ngrid; j++) { + nn = 2*nn - 1; + + IU[j] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IU[j]) throw(1); + IRHS[j] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IRHS[j]) throw(1); + IRES[j] = FreeImage_AllocateT(FIT_FLOAT, nn, nn); + if(!IRES[j]) throw(1); + + fmg_prolongate(IU[j], IU[j-1], nn); + + // interpolate from coarse grid to next finer grid + + // set up r.h.s. + fmg_copyArray(IRHS[j], j != (ngrid - 1) ? IRHO[j] : U); + + // V-cycle loop + for (jcycle = 0; jcycle < ncycle; jcycle++) { + nf = nn; + // downward stoke of the V + for (jj = j; jj >= 1; jj--) { + // pre-smoothing + for (jpre = 0; jpre < NPRE; jpre++) { + fmg_relaxation(IU[jj], IRHS[jj], nf); + } + fmg_residual(IRES[jj], IU[jj], IRHS[jj], nf); + nf = nf/2 + 1; + // restriction of the residual is the next r.h.s. + fmg_restrict(IRHS[jj-1], IRES[jj], nf); + // zero for initial guess in next relaxation + fmg_fillArrayWithZeros(IU[jj-1]); + } + // bottom of V: solve on coarsest grid + fmg_solve(IU[0], IRHS[0]); + nf = 3; + // upward stroke of V. + for (jj = 1; jj <= j; jj++) { + nf = 2*nf - 1; + // use res for temporary storage inside addint + fmg_addint(IU[jj], IU[jj-1], IRES[jj], nf); + // post-smoothing + for (jpost = 0; jpost < NPOST; jpost++) { + fmg_relaxation(IU[jj], IRHS[jj], nf); + } + } + } + } + + // return solution in U + fmg_copyArray(U, IU[ngrid-1]); + + // delete allocated arrays + _FREE_ARRAY_GRID_(IRES, ng); + _FREE_ARRAY_GRID_(IRHS, ng); + _FREE_ARRAY_GRID_(IU, ng); + _FREE_ARRAY_GRID_(IRHO, ng); + + return TRUE; + + } catch(int) { + // delete allocated arrays + _FREE_ARRAY_GRID_(IRES, ng); + _FREE_ARRAY_GRID_(IRHS, ng); + _FREE_ARRAY_GRID_(IU, ng); + _FREE_ARRAY_GRID_(IRHO, ng); + + return FALSE; + } +} + +// -------------------------------------------------------------------------- + +/** +Poisson solver based on a multigrig algorithm. +This routine solves a Poisson equation, remap result pixels to [0..1] and returns the solution. +NB: The input image is first stored inside a square image whose size is (2^j + 1)x(2^j + 1) for some integer j, +where j is such that 2^j is the nearest larger dimension corresponding to MAX(image width, image height). +@param Laplacian Laplacian image +@param ncycle Number of cycles in the multigrid algorithm (usually 2 or 3) +@return Returns the solved PDE equations if successful, returns NULL otherwise +*/ +FIBITMAP* DLL_CALLCONV +FreeImage_MultigridPoissonSolver(FIBITMAP *Laplacian, int ncycle) { + if(!Laplacian) return NULL; + + int width = FreeImage_GetWidth(Laplacian); + int height = FreeImage_GetHeight(Laplacian); + + // get nearest larger dimension length that is acceptable by the algorithm + int n = MAX(width, height); + int size = 0; + while((n >>= 1) > 0) size++; + // size must be of the form 2^j + 1 for some integer j + size = 1 + (1 << (size + 1)); + + // allocate a temporary square image I + FIBITMAP *I = FreeImage_AllocateT(FIT_FLOAT, size, size); + if(!I) return NULL; + + // copy Laplacian into I and shift pixels to create a boundary + FreeImage_Paste(I, Laplacian, 1, 1, 255); + + // solve the PDE equation + fmg_mglin(I, size, ncycle); + + // shift pixels back + FIBITMAP *U = FreeImage_Copy(I, 1, 1, width + 1, height + 1); + FreeImage_Unload(I); + + // remap pixels to [0..1] + NormalizeY(U, 0, 1); + + // copy metadata from src to dst + FreeImage_CloneMetadata(U, Laplacian); + + // return the integrated image + return U; +} + |