blob: 3b577cbd0a3184603d3c1241dbf35f97f182b48f [file] [log] [blame]
// ==========================================================
// 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 multigrid 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(!FreeImage_HasPixels(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++;
if((1 << size) < MAX(width, height)) {
size++;
}
// size must be of the form 2^j + 1 for some integer j
size = 1 + (1 << size);
// 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;
}