Adding fast distance calculation
This commit is contained in:
Mark Berrill committed
1 parent
a77fe2b914
commit
9aa3145e8a
3 files changed
+417
-2
No files matched your search
+2
-2
@@ -1,5 +1,5 @@
|
||||
#ifndef COMMON_H_INC
|
||||
#define COMMON_H_INC
|
||||
#ifndef Analysis_H_INC
|
||||
#define Analysis_H_INC
|
||||
|
||||
#include "common/Array.h"
|
||||
#include "common/Communication.h"
|
||||
|
||||
@@ -0,0 +1,56 @@
|
||||
#ifndef Eikonal_H_INC
|
||||
#define Eikonal_H_INC
|
||||
|
||||
|
||||
|
||||
/*!
|
||||
* @brief Calculate the distance solving the Eikonal equation
|
||||
* @details This routine converts the data in the Distance array to a signed distance
|
||||
* by solving the equation df/dt = sign*(1-|grad f|), where Distance provides
|
||||
* the values of f on the mesh associated with domain Dm
|
||||
* It has been tested with segmented data initialized to values [-1,1]
|
||||
* and will converge toward the signed distance to the surface bounding the associated phases
|
||||
*
|
||||
* Reference:
|
||||
* Min C (2010) On reinitializing level set functions, Journal of Computational Physics 229
|
||||
*
|
||||
* @return Returns the number of cubes in the blob
|
||||
* @param[in/out] Distance Distance function
|
||||
* @param[in] ID Segmentation id
|
||||
* @param[in] DM Domain information
|
||||
* @param[in] timesteps Maximum number of timesteps to process
|
||||
* @return Returns the global variation
|
||||
*/
|
||||
inline float Eikonal3D( Array<float> &Distance, const Array<char> &ID, const Domain &Dm, const int timesteps);
|
||||
|
||||
|
||||
/*!
|
||||
* @brief Calculate the distance using a simple method
|
||||
* @details This routine calculates the distance using a very simple method working off the segmentation id.
|
||||
*
|
||||
* @return Returns the number of cubes in the blob
|
||||
* @param[in/out] Distance Distance function
|
||||
* @param[in] ID Segmentation id
|
||||
* @param[in] DM Domain information
|
||||
* @return Returns the global variation
|
||||
*/
|
||||
inline void CalcDist3D( Array<float> &Distance, const Array<char> &ID, const Domain &Dm );
|
||||
|
||||
|
||||
/*!
|
||||
* @brief Calculate the distance using a multi-level method
|
||||
* @details This routine calculates the distance using a multi-grid method
|
||||
*
|
||||
* @return Returns the number of cubes in the blob
|
||||
* @param[in/out] Distance Distance function
|
||||
* @param[in] ID Segmentation id
|
||||
* @param[in] DM Domain information
|
||||
* @return Returns the global variation
|
||||
*/
|
||||
inline void CalcDistMultiLevel( Array<float> &Distance, const Array<char> &ID, const Domain &Dm );
|
||||
|
||||
|
||||
|
||||
#include "analysis/eikonal.hpp"
|
||||
|
||||
#endif
|
||||
@@ -0,0 +1,359 @@
|
||||
#ifndef Eikonal_HPP_INC
|
||||
#define Eikonal_HPP_INC
|
||||
|
||||
#include "analysis/eikonal.h"
|
||||
|
||||
|
||||
|
||||
|
||||
inline float minmod(float &a, float &b)
|
||||
{
|
||||
float value = a;
|
||||
if ( a*b < 0.0)
|
||||
value=0.0;
|
||||
else if (fabs(a) > fabs(b))
|
||||
value = b;
|
||||
return value;
|
||||
}
|
||||
|
||||
|
||||
/******************************************************************
|
||||
* Solve the eikonal equation *
|
||||
******************************************************************/
|
||||
inline float Eikonal3D( Array<float> &Distance, const Array<char> &ID, const Domain &Dm, const int timesteps)
|
||||
{
|
||||
PROFILE_START("Eikonal3D");
|
||||
|
||||
/*
|
||||
* This routine converts the data in the Distance array to a signed distance
|
||||
* by solving the equation df/dt = sign*(1-|grad f|), where Distance provides
|
||||
* the values of f on the mesh associated with domain Dm
|
||||
* It has been tested with segmented data initialized to values [-1,1]
|
||||
* and will converge toward the signed distance to the surface bounding the associated phases
|
||||
*
|
||||
* Reference:
|
||||
* Min C (2010) On reinitializing level set functions, Journal of Computational Physics 229
|
||||
*/
|
||||
|
||||
int i,j,k;
|
||||
float dt=0.1;
|
||||
float Dx,Dy,Dz;
|
||||
float Dxp,Dxm,Dyp,Dym,Dzp,Dzm;
|
||||
float Dxxp,Dxxm,Dyyp,Dyym,Dzzp,Dzzm;
|
||||
float sign,norm;
|
||||
float LocalVar,GlobalVar,LocalMax,GlobalMax;
|
||||
|
||||
int xdim,ydim,zdim;
|
||||
xdim=Dm.Nx-2;
|
||||
ydim=Dm.Ny-2;
|
||||
zdim=Dm.Nz-2;
|
||||
fillHalo<float> fillData(Dm.Comm, Dm.rank_info,xdim,ydim,zdim,1,1,1,0,1);
|
||||
|
||||
// Arrays to store the second derivatives
|
||||
Array<float> Dxx(Dm.Nx,Dm.Ny,Dm.Nz);
|
||||
Array<float> Dyy(Dm.Nx,Dm.Ny,Dm.Nz);
|
||||
Array<float> Dzz(Dm.Nx,Dm.Ny,Dm.Nz);
|
||||
|
||||
int count = 0;
|
||||
while (count < timesteps){
|
||||
|
||||
// Communicate the halo of values
|
||||
fillData.fill(Distance);
|
||||
|
||||
// Compute second order derivatives
|
||||
for (k=1;k<Dm.Nz-1;k++){
|
||||
for (j=1;j<Dm.Ny-1;j++){
|
||||
for (i=1;i<Dm.Nx-1;i++){
|
||||
Dxx(i,j,k) = Distance(i+1,j,k) + Distance(i-1,j,k) - 2*Distance(i,j,k);
|
||||
Dyy(i,j,k) = Distance(i,j+1,k) + Distance(i,j-1,k) - 2*Distance(i,j,k);
|
||||
Dzz(i,j,k) = Distance(i,j,k+1) + Distance(i,j,k-1) - 2*Distance(i,j,k);
|
||||
}
|
||||
}
|
||||
}
|
||||
fillData.fill(Dxx);
|
||||
fillData.fill(Dyy);
|
||||
fillData.fill(Dzz);
|
||||
|
||||
LocalMax=LocalVar=0.0;
|
||||
// Execute the next timestep
|
||||
// f(n+1) = f(n) + dt*sign(1-|grad f|)
|
||||
for (k=1;k<Dm.Nz-1;k++){
|
||||
for (j=1;j<Dm.Ny-1;j++){
|
||||
for (i=1;i<Dm.Nx-1;i++){
|
||||
|
||||
int n = k*Dm.Nx*Dm.Ny + j*Dm.Nx + i;
|
||||
|
||||
sign = -1;
|
||||
if (ID(i,j,k) == 1) sign = 1;
|
||||
|
||||
// local second derivative terms
|
||||
Dxxp = minmod(Dxx(i,j,k),Dxx(i+1,j,k));
|
||||
Dyyp = minmod(Dyy(i,j,k),Dyy(i,j+1,k));
|
||||
Dzzp = minmod(Dzz(i,j,k),Dzz(i,j,k+1));
|
||||
Dxxm = minmod(Dxx(i,j,k),Dxx(i-1,j,k));
|
||||
Dyym = minmod(Dyy(i,j,k),Dyy(i,j-1,k));
|
||||
Dzzm = minmod(Dzz(i,j,k),Dzz(i,j,k-1));
|
||||
|
||||
/* //............Compute upwind derivatives ...................
|
||||
Dxp = Distance(i+1,j,k) - Distance(i,j,k) + 0.5*Dxxp;
|
||||
Dyp = Distance(i,j+1,k) - Distance(i,j,k) + 0.5*Dyyp;
|
||||
Dzp = Distance(i,j,k+1) - Distance(i,j,k) + 0.5*Dzzp;
|
||||
|
||||
Dxm = Distance(i,j,k) - Distance(i-1,j,k) + 0.5*Dxxm;
|
||||
Dym = Distance(i,j,k) - Distance(i,j-1,k) + 0.5*Dyym;
|
||||
Dzm = Distance(i,j,k) - Distance(i,j,k-1) + 0.5*Dzzm;
|
||||
*/
|
||||
Dxp = Distance(i+1,j,k);
|
||||
Dyp = Distance(i,j+1,k);
|
||||
Dzp = Distance(i,j,k+1);
|
||||
|
||||
Dxm = Distance(i-1,j,k);
|
||||
Dym = Distance(i,j-1,k);
|
||||
Dzm = Distance(i,j,k-1);
|
||||
|
||||
// Compute upwind derivatives for Godunov Hamiltonian
|
||||
if (sign < 0.0){
|
||||
if (Dxp > Dxm) Dx = Dxp - Distance(i,j,k) + 0.5*Dxxp;
|
||||
else Dx = Distance(i,j,k) - Dxm + 0.5*Dxxm;
|
||||
|
||||
if (Dyp > Dym) Dy = Dyp - Distance(i,j,k) + 0.5*Dyyp;
|
||||
else Dy = Distance(i,j,k) - Dym + 0.5*Dyym;
|
||||
|
||||
if (Dzp > Dzm) Dz = Dzp - Distance(i,j,k) + 0.5*Dzzp;
|
||||
else Dz = Distance(i,j,k) - Dzm + 0.5*Dzzm;
|
||||
}
|
||||
else{
|
||||
if (Dxp < Dxm) Dx = Dxp - Distance(i,j,k) + 0.5*Dxxp;
|
||||
else Dx = Distance(i,j,k) - Dxm + 0.5*Dxxm;
|
||||
|
||||
if (Dyp < Dym) Dy = Dyp - Distance(i,j,k) + 0.5*Dyyp;
|
||||
else Dy = Distance(i,j,k) - Dym + 0.5*Dyym;
|
||||
|
||||
if (Dzp < Dzm) Dz = Dzp - Distance(i,j,k) + 0.5*Dzzp;
|
||||
else Dz = Distance(i,j,k) - Dzm + 0.5*Dzzm;
|
||||
}
|
||||
|
||||
norm=sqrt(Dx*Dx+Dy*Dy+Dz*Dz);
|
||||
if (norm > 1.0) norm=1.0;
|
||||
|
||||
Distance(i,j,k) += dt*sign*(1.0 - norm);
|
||||
LocalVar += dt*sign*(1.0 - norm);
|
||||
|
||||
if (fabs(dt*sign*(1.0 - norm)) > LocalMax)
|
||||
LocalMax = fabs(dt*sign*(1.0 - norm));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
MPI_Allreduce(&LocalVar,&GlobalVar,1,MPI_FLOAT,MPI_SUM,Dm.Comm);
|
||||
MPI_Allreduce(&LocalMax,&GlobalMax,1,MPI_FLOAT,MPI_MAX,Dm.Comm);
|
||||
GlobalVar /= (Dm.Nx-2)*(Dm.Ny-2)*(Dm.Nz-2)*Dm.nprocx*Dm.nprocy*Dm.nprocz;
|
||||
count++;
|
||||
|
||||
if (count%50 == 0 && Dm.rank==0 )
|
||||
printf(" Time=%i, Max variation=%f, Global variation=%f \n",count,GlobalMax,GlobalVar);
|
||||
|
||||
if (fabs(GlobalMax) < 1e-5){
|
||||
if (Dm.rank==0) printf(" Exiting with max tolerance of 1e-5 \n");
|
||||
count=timesteps;
|
||||
}
|
||||
}
|
||||
PROFILE_STOP("Eikonal3D");
|
||||
return GlobalVar;
|
||||
|
||||
}
|
||||
|
||||
|
||||
/******************************************************************
|
||||
* A fast distance calculation *
|
||||
******************************************************************/
|
||||
inline bool CalcDist3DIteration( Array<float> &Distance, const Domain &Dm )
|
||||
{
|
||||
const float sq2 = sqrt(2.0f);
|
||||
const float sq3 = sqrt(3.0f);
|
||||
float dist0[27];
|
||||
dist0[0] = sq3; dist0[1] = sq2; dist0[2] = sq3;
|
||||
dist0[3] = sq2; dist0[4] = 1; dist0[5] = sq2;
|
||||
dist0[6] = sq3; dist0[7] = sq2; dist0[8] = sq3;
|
||||
dist0[9] = sq2; dist0[10] = 1; dist0[11] = sq2;
|
||||
dist0[12] = 1; dist0[13] = 0; dist0[14] = 1;
|
||||
dist0[15] = sq2; dist0[16] = 1; dist0[17] = sq2;
|
||||
dist0[18] = sq3; dist0[19] = sq2; dist0[20] = sq3;
|
||||
dist0[21] = sq2; dist0[22] = 1; dist0[23] = sq2;
|
||||
dist0[24] = sq3; dist0[25] = sq2; dist0[26] = sq3;
|
||||
bool changed = false;
|
||||
for (size_t k=1; k<Distance.size(2)-1; k++) {
|
||||
for (size_t j=1; j<Distance.size(1)-1; j++) {
|
||||
for (size_t i=1; i<Distance.size(0)-1; i++) {
|
||||
float dist[27];
|
||||
dist[0] = Distance(i-1,j-1,k-1); dist[1] = Distance(i,j-1,k-1); dist[2] = Distance(i+1,j-1,k-1);
|
||||
dist[3] = Distance(i-1,j,k-1); dist[4] = Distance(i,j,k-1); dist[5] = Distance(i+1,j,k-1);
|
||||
dist[6] = Distance(i-1,j+1,k-1); dist[7] = Distance(i,j+1,k-1); dist[8] = Distance(i+1,j+1,k-1);
|
||||
dist[9] = Distance(i-1,j-1,k); dist[10] = Distance(i,j-1,k); dist[11] = Distance(i+1,j-1,k);
|
||||
dist[12] = Distance(i-1,j,k); dist[13] = Distance(i,j,k); dist[14] = Distance(i+1,j,k);
|
||||
dist[15] = Distance(i-1,j+1,k); dist[16] = Distance(i,j+1,k); dist[17] = Distance(i+1,j+1,k);
|
||||
dist[18] = Distance(i-1,j-1,k+1); dist[19] = Distance(i,j-1,k+1); dist[20] = Distance(i+1,j-1,k+1);
|
||||
dist[21] = Distance(i-1,j,k+1); dist[22] = Distance(i,j,k+1); dist[23] = Distance(i+1,j,k+1);
|
||||
dist[24] = Distance(i-1,j+1,k+1); dist[25] = Distance(i,j+1,k+1); dist[26] = Distance(i+1,j+1,k+1);
|
||||
float tmp = 1e100;
|
||||
for (int k=0; k<27; k++)
|
||||
tmp = std::min(tmp,dist[k]+dist0[k]);
|
||||
if ( tmp < Distance(i,j,k) ) {
|
||||
Distance(i,j,k) = tmp;
|
||||
changed = true;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return changed;
|
||||
}
|
||||
inline void CalcDist3D( Array<float> &Distance, const Array<char> &ID, const Domain &Dm )
|
||||
{
|
||||
PROFILE_START("Calc Distance");
|
||||
// Initialize the distance to be 0 fore the cells adjacent to the interface
|
||||
Distance.fill(1e100);
|
||||
for (size_t k=1; k<ID.size(2)-1; k++) {
|
||||
for (size_t j=1; j<ID.size(1)-1; j++) {
|
||||
for (size_t i=1; i<ID.size(0)-1; i++) {
|
||||
char id = ID(i,j,k);
|
||||
if ( id!=ID(i-1,j,k) || id!=ID(i+1,j,k) || id!=ID(i,j-1,k) || id!=ID(i,j+1,k) || id!=ID(i,j,k-1) || id!=ID(i,j,k+1) )
|
||||
Distance(i,j,k) = 0.5;
|
||||
}
|
||||
}
|
||||
}
|
||||
// Compute the distance everywhere
|
||||
fillHalo<float> fillData(Dm.Comm, Dm.rank_info,Dm.Nx,Dm.Ny,Dm.Nz,1,1,1,0,1);
|
||||
while ( true ) {
|
||||
// Communicate the halo of values
|
||||
fillData.fill(Distance);
|
||||
// The distance of the cell is the minimum of the distance of the neighbors plus the distance to that node
|
||||
bool changed = CalcDist3DIteration( Distance, Dm );
|
||||
changed = sumReduce(Dm.Comm,changed);
|
||||
if ( !changed )
|
||||
break;
|
||||
}
|
||||
// Update the sign of the distance
|
||||
for (size_t i=0; i<ID.length(); i++)
|
||||
Distance(i) *= ID(i)>0 ? 1:-1;
|
||||
PROFILE_STOP("Calc Distance");
|
||||
}
|
||||
|
||||
|
||||
/******************************************************************
|
||||
* A fast distance calculation *
|
||||
******************************************************************/
|
||||
inline void CalcDistMultiLevelHelper( Array<float> &Distance, const Domain &Dm )
|
||||
{
|
||||
size_t ratio = 4;
|
||||
std::function<float(const Array<float>&)> coarsen = [ratio]( const Array<float>& data )
|
||||
{
|
||||
float tmp = 1e100;
|
||||
int nx = data.size(0);
|
||||
int ny = data.size(1);
|
||||
int nz = data.size(2);
|
||||
for (int k=0; k<nz; k++) {
|
||||
float z = k-0.5*(nz-1);
|
||||
for (int j=0; j<ny; j++) {
|
||||
float y = j-0.5*(ny-1);
|
||||
for (int i=0; i<nx; i++) {
|
||||
float x = i-0.5*(nx-1);
|
||||
tmp = std::min(data(i,j,k)+sqrt(x*x+y*y+z*z),tmp);
|
||||
}
|
||||
}
|
||||
}
|
||||
return tmp/ratio;
|
||||
};
|
||||
int Nx = Dm.Nx-2;
|
||||
int Ny = Dm.Ny-2;
|
||||
int Nz = Dm.Nz-2;
|
||||
ASSERT(int(Distance.size(0))==Nx+2&&int(Distance.size(1))==Ny+2&&int(Distance.size(2))==Nz+2);
|
||||
fillHalo<float> fillData(Dm.Comm,Dm.rank_info,Nx,Ny,Nz,1,1,1,0,1);
|
||||
if ( Nx%ratio==0 && Nx>8 && Ny%ratio==0 && Ny>8 && Nz%ratio==0 && Nz>8 ) {
|
||||
// Use recursive version
|
||||
int Nr = std::max(std::max(ratio,ratio),ratio);
|
||||
// Run Nr iterations, communicate, run Nr iterations
|
||||
for (int i=0; i<Nr; i++)
|
||||
CalcDist3DIteration( Distance, Dm );
|
||||
/*fillData.fill(Distance);
|
||||
for (int i=0; i<Nr; i++)
|
||||
CalcDist3DIteration( Distance, Dm );*/
|
||||
// Coarsen
|
||||
Array<float> dist(Nx,Ny,Nz);
|
||||
fillData.copy(Distance,dist);
|
||||
Domain Dm2(Nx/ratio,Ny/ratio,Nz/ratio,Dm.rank,Dm.nprocx,Dm.nprocy,Dm.nprocz,Dm.Lx,Dm.Ly,Dm.Lz,0);
|
||||
Dm2.CommInit(Dm.Comm);
|
||||
fillHalo<float> fillData2(Dm2.Comm,Dm2.rank_info,Nx/ratio,Ny/ratio,Nz/ratio,1,1,1,0,1);
|
||||
auto dist2 = dist.coarsen( {ratio,ratio,ratio}, coarsen );
|
||||
Array<float> Distance2(Nx/ratio+2,Ny/ratio+2,Nz/ratio+2);
|
||||
fillData2.copy(dist2,Distance2);
|
||||
// Solve
|
||||
CalcDistMultiLevelHelper( Distance2, Dm2 );
|
||||
// Interpolate the coarse grid to the fine grid
|
||||
fillData2.copy(Distance2,dist2);
|
||||
for (int k=0; k<Nz; k++) {
|
||||
int k2 = k/ratio;
|
||||
float z = (k-k2*ratio)-0.5*(ratio-1);
|
||||
for (int j=0; j<Ny; j++) {
|
||||
int j2 = j/ratio;
|
||||
float y = (j-j2*ratio)-0.5*(ratio-1);
|
||||
for (int i=0; i<Nx; i++) {
|
||||
int i2 = i/ratio;
|
||||
float x = (i-i2*ratio)-0.5*(ratio-1);
|
||||
dist(i,j,k) = std::min(dist(i,j,k),ratio*dist2(i2,j2,k2)+sqrt(x*x+y*y+z*z));
|
||||
}
|
||||
}
|
||||
}
|
||||
fillData.copy(dist,Distance);
|
||||
// Run Nr iterations, communicate, run Nr iterations
|
||||
for (int i=0; i<Nr; i++)
|
||||
CalcDist3DIteration( Distance, Dm );
|
||||
fillData.fill(Distance);
|
||||
for (int i=0; i<Nr; i++)
|
||||
CalcDist3DIteration( Distance, Dm );
|
||||
} else {
|
||||
// Use coarse-grid version
|
||||
while ( true ) {
|
||||
// Communicate the halo of values
|
||||
fillData.fill(Distance);
|
||||
// The distance of the cell is the minimum of the distance of the neighbors plus the distance to that node
|
||||
bool changed = CalcDist3DIteration( Distance, Dm );
|
||||
changed = sumReduce(Dm.Comm,changed);
|
||||
if ( !changed )
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
inline void CalcDistMultiLevel( Array<float> &Distance, const Array<char> &ID, const Domain &Dm )
|
||||
{
|
||||
PROFILE_START("Calc Distance Multilevel");
|
||||
int Nx = Dm.Nx-2;
|
||||
int Ny = Dm.Ny-2;
|
||||
int Nz = Dm.Nz-2;
|
||||
ASSERT(int(Distance.size(0))==Nx+2&&int(Distance.size(1))==Ny+2&&int(Distance.size(2))==Nz+2);
|
||||
fillHalo<float> fillData(Dm.Comm,Dm.rank_info,Nx,Ny,Nz,1,1,1,0,1);
|
||||
// Initialize the distance to be 0 fore the cells adjacent to the interface
|
||||
Distance.fill(1e100);
|
||||
for (size_t k=1; k<ID.size(2)-1; k++) {
|
||||
for (size_t j=1; j<ID.size(1)-1; j++) {
|
||||
for (size_t i=1; i<ID.size(0)-1; i++) {
|
||||
char id = ID(i,j,k);
|
||||
if ( id!=ID(i-1,j,k) || id!=ID(i+1,j,k) || id!=ID(i,j-1,k) || id!=ID(i,j+1,k) || id!=ID(i,j,k-1) || id!=ID(i,j,k+1) )
|
||||
Distance(i,j,k) = 0.5;
|
||||
}
|
||||
}
|
||||
}
|
||||
// Solve the for the distance using a recursive method
|
||||
CalcDistMultiLevelHelper( Distance, Dm );
|
||||
// Update the sign of the distance
|
||||
for (size_t i=0; i<ID.length(); i++)
|
||||
Distance(i) *= ID(i)>0 ? 1:-1;
|
||||
fillData.fill(Distance);
|
||||
// Run a quick filter to smooth the data
|
||||
float sigma = 0.6;
|
||||
Array<float> H = imfilter::create_filter<float>( { 1 }, "gaussian", &sigma );
|
||||
std::vector<imfilter::BC> BC(3,imfilter::BC::replicate);
|
||||
Distance = imfilter::imfilter_separable<float>( Distance, {H,H,H}, BC );
|
||||
PROFILE_STOP("Calc Distance Multilevel");
|
||||
}
|
||||
|
||||
#endif
|
||||
Reference in new issue
Block a user