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OpticalFlow.cpp
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#include "OpticalFlow.h"
#include "ImageProcessing.h"
#include "ImagePyramid.h"
#include <cstdlib>
#include <iostream>
#include "OpticFlowIO.h"
using namespace std;
bool OpticalFlow::IsDisplay=false;
//OpticalFlow::InterpolationMethod OpticalFlow::interpolation = OpticalFlow::Bicubic;
OpticalFlow::InterpolationMethod OpticalFlow::interpolation = OpticalFlow::Bilinear;
OpticalFlow::NoiseModel OpticalFlow::noiseModel = OpticalFlow::Lap;
GaussianMixture OpticalFlow::GMPara;
Vector<float> OpticalFlow::LapPara;
OpticalFlow::OpticalFlow(void)
{
}
OpticalFlow::~OpticalFlow(void)
{
}
//--------------------------------------------------------------------------------------------------------
// function to compute dx, dy and dt for motion estimation
//--------------------------------------------------------------------------------------------------------
void OpticalFlow::getDxs(FImage &imdx, FImage &imdy, FImage &imdt, const FImage &im1, const FImage &im2)
{
//float gfilter[5]={0.01,0.09,0.8,0.09,0.01};
float gfilter[5]={0.02,0.11,0.74,0.11,0.02};
//float gfilter[5]={0,0,1,0,0};
if(1)
{
//DImage foo,Im;
//Im.Add(im1,im2);
//Im.Multiplywith(0.5);
////foo.imfilter_hv(Im,gfilter,2,gfilter,2);
//Im.dx(imdx,true);
//Im.dy(imdy,true);
//imdt.Subtract(im2,im1);
FImage Im1,Im2,Im;
im1.imfilter_hv(Im1,gfilter,2,gfilter,2);
im2.imfilter_hv(Im2,gfilter,2,gfilter,2);
Im.copyData(Im1);
Im.Multiplywith(0.4);
Im.Add(Im2,0.6);
//Im.Multiplywith(0.5);
//Im1.copyData(im1);
//Im2.copyData(im2);
Im.dx(imdx,true);
Im.dy(imdy,true);
imdt.Subtract(Im2,Im1);
}
else
{
// Im1 and Im2 are the smoothed version of im1 and im2
FImage Im1,Im2;
im1.imfilter_hv(Im1,gfilter,2,gfilter,2);
im2.imfilter_hv(Im2,gfilter,2,gfilter,2);
//Im1.copyData(im1);
//Im2.copyData(im2);
Im2.dx(imdx,true);
Im2.dy(imdy,true);
imdt.Subtract(Im2,Im1);
}
imdx.setDerivative();
imdy.setDerivative();
imdt.setDerivative();
}
//--------------------------------------------------------------------------------------------------------
// Yinlin.Hu: function to compute dxx, dyy, dxy, dxt and dyt for motion estimation
//--------------------------------------------------------------------------------------------------------
void OpticalFlow::getDxxs(FImage& imdxx, FImage& imdyy, FImage& imdxy, FImage& imdxt, FImage& imdyt, const FImage& im1, const FImage& im2)
{
float gfilter[5] = { 0.02, 0.11, 0.74, 0.11, 0.02 };
// Im1 and Im2 are the smoothed version of im1 and im2
FImage Im1, Im2;
FImage dx1, dy1, dx2, dy2;
im1.imfilter_hv(Im1, gfilter, 2, gfilter, 2);
im2.imfilter_hv(Im2, gfilter, 2, gfilter, 2);
//Im1.copyData(im1);
//Im2.copyData(im2);
Im2.dxx(imdxx);
Im2.dyy(imdyy);
Im2.dxy(imdxy);
Im1.dx(dx1, true);
Im1.dy(dy1, true);
Im2.dx(dx2, true);
Im2.dy(dy2, true);
imdxt.Subtract(dx2, dx1);
imdyt.Subtract(dy2, dy1);
imdxx.setDerivative();
imdyy.setDerivative();
imdxy.setDerivative();
imdxt.setDerivative();
imdyt.setDerivative();
}
//--------------------------------------------------------------------------------------------------------
// function to do sanity check: imdx*du+imdy*dy+imdt=0
//--------------------------------------------------------------------------------------------------------
void OpticalFlow::SanityCheck(const FImage &imdx, const FImage &imdy, const FImage &imdt, float du, float dv)
{
if(imdx.matchDimension(imdy)==false || imdx.matchDimension(imdt)==false)
{
cout<<"The dimensions of the derivatives don't match!"<<endl;
return;
}
const _FlowPrecision* pImDx,*pImDy,*pImDt;
pImDx=imdx.data();
pImDy=imdy.data();
pImDt=imdt.data();
float error=0;
for(int i=0;i<imdx.height();i++)
for(int j=0;j<imdx.width();j++)
for(int k=0;k<imdx.nchannels();k++)
{
int offset=(i*imdx.width()+j)*imdx.nchannels()+k;
float temp=pImDx[offset]*du+pImDy[offset]*dv+pImDt[offset];
error+=fabs(temp);
}
error/=imdx.nelements();
cout<<"The mean error of |dx*u+dy*v+dt| is "<<error<<endl;
}
//--------------------------------------------------------------------------------------------------------
// function to warp image based on the flow field
//--------------------------------------------------------------------------------------------------------
void OpticalFlow::warpFL(FImage &warpIm2, const FImage &Im1, const FImage &Im2, const FImage &vx, const FImage &vy)
{
if(warpIm2.matchDimension(Im2)==false)
warpIm2.allocate(Im2.width(),Im2.height(),Im2.nchannels());
ImageProcessing::warpImage(warpIm2.data(),Im1.data(),Im2.data(),vx.data(),vy.data(),Im2.width(),Im2.height(),Im2.nchannels());
}
void OpticalFlow::warpFL(FImage &warpIm2, const FImage &Im1, const FImage &Im2, const FImage &Flow)
{
if(warpIm2.matchDimension(Im2)==false)
warpIm2.allocate(Im2.width(),Im2.height(),Im2.nchannels());
ImageProcessing::warpImageFlow(warpIm2.data(),Im1.data(),Im2.data(),Flow.data(),Im2.width(),Im2.height(),Im2.nchannels());
}
//--------------------------------------------------------------------------------------------------------
// function to generate mask of the pixels that move inside the image boundary
//--------------------------------------------------------------------------------------------------------
void OpticalFlow::genInImageMask(FImage &mask, const FImage &vx, const FImage &vy,int interval)
{
int imWidth,imHeight;
imWidth=vx.width();
imHeight=vx.height();
if(mask.matchDimension(vx)==false)
mask.allocate(imWidth,imHeight);
const _FlowPrecision *pVx,*pVy;
_FlowPrecision *pMask;
pVx=vx.data();
pVy=vy.data();
mask.reset();
pMask=mask.data();
float x,y;
for(int i=0;i<imHeight;i++)
for(int j=0;j<imWidth;j++)
{
int offset=i*imWidth+j;
y=i+pVx[offset];
x=j+pVy[offset];
if(x<interval || x>imWidth-1-interval || y<interval || y>imHeight-1-interval)
continue;
pMask[offset]=1;
}
}
void OpticalFlow::genInImageMask(FImage &mask, const FImage &flow,int interval)
{
int imWidth,imHeight;
imWidth=flow.width();
imHeight=flow.height();
if(mask.matchDimension(flow.width(),flow.height(),1)==false)
mask.allocate(imWidth,imHeight);
else
mask.reset();
const _FlowPrecision *pFlow;
_FlowPrecision *pMask;
pFlow = flow.data();;
pMask=mask.data();
float x,y;
for(int i=0;i<imHeight;i++)
for(int j=0;j<imWidth;j++)
{
int offset=i*imWidth+j;
y=i+pFlow[offset*2+1];
x=j+pFlow[offset*2];
if(x<interval || x>imWidth-1-interval || y<interval || y>imHeight-1-interval)
continue;
pMask[offset]=1;
}
}
//--------------------------------------------------------------------------------------------------------
// function to compute optical flow field using two fixed point iterations
// Input arguments:
// Im1, Im2: frame 1 and frame 2
// warpIm2: the warped frame 2 according to the current flow field u and v
// u,v: the current flow field, NOTICE that they are also output arguments
//
//--------------------------------------------------------------------------------------------------------
void OpticalFlow::SmoothFlowSOR(const FImage &Im1, const FImage &Im2, FImage &warpIm2, FImage &u, FImage &v,
float alpha, int nOuterFPIterations, int nInnerFPIterations, int nSORIterations)
{
FImage mask,imdx,imdy,imdt;
int imWidth,imHeight,nChannels,nPixels;
imWidth=Im1.width();
imHeight=Im1.height();
nChannels=Im1.nchannels();
nPixels=imWidth*imHeight;
FImage du(imWidth,imHeight),dv(imWidth,imHeight);
FImage uu(imWidth,imHeight),vv(imWidth,imHeight);
FImage uux(imWidth,imHeight),uuy(imWidth,imHeight);
FImage vvx(imWidth,imHeight),vvy(imWidth,imHeight);
FImage Phi_1st(imWidth,imHeight);
FImage Psi_1st(imWidth,imHeight,nChannels);
FImage imdxdy,imdx2,imdy2,imdtdx,imdtdy;
FImage ImDxDy,ImDx2,ImDy2,ImDtDx,ImDtDy;
FImage foo1,foo2;
float prob1,prob2,prob11,prob22;
float varepsilon_phi=pow(0.001,2);
float varepsilon_psi=pow(0.001,2);
//--------------------------------------------------------------------------
// the outer fixed point iteration
//--------------------------------------------------------------------------
for(int count=0;count<nOuterFPIterations;count++)
{
// compute the gradient
getDxs(imdx,imdy,imdt,Im1,warpIm2);
// generate the mask to set the weight of the pixels moving outside of the image boundary to be zero
genInImageMask(mask,u,v);
// set the derivative of the flow field to be zero
du.reset();
dv.reset();
//--------------------------------------------------------------------------
// the inner fixed point iteration
//--------------------------------------------------------------------------
for(int hh=0;hh<nInnerFPIterations;hh++)
{
// compute the derivatives of the current flow field
if(hh==0)
{
uu.copyData(u);
vv.copyData(v);
}
else
{
uu.Add(u,du);
vv.Add(v,dv);
}
uu.dx(uux);
uu.dy(uuy);
vv.dx(vvx);
vv.dy(vvy);
// compute the weight of phi
Phi_1st.reset();
_FlowPrecision* phiData=Phi_1st.data();
float temp;
const _FlowPrecision *uuxData,*uuyData,*vvxData,*vvyData;
uuxData=uux.data();
uuyData=uuy.data();
vvxData=vvx.data();
vvyData=vvy.data();
float power_alpha = 0.5;
for(int i=0;i<nPixels;i++)
{
temp=uuxData[i]*uuxData[i]+uuyData[i]*uuyData[i]+vvxData[i]*vvxData[i]+vvyData[i]*vvyData[i];
//phiData[i]=power_alpha*pow(temp+varepsilon_phi,power_alpha-1);
phiData[i] = 0.5/sqrt(temp+varepsilon_phi);
//phiData[i] = 1/(power_alpha+temp);
}
// compute the nonlinear term of psi
Psi_1st.reset();
_FlowPrecision* psiData=Psi_1st.data();
const _FlowPrecision *imdxData,*imdyData,*imdtData;
const _FlowPrecision *duData,*dvData;
imdxData=imdx.data();
imdyData=imdy.data();
imdtData=imdt.data();
duData=du.data();
dvData=dv.data();
float _a = 10000, _b = 0.1;
if(nChannels==1)
for(int i=0;i<nPixels;i++)
{
temp=imdtData[i]+imdxData[i]*duData[i]+imdyData[i]*dvData[i];
//if(temp*temp<0.04)
// psiData[i]=1/(2*sqrt(temp*temp+varepsilon_psi));
//psiData[i] = _a*_b/(1+_a*temp*temp);
// the following code is for log Gaussian mixture probability model
temp *= temp;
switch(noiseModel)
{
case GMixture:
prob1 = GMPara.Gaussian(temp,0,0)*GMPara.alpha[0];
prob2 = GMPara.Gaussian(temp,1,0)*(1-GMPara.alpha[0]);
prob11 = prob1/(2*GMPara.sigma_square[0]);
prob22 = prob2/(2*GMPara.beta_square[0]);
psiData[i] = (prob11+prob22)/(prob1+prob2);
break;
case Lap:
if(LapPara[0]<1E-20)
continue;
//psiData[i]=1/(2*sqrt(temp+varepsilon_psi)*LapPara[0]);
psiData[i]=1/(2*sqrt(temp+varepsilon_psi));
break;
}
}
else
for(int i=0;i<nPixels;i++)
for(int k=0;k<nChannels;k++)
{
int offset=i*nChannels+k;
temp=imdtData[offset]+imdxData[offset]*duData[i]+imdyData[offset]*dvData[i];
//if(temp*temp<0.04)
// psiData[offset]=1/(2*sqrt(temp*temp+varepsilon_psi));
//psiData[offset] = _a*_b/(1+_a*temp*temp);
temp *= temp;
switch(noiseModel)
{
case GMixture:
prob1 = GMPara.Gaussian(temp,0,k)*GMPara.alpha[k];
prob2 = GMPara.Gaussian(temp,1,k)*(1-GMPara.alpha[k]);
prob11 = prob1/(2*GMPara.sigma_square[k]);
prob22 = prob2/(2*GMPara.beta_square[k]);
psiData[offset] = (prob11+prob22)/(prob1+prob2);
break;
case Lap:
if(LapPara[k]<1E-20)
continue;
//psiData[offset]=1/(2*sqrt(temp+varepsilon_psi)*LapPara[k]);
psiData[offset]=1/(2*sqrt(temp+varepsilon_psi));
break;
}
}
// prepare the components of the large linear system
ImDxDy.Multiply(Psi_1st,imdx,imdy);
ImDx2.Multiply(Psi_1st,imdx,imdx);
ImDy2.Multiply(Psi_1st,imdy,imdy);
ImDtDx.Multiply(Psi_1st,imdx,imdt);
ImDtDy.Multiply(Psi_1st,imdy,imdt);
ImDxDy.collapse(imdxdy);
ImDx2.collapse(imdx2);
ImDy2.collapse(imdy2);
ImDtDx.collapse(imdtdx);
ImDtDy.collapse(imdtdy);
// laplacian filtering of the current flow field
Laplacian(foo1,u,Phi_1st);
Laplacian(foo2,v,Phi_1st);
for(int i=0;i<nPixels;i++)
{
imdtdx.data()[i] = -imdtdx.data()[i] + alpha*foo1.data()[i];
imdtdy.data()[i] = -imdtdy.data()[i] + alpha*foo2.data()[i];
}
// here we start SOR
// set omega
float omega = 1.9;
du.reset();
dv.reset();
for(int k = 0; k<nSORIterations; k++)
for(int i = 0; i<imHeight; i++)
for(int j = 0; j<imWidth; j++)
{
int offset = i * imWidth+j;
float sigma1 = 0, sigma2 = 0, coeff = 0;
float _weight;
if(j>0)
{
_weight = phiData[offset-1];
sigma1 += _weight*du.data()[offset-1];
sigma2 += _weight*dv.data()[offset-1];
coeff += _weight;
}
if(j<imWidth-1)
{
_weight = phiData[offset];
sigma1 += _weight*du.data()[offset+1];
sigma2 += _weight*dv.data()[offset+1];
coeff += _weight;
}
if(i>0)
{
_weight = phiData[offset-imWidth];
sigma1 += _weight*du.data()[offset-imWidth];
sigma2 += _weight*dv.data()[offset-imWidth];
coeff += _weight;
}
if(i<imHeight-1)
{
_weight = phiData[offset];
sigma1 += _weight*du.data()[offset+imWidth];
sigma2 += _weight*dv.data()[offset+imWidth];
coeff += _weight;
}
sigma1 *= -alpha;
sigma2 *= -alpha;
coeff *= alpha;
// compute du
sigma1 += imdxdy.data()[offset]*dv.data()[offset];
du.data()[offset] = (1-omega)*du.data()[offset] +
omega/(imdx2.data()[offset] /*+ alpha*0.05*/ + coeff)*(imdtdx.data()[offset] - sigma1);
// compute dv
sigma2 += imdxdy.data()[offset]*du.data()[offset];
dv.data()[offset] = (1-omega)*dv.data()[offset] +
omega/(imdy2.data()[offset] /*+ alpha*0.05*/ + coeff)*(imdtdy.data()[offset] - sigma2);
}
}
u.Add(du);
v.Add(dv);
if(interpolation == Bilinear)
warpFL(warpIm2,Im1,Im2,u,v);
else
{
Im2.warpImageBicubicRef(Im1,warpIm2,u,v);
warpIm2.threshold();
}
//Im2.warpImageBicubicRef(Im1,warpIm2,BicubicCoeff,u,v);
// estimate noise level
switch(noiseModel)
{
case GMixture:
estGaussianMixture(Im1,warpIm2,GMPara);
break;
case Lap:
estLaplacianNoise(Im1,warpIm2,LapPara);
}
}
}
void OpticalFlow::OneLevelFlow(const FImage &Im1, const FImage &Im2, FImage &warpIm2, FImage &u, FImage &v,
float alpha, int nOuterFPIterations, int nInnerFPIterations, int nSORIterations)
{
FImage mask, imdx, imdy, imdt;
int imWidth, imHeight, nChannels, nPixels;
imWidth = Im1.width();
imHeight = Im1.height();
nChannels = Im1.nchannels();
nPixels = imWidth*imHeight;
FImage du(imWidth, imHeight), dv(imWidth, imHeight);
FImage uu(imWidth, imHeight), vv(imWidth, imHeight);
FImage uux(imWidth, imHeight), uuy(imWidth, imHeight);
FImage vvx(imWidth, imHeight), vvy(imWidth, imHeight);
FImage psi_d(imWidth, imHeight, nChannels);
FImage psi_s(imWidth, imHeight);
FImage D, Du, Dv, Au, Av;
FImage dD, dDu, dDv, dAu, dAv;
FImage div_u, div_v;
float prob1, prob2, prob11, prob22;
float varepsilon_psi_d = pow(0.001, 2);
float varepsilon_psi_s = pow(0.001, 2);
//--------------------------------------------------------------------------
// the outer fixed point iteration
//--------------------------------------------------------------------------
for (int count = 0; count < nOuterFPIterations; count++)
{
// compute the gradient
getDxs(imdx, imdy, imdt, Im1, warpIm2);
// generate the mask to set the weight of the pixels moving outside of the image boundary to be zero
// genInImageMask(mask, u, v);
// set the derivative of the flow field to be zero
du.reset();
dv.reset();
//--------------------------------------------------------------------------
// the inner fixed point iteration
//--------------------------------------------------------------------------
for (int hh = 0; hh < nInnerFPIterations; hh++)
{
// compute the derivatives of the current flow field
if (hh == 0)
{
uu.copyData(u);
vv.copyData(v);
}
else
{
uu.Add(u, du);
vv.Add(v, dv);
}
uu.dx(uux);
uu.dy(uuy);
vv.dx(vvx);
vv.dy(vvy);
// compute the weight of phi
psi_s.reset();
_FlowPrecision* psi_sData = psi_s.data();
float temp;
const _FlowPrecision *uuxData, *uuyData, *vvxData, *vvyData;
uuxData = uux.data();
uuyData = uuy.data();
vvxData = vvx.data();
vvyData = vvy.data();
float power_alpha = 0.5;
for (int i = 0; i < nPixels; i++)
{
temp = uuxData[i] * uuxData[i] + uuyData[i] * uuyData[i] + vvxData[i] * vvxData[i] + vvyData[i] * vvyData[i];
//phiData[i]=power_alpha*pow(temp+varepsilon_phi,power_alpha-1);
psi_sData[i] = 0.5 / sqrt(temp + varepsilon_psi_s);
//phiData[i] = 1/(power_alpha+temp);
}
// compute the nonlinear term of psi
psi_d.reset();
_FlowPrecision* psi_dData = psi_d.data();
const _FlowPrecision *imdxData, *imdyData, *imdtData;
const _FlowPrecision *duData, *dvData;
imdxData = imdx.data();
imdyData = imdy.data();
imdtData = imdt.data();
duData = du.data();
dvData = dv.data();
float _a = 10000, _b = 0.1;
if (nChannels == 1)
for (int i = 0; i < nPixels; i++)
{
temp = imdtData[i] + imdxData[i] * duData[i] + imdyData[i] * dvData[i];
//if(temp*temp<0.04)
// psiData[i]=1/(2*sqrt(temp*temp+varepsilon_psi));
//psiData[i] = _a*_b/(1+_a*temp*temp);
// the following code is for log Gaussian mixture probability model
temp *= temp;
switch (noiseModel)
{
case GMixture:
prob1 = GMPara.Gaussian(temp, 0, 0)*GMPara.alpha[0];
prob2 = GMPara.Gaussian(temp, 1, 0)*(1 - GMPara.alpha[0]);
prob11 = prob1 / (2 * GMPara.sigma_square[0]);
prob22 = prob2 / (2 * GMPara.beta_square[0]);
psi_dData[i] = (prob11 + prob22) / (prob1 + prob2);
break;
case Lap:
if (LapPara[0] < 1E-20)
continue;
//psiData[i]=1/(2*sqrt(temp+varepsilon_psi)*LapPara[0]);
psi_dData[i] = 1 / (2 * sqrt(temp + varepsilon_psi_d));
break;
}
}
else
for (int i = 0; i < nPixels; i++)
for (int k = 0; k < nChannels; k++)
{
int offset = i*nChannels + k;
temp = imdtData[offset] + imdxData[offset] * duData[i] + imdyData[offset] * dvData[i];
//if(temp*temp<0.04)
// psiData[offset]=1/(2*sqrt(temp*temp+varepsilon_psi));
//psiData[offset] = _a*_b/(1+_a*temp*temp);
temp *= temp;
switch (noiseModel)
{
case GMixture:
prob1 = GMPara.Gaussian(temp, 0, k)*GMPara.alpha[k];
prob2 = GMPara.Gaussian(temp, 1, k)*(1 - GMPara.alpha[k]);
prob11 = prob1 / (2 * GMPara.sigma_square[k]);
prob22 = prob2 / (2 * GMPara.beta_square[k]);
psi_dData[offset] = (prob11 + prob22) / (prob1 + prob2);
break;
case Lap:
if (LapPara[k] < 1E-20)
continue;
//psiData[offset]=1/(2*sqrt(temp+varepsilon_psi)*LapPara[k]);
psi_dData[offset] = 1 / (2 * sqrt(temp + varepsilon_psi_d));
break;
}
}
// prepare the components of the large linear system
dD.Multiply(psi_d, imdx, imdy);
dDu.Multiply(psi_d, imdx, imdx);
dDv.Multiply(psi_d, imdy, imdy);
dAu.Multiply(psi_d, imdx, imdt);
dAv.Multiply(psi_d, imdy, imdt);
dD.collapse(D);
dDu.collapse(Du);
dDv.collapse(Dv);
dAu.collapse(Au);
dAv.collapse(Av);
// laplacian filtering of the current flow field
Laplacian(div_u, u, psi_s);
Laplacian(div_v, v, psi_s);
for (int i = 0; i < nPixels; i++)
{
Au.data()[i] = -Au.data()[i] + alpha*div_u.data()[i];
Av.data()[i] = -Av.data()[i] + alpha*div_v.data()[i];
}
// here we start SOR
// set omega
float omega = 1.9;
du.reset();
dv.reset();
for (int k = 0; k < nSORIterations; k++)
for (int i = 0; i < imHeight; i++)
for (int j = 0; j < imWidth; j++)
{
int offset = i*imWidth+j;
float div_du = 0, div_dv = 0, div_d = 0;
float _weight;
if (j > 0){
_weight = psi_sData[offset - 1];
div_du += _weight*du.data()[offset - 1];
div_dv += _weight*dv.data()[offset - 1];
div_d += _weight;
}
if (j < imWidth - 1){
_weight = psi_sData[offset];
div_du += _weight*du.data()[offset + 1];
div_dv += _weight*dv.data()[offset + 1];
div_d += _weight;
}
if (i > 0){
_weight = psi_sData[offset - imWidth];
div_du += _weight*du.data()[offset - imWidth];
div_dv += _weight*dv.data()[offset - imWidth];
div_d += _weight;
}
if (i < imHeight - 1){
_weight = psi_sData[offset];
div_du += _weight*du.data()[offset + imWidth];
div_dv += _weight*dv.data()[offset + imWidth];
div_d += _weight;
}
// compute du
du.data()[offset] =
(1 - omega)*du.data()[offset] + omega *
(Au.data()[offset] - D.data()[offset]*dv.data()[offset] + alpha*div_du) /
(Du.data()[offset] + alpha*div_d);
// compute dv
dv.data()[offset] =
(1 - omega)*dv.data()[offset] + omega *
(Av.data()[offset] - D.data()[offset]*du.data()[offset] + alpha*div_dv) /
(Dv.data()[offset] + alpha*div_d);
}
}
u.Add(du);
v.Add(dv);
//
// u.MedianFiltering(1);
// v.MedianFiltering(1);
if (interpolation == Bilinear)
warpFL(warpIm2, Im1, Im2, u, v);
else
{
Im2.warpImageBicubicRef(Im1, warpIm2, u, v);
warpIm2.threshold();
}
//Im2.warpImageBicubicRef(Im1,warpIm2,BicubicCoeff,u,v);
// estimate noise level
switch (noiseModel)
{
case GMixture:
estGaussianMixture(Im1, warpIm2, GMPara);
break;
case Lap:
estLaplacianNoise(Im1, warpIm2, LapPara);
}
}
}
void OpticalFlow::OneLevelFlow_Brox(const FImage &Im1, const FImage &Im2, FImage &warpIm2, FImage &u, FImage &v,
float alpha, float gamma, int nOuterFPIterations, int nInnerFPIterations, int nSORIterations)
{
FImage mask, imdx, imdy, imdt;
FImage imdxx, imdyy, imdxy, imdxt, imdyt;
int imWidth, imHeight, nChannels, nElements, nPixels;
imWidth = Im1.width();
imHeight = Im1.height();
nChannels = Im1.nchannels();
nElements = Im1.nelements();
nPixels = imWidth*imHeight;
FImage du(imWidth, imHeight), dv(imWidth, imHeight);
FImage uu(imWidth, imHeight), vv(imWidth, imHeight);
FImage uux(imWidth, imHeight), uuy(imWidth, imHeight);
FImage vvx(imWidth, imHeight), vvy(imWidth, imHeight);
FImage psi_d(imWidth, imHeight, nChannels);
FImage psi_g(imWidth, imHeight, nChannels);
FImage psi_s(imWidth, imHeight);
FImage Au(imWidth, imHeight);
FImage Av(imWidth, imHeight);
FImage Du(imWidth, imHeight);
FImage Dv(imWidth, imHeight);
FImage D(imWidth, imHeight);
FImage dAu, dAv, dDu, dDv, dD;
FImage gAu, gAv, gDu, gDv, gD;
FImage div_u, div_v;
float prob1, prob2, prob11, prob22;
float varepsilon_psi_d = pow(0.001, 2);
float varepsilon_psi_g = pow(0.001, 2);
float varepsilon_psi_s = pow(0.001, 2);
//--------------------------------------------------------------------------
// the outer fixed point iteration
//--------------------------------------------------------------------------
for (int count = 0; count < nOuterFPIterations; count++)
{
// compute the gradient
getDxs(imdx, imdy, imdt, Im1, warpIm2);
getDxxs(imdxx, imdyy, imdxy, imdxt, imdyt, Im1, warpIm2);
// generate the mask to set the weight of the pixels moving outside of the image boundary to be zero
// genInImageMask(mask, u, v);
// set the derivative of the flow field to be zero
du.reset();
dv.reset();
//--------------------------------------------------------------------------
// the inner fixed point iteration
//--------------------------------------------------------------------------
for (int hh = 0; hh < nInnerFPIterations; hh++)
{
// compute the derivatives of the current flow field
if (hh == 0)
{
uu.copyData(u);
vv.copyData(v);
}
else
{
uu.Add(u, du);
vv.Add(v, dv);
}
uu.dx(uux);
uu.dy(uuy);
vv.dx(vvx);
vv.dy(vvy);
// compute the weight of smoothness
psi_s.reset();
_FlowPrecision* psi_sData = psi_s.data();
float temp;
const _FlowPrecision *uuxData, *uuyData, *vvxData, *vvyData;
uuxData = uux.data();
uuyData = uuy.data();
vvxData = vvx.data();
vvyData = vvy.data();
float power_alpha = 0.5;
for (int i = 0; i < nPixels; i++)
{
temp = uuxData[i] * uuxData[i] + uuyData[i] * uuyData[i] + vvxData[i] * vvxData[i] + vvyData[i] * vvyData[i];
//phiData[i]=power_alpha*pow(temp+varepsilon_phi,power_alpha-1);
psi_sData[i] = 0.5 / sqrt(temp + varepsilon_psi_s);
//phiData[i] = 1/(power_alpha+temp);
}
// compute the weight of gradient
psi_g.reset();
_FlowPrecision* psi_gData = psi_g.data();
const _FlowPrecision *imdxxData, *imdyyData, *imdxyData, *imdxtData, *imdytData;
const _FlowPrecision *duData, *dvData;
imdxxData = imdxx.data();
imdyyData = imdyy.data();
imdxyData = imdxy.data();
imdxtData = imdxt.data();
imdytData = imdyt.data();
duData = du.data();
dvData = dv.data();
float tempu, tempv;
for (int i = 0; i < nPixels; i++){
for (int k = 0; k < nChannels; k++){
int offset = i*nChannels + k;
tempu = imdxtData[offset] + imdxxData[offset] * duData[i] + imdxyData[offset] * dvData[i];
tempv = imdytData[offset] + imdxyData[offset] * duData[i] + imdyyData[offset] * dvData[i];
tempu *= tempu;
tempv *= tempv;
psi_gData[offset] = 1 / (2 * sqrt(tempu + tempv + varepsilon_psi_g));
}
}
// compute the weight of data
psi_d.reset();
_FlowPrecision* psi_dData = psi_d.data();
const _FlowPrecision *imdxData, *imdyData, *imdtData;
imdxData = imdx.data();
imdyData = imdy.data();
imdtData = imdt.data();
float _a = 10000, _b = 0.1;
if (nChannels == 1)
for (int i = 0; i < nPixels; i++)
{
temp = imdtData[i] + imdxData[i] * duData[i] + imdyData[i] * dvData[i];
//if(temp*temp<0.04)
// psiData[i]=1/(2*sqrt(temp*temp+varepsilon_psi));
//psiData[i] = _a*_b/(1+_a*temp*temp);
// the following code is for log Gaussian mixture probability model
temp *= temp;
switch (noiseModel)
{
case GMixture:
prob1 = GMPara.Gaussian(temp, 0, 0)*GMPara.alpha[0];
prob2 = GMPara.Gaussian(temp, 1, 0)*(1 - GMPara.alpha[0]);
prob11 = prob1 / (2 * GMPara.sigma_square[0]);
prob22 = prob2 / (2 * GMPara.beta_square[0]);
psi_dData[i] = (prob11 + prob22) / (prob1 + prob2);
break;
case Lap:
if (LapPara[0] < 1E-20)
continue;
//psiData[i]=1/(2*sqrt(temp+varepsilon_psi)*LapPara[0]);
psi_dData[i] = 1 / (2 * sqrt(temp + varepsilon_psi_d));
break;
}
}
else
for (int i = 0; i < nPixels; i++)
for (int k = 0; k < nChannels; k++)
{
int offset = i*nChannels + k;
temp = imdtData[offset] + imdxData[offset] * duData[i] + imdyData[offset] * dvData[i];
//if(temp*temp<0.04)
// psiData[offset]=1/(2*sqrt(temp*temp+varepsilon_psi));
//psiData[offset] = _a*_b/(1+_a*temp*temp);
temp *= temp;
switch (noiseModel)
{
case GMixture:
prob1 = GMPara.Gaussian(temp, 0, k)*GMPara.alpha[k];
prob2 = GMPara.Gaussian(temp, 1, k)*(1 - GMPara.alpha[k]);
prob11 = prob1 / (2 * GMPara.sigma_square[k]);
prob22 = prob2 / (2 * GMPara.beta_square[k]);
psi_dData[offset] = (prob11 + prob22) / (prob1 + prob2);
break;
case Lap:
if (LapPara[k] < 1E-20)
continue;
//psiData[offset]=1/(2*sqrt(temp+varepsilon_psi)*LapPara[k]);
psi_dData[offset] = 1 / (2 * sqrt(temp + varepsilon_psi_d));
break;
}
}
// prepare the components of the large linear system
gAu.allocate(Im1);
gAv.allocate(Im1);
gDu.allocate(Im1);
gDv.allocate(Im1);
gD.allocate(Im1);
for (int i = 0; i < nElements; i++){
gAu.pData[i] = psi_gData[i] * (imdxtData[i] * imdxxData[i] + imdytData[i] * imdxyData[i]);
gAv.pData[i] = psi_gData[i] * (imdxtData[i] * imdxyData[i] + imdytData[i] * imdyyData[i]);
gDu.pData[i] = psi_gData[i] * (imdxxData[i] * imdxxData[i] + imdxyData[i] * imdxyData[i]);
gDv.pData[i] = psi_gData[i] * (imdyyData[i] * imdyyData[i] + imdxyData[i] * imdxyData[i]);
gD.pData[i] = psi_gData[i] * (imdxxData[i] + imdyyData[i]) * imdxyData[i];
}
dD.Multiply(psi_d, imdx, imdy);
dDu.Multiply(psi_d, imdx, imdx);
dDv.Multiply(psi_d, imdy, imdy);
dAu.Multiply(psi_d, imdx, imdt);
dAv.Multiply(psi_d, imdy, imdt);
dD.collapse();
dDu.collapse();
dDv.collapse();
dAu.collapse();
dAv.collapse();
gD.collapse();
gDu.collapse();
gDv.collapse();
gAu.collapse();
gAv.collapse();
// laplacian filtering of the current flow field
Laplacian(div_u, u, psi_s);
Laplacian(div_v, v, psi_s);
for (int i = 0; i < nPixels; i++){
Au.pData[i] = -dAu.pData[i] + alpha*div_u.pData[i] - gamma*gAu.pData[i];
Av.pData[i] = -dAv.pData[i] + alpha*div_v.pData[i] - gamma*gAv.pData[i];
Du.pData[i] = dDu.pData[i] + gamma*gDu.pData[i];
Dv.pData[i] = dDv.pData[i] + gamma*gDv.pData[i];
D.pData[i] = dD.pData[i] + gamma*gD.pData[i];
}
// here we start SOR
// set omega
float omega = 1.9;
du.reset();
dv.reset();
for (int k = 0; k < nSORIterations; k++)
for (int i = 0; i < imHeight; i++)
for (int j = 0; j < imWidth; j++)
{
int offset = i*imWidth + j;
float div_du = 0, div_dv = 0, div_d = 0;
float _weight;
if (j > 0){
_weight = psi_sData[offset - 1];
div_du += _weight*du.data()[offset - 1];
div_dv += _weight*dv.data()[offset - 1];
div_d += _weight;
}
if (j < imWidth - 1){
_weight = psi_sData[offset];
div_du += _weight*du.data()[offset + 1];
div_dv += _weight*dv.data()[offset + 1];
div_d += _weight;
}
if (i > 0){
_weight = psi_sData[offset - imWidth];
div_du += _weight*du.data()[offset - imWidth];
div_dv += _weight*dv.data()[offset - imWidth];
div_d += _weight;
}
if (i < imHeight - 1){
_weight = psi_sData[offset];
div_du += _weight*du.data()[offset + imWidth];
div_dv += _weight*dv.data()[offset + imWidth];
div_d += _weight;
}