returnValue Power::AD_symmetric( int dim , /**< number of directions */
VariableType *varType , /**< the variable types */
int *component , /**< and their components */
Operator *l , /**< the backward seed */
Operator **S , /**< forward seed matrix */
int dimS , /**< dimension of forward seed */
Operator **dfS , /**< first order foward result */
Operator **ldf , /**< first order backward result */
Operator **H , /**< upper trianglular part of the Hessian */
int &nNewLIS , /**< the number of newLIS */
TreeProjection ***newLIS , /**< the new LIS-pointer */
int &nNewSIS , /**< the number of newSIS */
TreeProjection ***newSIS , /**< the new SIS-pointer */
int &nNewHIS , /**< the number of newHIS */
TreeProjection ***newHIS /**< the new HIS-pointer */ ){
TreeProjection dyy, dy;
TreeProjection dx( *derivative12 );
dy = Product( clone(), derivative02->clone());
TreeProjection dxx( *derivative22 );
TreeProjection dxy( *derivative23 );
dyy = Product( dy.clone(), derivative02->clone() );
return ADsymCommon2( argument1,argument2,dx,dy,dxx,dxy,dyy, dim, varType, component, l, S, dimS, dfS,
ldf, H, nNewLIS, newLIS, nNewSIS, newSIS, nNewHIS, newHIS );
}
void computeCorners(CTensor<float>& aImage, CMatrix<float>& aCorners, float aRho) {
aCorners.setSize(aImage.xSize(),aImage.ySize());
int aXSize = aImage.xSize();
int aYSize = aImage.ySize();
int aSize = aXSize*aYSize;
// Compute gradient
CTensor<float> dx(aXSize,aYSize,aImage.zSize());
CTensor<float> dy(aXSize,aYSize,aImage.zSize());
CDerivative<float> aDerivative(3);
NFilter::filter(aImage,dx,aDerivative,1,1);
NFilter::filter(aImage,dy,1,aDerivative,1);
// Compute second moment matrix
CMatrix<float> dxx(aXSize,aYSize,0);
CMatrix<float> dyy(aXSize,aYSize,0);
CMatrix<float> dxy(aXSize,aYSize,0);
int i2 = 0;
for (int k = 0; k < aImage.zSize(); k++)
for (int i = 0; i < aSize; i++,i2++) {
dxx.data()[i] += dx.data()[i2]*dx.data()[i2];
dyy.data()[i] += dy.data()[i2]*dy.data()[i2];
dxy.data()[i] += dx.data()[i2]*dy.data()[i2];
}
// Smooth second moment matrix
NFilter::recursiveSmoothX(dxx,aRho);
NFilter::recursiveSmoothY(dxx,aRho);
NFilter::recursiveSmoothX(dyy,aRho);
NFilter::recursiveSmoothY(dyy,aRho);
NFilter::recursiveSmoothX(dxy,aRho);
NFilter::recursiveSmoothY(dxy,aRho);
// Compute smallest eigenvalue
for (int i = 0; i < aSize; i++) {
float a = dxx.data()[i];
float b = dxy.data()[i];
float c = dyy.data()[i];
float temp = 0.5*(a+c);
float temp2 = temp*temp+b*b-a*c;
if (temp2 < 0.0f) aCorners.data()[i] = 0.0f;
else aCorners.data()[i] = temp-sqrt(temp2);
}
}
//----------------------------------------------------------------------------
int ExtractRidges::Main (int, char**)
{
std::string imageName = Environment::GetPathR("Head.im");
ImageDouble2D image(imageName.c_str());
// Normalize the image values to be in [0,1].
int quantity = image.GetQuantity();
double minValue = image[0], maxValue = minValue;
int i;
for (i = 1; i < quantity; ++i)
{
if (image[i] < minValue)
{
minValue = image[i];
}
else if (image[i] > maxValue)
{
maxValue = image[i];
}
}
double invRange = 1.0/(maxValue - minValue);
for (i = 0; i < quantity; ++i)
{
image[i] = (image[i] - minValue)*invRange;
}
// Use first-order centered finite differences to estimate the image
// derivatives. The gradient is DF = (df/dx, df/dy) and the Hessian
// is D^2F = {{d^2f/dx^2, d^2f/dxdy}, {d^2f/dydx, d^2f/dy^2}}.
int xBound = image.GetBound(0);
int yBound = image.GetBound(1);
int xBoundM1 = xBound - 1;
int yBoundM1 = yBound - 1;
ImageDouble2D dx(xBound, yBound);
ImageDouble2D dy(xBound, yBound);
ImageDouble2D dxx(xBound, yBound);
ImageDouble2D dxy(xBound, yBound);
ImageDouble2D dyy(xBound, yBound);
int x, y;
for (y = 1; y < yBoundM1; ++y)
{
for (x = 1; x < xBoundM1; ++x)
{
dx(x, y) = 0.5*(image(x+1, y) - image(x-1, y));
dy(x, y) = 0.5*(image(x, y+1) - image(x, y-1));
dxx(x, y) = image(x+1, y) - 2.0*image(x, y) + image(x-1, y);
dxy(x, y) = 0.25*(image(x+1, y+1) + image(x-1, y-1)
- image(x+1, y-1) - image(x-1, y+1));
dyy(x, y) = image(x, y+1) - 2.0*image(x, y) + image(x, y+1);
}
}
dx.Save("dx.im");
dy.Save("dy.im");
dxx.Save("dxx.im");
dxy.Save("dxy.im");
dyy.Save("dyy.im");
// The eigensolver produces eigenvalues a and b and corresponding
// eigenvectors U and V: D^2F*U = a*U, D^2F*V = b*V. Define
// P = Dot(U,DF) and Q = Dot(V,DF). The classification is as follows.
// ridge: P = 0 with a < 0
// valley: Q = 0 with b > 0
ImageDouble2D aImage(xBound, yBound);
ImageDouble2D bImage(xBound, yBound);
ImageDouble2D pImage(xBound, yBound);
ImageDouble2D qImage(xBound, yBound);
for (y = 1; y < yBoundM1; ++y)
{
for (x = 1; x < xBoundM1; ++x)
{
Vector2d gradient(dx(x, y), dy(x, y));
Matrix2d hessian(dxx(x, y), dxy(x, y), dxy(x, y), dyy(x, y));
EigenDecompositiond decomposer(hessian);
decomposer.Solve(true);
aImage(x,y) = decomposer.GetEigenvalue(0);
bImage(x,y) = decomposer.GetEigenvalue(1);
Vector2d u = decomposer.GetEigenvector2(0);
Vector2d v = decomposer.GetEigenvector2(1);
pImage(x,y) = u.Dot(gradient);
qImage(x,y) = v.Dot(gradient);
}
}
aImage.Save("a.im");
bImage.Save("b.im");
pImage.Save("p.im");
qImage.Save("q.im");
// Use a cheap classification of the pixels by testing for sign changes
// between neighboring pixels.
ImageRGB82D result(xBound, yBound);
for (y = 1; y < yBoundM1; ++y)
{
for (x = 1; x < xBoundM1; ++x)
{
unsigned char gray = (unsigned char)(255.0f*image(x, y));
double pValue = pImage(x, y);
bool isRidge = false;
if (pValue*pImage(x-1 ,y) < 0.0
|| pValue*pImage(x+1, y) < 0.0
|| pValue*pImage(x, y-1) < 0.0
|| pValue*pImage(x, y+1) < 0.0)
{
if (aImage(x, y) < 0.0)
{
isRidge = true;
}
}
double qValue = qImage(x,y);
bool isValley = false;
if (qValue*qImage(x-1, y) < 0.0
|| qValue*qImage(x+1, y) < 0.0
|| qValue*qImage(x, y-1) < 0.0
|| qValue*qImage(x, y+1) < 0.0)
{
if (bImage(x,y) > 0.0)
{
isValley = true;
}
}
if (isRidge)
{
if (isValley)
{
result(x, y) = GetColor24(gray, 0, gray);
}
else
{
result(x, y) = GetColor24(gray, 0, 0);
}
}
else if (isValley)
{
result(x, y) = GetColor24(0, 0, gray);
}
else
{
result(x, y) = GetColor24(gray, gray, gray);
}
}
}
result.Save("result.im");
return 0;
}