Applying Singular Value Decomposition to bitmap images (experimenting with compression)
- Loads a bitmap image into an image matrix
- Applies SVD
- Lets user choose the amount of singular values to be included in the compressed image
This demo uses:
- The C++ Eigen library for matrix functions (all header files included in solution)
- The Chili DirectX Framework for the putpixel calls & graphics window
Demo:
- Visualizes the increase in rank r (i.e. how many singular values are used to build the compressed image matrix)
- The composite matrix is the sum over r of: r’th left singular vector * r’th singular value * r’th right singular vector
Note: The essence of the code is in “SurfaceMat.h” (Surface is the type that holds the original sprite):
SurfaceMatrix(Surface& surf)
{
// Define A using Eigen matrix type for floats
MatrixXf A(surf.GetHeight(), surf.GetWidth());
// Fill Matrix with image information (convert RGB to GreyColor)
for (size_t y = 0; y < surf.GetHeight(); y++)
{
for (size_t x = 0; x < surf.GetWidth(); x++)
{
auto r = surf.GetPixel(x, y).GetR();
auto g = surf.GetPixel(x, y).GetG();
auto b = surf.GetPixel(x, y).GetB();
float avg = (r + g + b) / 3.0f;
A(y, x) = avg;
}
}
// Perform SVD decomposition
JacobiSVD<MatrixXf> svd(A, ComputeThinU | ComputeThinV);
// Fill the vector Mvec (class data member) with composite matrices with increasing rank
Mvec.push_back(svd.matrixU().col(0)* svd.matrixV().col(0).transpose()* svd.singularValues()(0));
for (int i = 1; i < maxResolution; i++)
{
Mvec.push_back(Mvec[i - 1] + svd.matrixU().col(i) * svd.matrixV().col(i).transpose() * svd.singularValues()(i));
}
...
}
https://github.com/rvdweerd/SVDtoSurfaces
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