dgrzech
Potential mathmatics error
Hello, I'm re-reading the Sobolev fusion paper and I was confused by the Sobolev approximation part. So I re-read your code for a better comprehension, then I found the way that you calculate the laplacien matrix is weird :
`cv::Mat L_mat = -6.f * cv::Mat::eye(s3, s3, CV_32FC1);
for (int i = 0; i <= static_cast
if (idx_y + 1 < params.s) {
int pos = idx_x + (idx_y + 1) * params.s + idx_z * params.s * params.s;
L_mat.at<float>(i, pos) = 1.f;
}
if (idx_y - 1 >= 0) {
int pos = idx_x + (idx_y - 1) * params.s + idx_z * params.s * params.s;
L_mat.at<float>(i, pos) = 1.f;
}
if (idx_z + 1 < params.s) {
int pos = idx_x + idx_y * params.s + (idx_z + 1) * params.s * params.s;
L_mat.at<float>(i, pos) = 1.f;
}
if (idx_z - 1 >= 0) {
int pos = idx_x + idx_y * params.s + (idx_z - 1) * params.s * params.s;
L_mat.at<float>(i, pos) = 1.f;
}
}`
I checked the definition of laplacian matrix on wikipedia,
As the diagonal of tha laplacian matrix should be the row-wise sum of the correspondant adjacency matrix, it shouldn't be -6 for all, and the L_mat.at<float>(i,pos) should be -1.f, am I right?
here's a document that shows how to construct a sparse Laplacian matrix for a 3D grid: https://www.12000.org/my_notes/mma_matlab_control/KERNEL/KEse83.htm why would the diagonal of L be the row-wise sum of the adjacency matrix, and not simply be equal to the diagonal of the adjacency matrix?
