HKUST COMP 5421 dense photometric stereo using two methods, linear regression and graph cut.
The main algorithm is based on Tai-Pang Wu and Chi-Keung Tang, Dense Photometric Stereo Using a Mirror Sphere and Graph Cut, IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2005) pp 140-147. You may find the reference with the following link: Dense Photometric Stereo Using a Mirror Sphere and Graph Cut.
Graph Cut maxflow algorithm toolbox downloaded from http://vision.ucla.edu/~brian/gcmex.html.
Shape from shapelet reconstruction is from Peter Kovesi, Shapelets Correlated with Surface Normals Produce Surfaces. IEEE International Conference on Computer Vision. (2005) pp 994-1001. Toolbox downloaded from http://www.csse.uwa.edu.au/~pk/Research/MatlabFns/.
Main reference code is from Mao Hongzi's work https://github.com/hongzimao/shapeFromShading, Thanks to him.
We follows the steps in the paper. First, to construct a simple system, we use only linear regression to generate the normal image. After all the parts are tested, we move on the graph cut based combination optimization to get shaper edges.
The icosahedron_cosntruction.m and subdivide.m handle the generation of the creation of a subdivided half icosahedron to uniformly resample the light vector. And resampling_light_vector.m find the one light vectors closest to the resample base. To create a icosahedron, we follow the instruction in the /reference/uniform_sampling.jpg to get each vertices and midpoints from the gloden ratio. To subdivide the icosahedron, a simple method to divide the edge evenly and create a triangle is used. To find the closest light vector, we sorted the light vectors by its distance to the resulted vertices and select the top.
After the light vectors are selected, since the light vector and the data are indexed in the same order, we only read the image indexes the same as the light vectors.
The denominator image is selected by image intensity ranking. The ideal denominator image is free from shadows and highlight. Using only the gray scale image, the pixel intensity is defined by its pixel value. At each pixel, we sorted through all images and recreate a set of pixel rank images. Then the image is selected by two categories:
- To remove shallows, the image should have the maximum number of pixels with each pixel ranking higher than 70th percentiles;
- To remove highlights, the mean rank amount the image should be lower than 90th percentiles.
The local normal estimation from the ratio images to remove the unknown light amount. For each pixel, k-1 set of equations are formed. The normal is estimated by linear regression, by minimizing the l2 norm of x * A * A' * x'. Using the singular-value decomposition, and get the eigen vector regarding to the smallest eigen value, we have the normal vector.
Using graph cut.
Select the scale for each image. Then create the slant and tilt, the toolbox handles for us. Notice that the final image will rotate by 90
normal image
simple system
refined system
More images could be found in /results
% dataset scale samples denominator_index time
% data02 2 220 206 1.745762
% data03 4 344 298 5.750543
% data04 4 354 354 6.741049
% data05 4 334 326 8.101798
% data06 4 348 348 9.162170
% data07 6 365 351 8.628281
% data08 6 359 346 9.654362
% data09 6 365 299 11.449866
% data10 4 373 373 12.705782