3D supervoxel for brain image
A supervoxel is a group of voxels with similar properties (e.g., correlated, similar response) that are contiguous in the brain voxel space. This process can also be seen as a clustering algorithm in feature space with a constrain that voxels in the same clusters must be contiguous. Unfortunately, such a constrain is usually not the case in traditional k-mean clustering or Gaussian mixture model (GMM) clustering. Therefore, I modify k-mean algorithm such that the clusters are more contiguous by enforcing the local (rather than global) neighbor search space. Still there are some supervoxels with undesired small number of voxels (e.g., 1 or 2), in which case I apply post-processing step to merge such invalid supervoxels to the valid neighborhood supervoxel with most connected regions to the supervoxels of interest.
The MATLAB code is available here.
Good resources
- SLIC superpixels [pdf],[TPAMI] -- very similar approach to ours
- UCSD lecture note on k-mean [url] -- very concise tutorial on k-mean clustering problem
- "Supervoxel-Based Segmentation of EM Image Stacks with Learned Shape Features" -- segmenting the high-resolution brain image using supervoxels. I think they used the SLIC in 3D
Code example
Below is the example on how to use the function.
% Get all the parameters step = 8*[1 1 1]; % [R, C, D] stepsize-- this determines the average size of supervoxel epsilon = 0.001; % the stop criteria num_max_itt = 100; num_min_voxel = 3; lambda = [ones(1,size(x,2)),ones(1,3)*3]; % The last 3 are for r, c, and d dimension % Run local k-mean supervoxels [supervoxel_id, vk, vol_supervoxel,... num_voxels_in_supervoxels, delta_s_final, t_final]... = makeSupervoxel3d(x, vol_mask, step, epsilon,... lambda, num_max_itt, num_min_voxel); Results
(click to see bigger images)
step size
3
5
8
# supervoxels
115
122
50
slices of the brain
histogram of the supervoxel size
