Using non-negative matrix factorization toward finding an informative basis in spin-image data

Three-dimensional (3D) Laser Detection and Ranging (LADAR) range data is being investigated for automatic target recognition applications. The spin-image provides a useful data representation for 3D point cloud data. In the spirit of recent work that shows ℓ1-sparseness to be a useful data compression metric, we propose to use Nonnegative Matrix Factorization (NMF) to help find features that capture the salient information resident in the spin-image representation. NMF is a technique for decomposing nonnegative multivariate data into its 'parts', resulting in a compressed and usually sparse representation. As a surrogate for measured 3D LADAR data, we generate 3D point clouds from computer-aided-design models of two land targets, and we generate spin-images at multiple support scales. We select the support scale that provides the highest separability between the spin-image stacks from the two land targets. We then apply NMF to the spin-images at this support scale, and seek elements corresponding to meaningful parts of the land vehicles (e.g., a tank turret or truck wheels), that in a joint sense should provide significant discriminative capability. We measure the separability in the sparse NMF subspace. For measuring separability, we use the Henze-Penrose measure of multivariate distributional divergence.