Nonlinear k-subspaces based appearances clustering of objects under varying illumination conditions

Unsupervised clustering of image sets of 3D objects has been an active research field within vision community. It is a challenging task since the appearance variation of the same object under different illumination condition is often larger than the appearance variation of different object under the same illumination condition. Some previous methods perform the appearance clustering using k-subspaces algorithm by assuming that the set of images of a Lambertian object approximately reside in a low dimensional linear subspace. This paper further extends the original ksubspaces clustering algorithm to the nonlinear case. The sum of the squares of distance to corresponding feature points of each nonlinear subspace cluster centers is minimized using Expectation-Maximization like iteration procedure. Those distances can be novelly defined via inner product by kernel trick. Experiments on different datasets show that the proposed kernel-based nonlinear k-subspaces clustering algorithm achieves much higher clustering rate than its linear counterpart.