Non-negative matrix factorization for non-parametric and unsupervised image clustering and segmentation

We propose a new non-parametric level set model for automatic image clustering and segmentation based on non-negative matrix factorization (NMF). We show that NMF: (i) clusters the image into distinct homogeneous regions and (ii) provides the local spatial distribution of each region within the image. Furthermore, NMF has a controllable resolution and can discover homogeneous regions as small as one pixel. Coupled with the level-set approach, NMF is an efficient method for image segmentation. The proposed model is unsupervised and relies on local histogram modeling to define an energy functional, whose optimization leads to the final segmentation. A unique and desirable feature of the proposed method is that it does not incorporate any spurious model parameters; hence, the optimization is performed only w.r.t level set functions. We apply the proposed Non-parametrIc Unsupervised SegmentatioN approach (geNIUS) to synthetic and real images and compare it to three state-of-the-art parametric and non-parametric level set approaches: the localized Gaussian distribution fitting model (LGDF) [1], the local histogram fitting (LHF) model [2], and our recent work: NMF-LSM in [3]. The proposed geNIUS model results in a superior accuracy and more efficient implementation, which is a result of its free-model parameter feature.