A continuous linear optimal transport approach for pattern analysis in image datasets. (March 2016) - Kolouri, Soheil; Tosun, Akif B.; Ozolek, John A.; Rohde, Gustavo K.
Abstract: We present a new approach to facilitate the application of the optimal transport metric to pattern recognition on image databases. The method is based on a linearized version of the optimal transport metric, which provides a linear embedding for the images. Hence, it enables shape and appearance modeling using linear geometric analysis techniques in the embedded space. In contrast to previous work, we use Monge׳s formulation of the optimal transport problem, which allows for reasonably fast computation of the linearized optimal transport embedding for large images. We demonstrate the application of the method to recover and visualize meaningful variations in a supervised-learning setting on several image datasets, including chromatin distribution in the nuclei of cells, galaxy morphologies, facial expressions, and bird species identification. We show that the new approach allows for high-resolution construction of modes of variations and discrimination and can enhance classification accuracy in a variety of image discrimination problems. Abstract : Highlights: A continuous version of the LOT framework is described that bypasses many of the difficulties associated with the discrete formulation. Using continuous transport maps, a forward and inverse transform operation is defined for images. An improved reference/average image estimation algorithm is proposed. The range within which points in LOT space are invertible according to the continuous formulation is calculated. We show that our method significantly speeds up the computation of the LOT embedding.