title: A continuous linear optimal transport approach for pattern analysis in image datasets.
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.
authors: Biomedical Engineering Department, Carnegie Mellon University, C120 Hamerschlag Hall, Pittsburgh, PA 15213, USA.
authors: Soheil
authors: S
authors: Kolouri
authors: Biomedical Engineering Department, Carnegie Mellon University, C120 Hamerschlag Hall, Pittsburgh, PA 15213, USA.
authors: Akif B
authors: AB
authors: Tosun
authors: Biomedical Engineering Department, Carnegie Mellon University, C120 Hamerschlag Hall, Pittsburgh, PA 15213, USA; Department of Pathology, Children's Hospital of Pittsburgh, Pittsburgh, PA 15224, USA.
authors: John A
authors: JA
authors: Ozolek
authors: Biomedical Engineering Department, Carnegie Mellon University, C120 Hamerschlag Hall, Pittsburgh, PA 15213, USA; Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
authors: Gustavo K
authors: GK
authors: Rohde
keywords: Generative image modeling; Linear embedding; Optimal transport; Pattern visualization