Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 16-CNA-023 A Transportation $L^p$ Distance for Signal Analysis Matthew ThorpeDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213mthorpe@andrew.cmu.edu Serim ParkCarnegie Mellon University Pittsburgh, PA 15213 Soheil KolouriHRL Laboratories Malibu, CA 90265, USA Gustavo K. RohdeUniversity of Virginia Charlottesville, VA 22908, USA Dejan SlepčevDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213slepcev@andrew.cmu.eduAbstract: Transport based distances, such as the Wasserstein distance and earth mover’s distance, have been shown to be an effective tool in signal and image analysis. The success of transport based distances is in part due to their Lagrangian nature which allows it to capture the important variations in many signal classes. However these distances require the signal to be nonnegative and normalized. Furthermore, the signals are considered as measures and compared by redistributing (transporting) them, which does not directly take into account the signal intensity. Here we study a transport-based distance, called the $TL^p$ distance, that combines Lagrangian and intensity modelling and is directly applicable to general,non-positive and multi-channelled signals. The framework allows the application of existing numerical methods. We give an overview of the basic properties of this distance and applications to classification, with multi-channelled, non-positive one and two-dimensional signals, and color transfer. Get the paper in its entirety as  16-CNA-023.pdf