Selected Publications

Transport-based techniques for signal and data analysis have recently received increased interest. Given their ability to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications, including content-based retrieval, cancer detection, image superresolution, and statistical machine learning, to name a few, and they have been shown to produce state-of-the-art results. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here, we provide a practical overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications.
In IEEE Signal Process Mag.

A new family of positive definite kernels are defined based on the mathematics of optimal mass transportation. The performance of the presented kernel is evaluated in various machine learning applications including classification and clustering.
In CVPR16

Much of what is currently known about how cells work has been derived through visual interpretation of microscopy images. Computational methods for image analysis have emerged as quantitative alternatives to visual interpretation. We describe an analysis pipeline for cell image databases that combines statistical pattern recognition with the mathematics of optimal mass transport. The approach is fully automated and does not require the use of ad hoc numerical features. It enables the identification of discriminant phenotypic variations, or bio- markers, between sets of cells (e.g., normal vs. diseased) while at the same time allowing for the visualization of meaningful differences. The approach can be used for fully automated high content screening with a variety of microscopic image modalities.
In PNAS, Jan 2014

Recent Publications

More Publications

  • Automatic Tactical Adjustment in Real-time; Modeling Adversary Formations with Radon-Cumulative Distribution Transform and Canonical Correlation Analysis - CVPRW 2017

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  • Explaining Distributed Neural Activations via Unsupervised Learning - CVPRW 2017

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  • Zero Shot Learning via Multi-Scale Manifold Regularization - CVPR 2017

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  • Optimal Mass Transport: Signal processing and machine-learning applications - IEEE Signal Process Mag. 2017

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  • Discovery and visualization of structural biomarkers from MRI using transport-based morphometry - Preprint

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  • A Transportation $L^p$ Distance for Signal Analysis - J. Math. Imaging Vision 2017

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  • The Cumulative Distribution Transform and Linear Pattern Classification - ACHA 2017

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  • Sliced Wasserstein Kernels for Probability Distributions - CVPR 2016

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  • A Continuous Linear Optimal Transport Approach for Pattern Analysis in Image Datasets - PR 2016

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  • The Radon cumulative distribution transform and its application to image classification - TIP 2016

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Recent Posts

We organized a tutorial on ‘Transport and other Lagrangian transports for image modeling, estimation, and classification’ at ICIP 2016, Phoenix, Arizona. We presented a set of recently developed image analysis techniques, based on the mathematics of optimal transport, to address important problems related to sensor data modeling, estimation, and pattern recognition (e.g. classification). These techniques can be interpreted as nonlinear image transforms with well defined forward (analysis) and inverse (synthesis) operations with demonstrable advantages over standard linear transforms (Fourier, Wavelet, Radon, Ridgelet, etc.

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Teaching

I was a guest lecturer for the following courses at Carnegie Mellon University:

  • Computational Methods in Biomedical Engineering, Spring 2016
  • Introduction to Biomedical Imaging and Image Analysis, Fall 2015
  • Computational Methods in Biomedical Engineering, Spring 2015

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