We consider the challenge of detection of chemical plumes in hyperspectral image data. Segmentation of gas is difficult due to the diffusive nature of the cloud. The use of hyperspectral imagery provides non-visual data for this problem, allowing for the utilization of a richer array of sensing information. In this paper, we present a method to track and classify objects in hyperspectral videos. The method involves the application of a new algorithm recently developed for high dimensional data. It is made efficient by the application of spectral methods and the Nyström extension to calculate the eigenvalues/eigenvectors of the graph Laplacian. Results are shown on plume detection in LWIR standoff detection.

This work develops a global minimization framework for segmentation of high-dimensional data into two classes. It combines recent convex optimization methods from imaging with recent graph- based variational models for data segmentation. Two convex splitting algorithms are proposed, where graph-based PDE techniques are used to solve some of the subproblems. It is shown that global minimizers can be guaranteed for semi-supervised segmentation with two regions. If constraints on the volume of the regions are incorporated, global minimizers cannot be guaranteed, but can often be obtained in practice and otherwise be closely approximated. Experiments on benchmark data sets show that our models produce segmentation results that are comparable with or outperform the state-of-the-art algorithms. In particular, we perform a thorough comparison to recent MBO (Merriman–Bence–Osher, AMS-Selected Lectures in Mathematics Series: Computational Crystal Growers Workshop, 1992) and phase field methods, and show the advantage of the algorithms proposed in this paper.