EQUIPS
Abstract
Our goal is to investigate the use of persistent homology, a tool from the field of topological data analysis, to address problems in three paradigms of image analysis: Keypoint selection for object recognition Image segmentation Spatiotemporal feature tracking We state our goals and the expected impact for each of the above problems separately. Keypoint selection for object recognition. Object recognition algorithms typically involve an initial step that annotates an image with points of interest, or keypoints. While there are many algorithms that generate keypoints, they are typically based on finding edges, corners, or points of high contrast in an image [1,2]. These algorithms are not well suited to smooth images, and thus are not applicable to the study of, e.g., fluid flows, liquid crystals, or low‐resolution (blurry) images. Our two major goals for this part of the project are to continue a current line of research into keypoint generation for locally‐striped (smooth) patterns and then extend our results to more general classes of smooth images. Our results will open up existing methods in computer vision and object recognition to the field of complex physical systems, as well as performing object recognition on images with low resolution. Image segmentation. Image segmentation concerns partitioning an image into regions, each of which contains pixels that describe a single object or texture. While there are many image segmentation algorithms available, none of them performs as well as humans asked to segment a collection of images [3]. Our goal is to establish the use of persistence diagrams, together with the spatial distribution of the corresponding critical point pairings, for image segmentation. We will compare our approach to existing methods using a well‐studied benchmark dataset for image segmentation. Even if the method is not shown to outperform existing methods, this work will provide additional foundations for rigorous spatiotemporal feature tracking, which we discuss next. Spatiotemporal feature tracking. Many spatiotemporal feature tracking algorithms are rooted in object recognition algorithms, which, as stated above, encounter limitations when applied to smooth images. Our work in keypoint generation and image segmentation will establish persistent homology as a tool that can be used for object recognition even when an image is smooth. Even with this obstacle overcome, feature tracking is typically ad‐hoc and superficial mathematically, relying on probabilistic reasoning to justify a positive match. Our goal is to develop a rigorous mathematical framework that can be used to unambiguously match persistence diagrams generated from the sublevel set (or superlevel set) filtrations of digital images forward in time. By doing so, any features in the underlying image tied to matched persistence points may then also be tracked at the algebraic level. This problem lies at the forefront of the theory of persistence modules, and thus a solution to this problem will require the development of new mathematical techniques. This focused program will return novel results and algorithms, tested on community‐accepted benchmark datasets, in the span of 12 months at a projected cost of $129,964. Success of the program will be measured at set periods using an extensive set of milestones
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 12, 2017
- Source ID
- HR00111710004
Entities
People
- Robert Ghrist
Organizations
- Defense Advanced Research Projects Agency
- University of Pennsylvania