Exploring Classification of Topological Priors With Machine Learning for Feature Extraction

• Published in: IEEE transactions on visualization and computer graphics 2024-07, Vol.30 (7), p.3959-3972
• Main Authors: Leventhal, Samuel, Gyulassy, Attila, Heimann, Mark, Pascucci, Valerio
• Format: Article
• Language: English
• Subjects: Artificial neural networks; Classification; Computational topology; Feature detection; Gradient flow; Graph learning; Graph neural networks; Image segmentation; Labeling; Machine learning; MATHEMATICS AND COMPUTING; Morse-Smale complex; Neural networks; Pixels; Scientific visualization; Segmentation; Semantics; Target recognition; Task analysis; Topological data analysis; Topology; Training
• ISSN: 1077-2626; 1941-0506; 1941-0506
• DOI: 10.1109/TVCG.2023.3248632

In many scientific endeavors, increasingly abstract representations of data allow for new interpretive methodologies and conceptualization of phenomena. For example, moving from raw imaged pixels to segmented and reconstructed objects allows researchers new insights and means to direct their studies toward relevant areas. Thus, the development of new and improved methods for segmentation remains an active area of research. With advances in machine learning and neural networks, scientists have been focused on employing deep neural networks such as U-Net to obtain pixel-level segmentations, namely, defining associations between pixels and corresponding/referent objects and gathering those objects afterward. Topological analysis, such as the use of the Morse-Smale complex to encode regions of uniform gradient flow behavior, offers an alternative approach: first, create geometric priors, and then apply machine learning to classify. This approach is empirically motivated since phenomena of interest often appear as subsets of topological priors in many applications. Using topological elements not only reduces the learning space but also introduces the ability to use learnable geometries and connectivity to aid the classification of the segmentation target. In this article, we describe an approach to creating learnable topological elements, explore the application of ML techniques to classification tasks in a number of areas, and demonstrate this approach as a viable alternative to pixel-level classification, with similar accuracy, improved execution time, and requiring marginal training data.