A1313
Title: Nested sequential inference for hotspot detection in noisy images with cubical persistent homology
Authors: Andrew Thomas - University of Iowa (United States) [presenting]
Ranjan Maitra - Iowa State University (United States)
Abstract: Given an image that primarily consists of noise, segmentation into regions of signal deemed hotspots is often desired. Of equal importance is quantifying the statistical significance of each estimated hotspot, also known as peaks or regions of interest. A topological data analysis method, termed IMPHR, is developed to sequentially estimate hotspots and assess the statistical significance of each subsequent noise hypothesis in the image domain outside the union of iteratively identified regions of interest. The method employs newly developed advanced statistical methodology from the sequential testing and selective inference literatures to ensure both highly rigorous and computationally efficient performance. The algorithm is applied to simulated data and compared with various methods for hotspot detection and spatial clustering in the literature; performance is also demonstrated on real-world vibrothermography and fMRI data. The IMPHR algorithm provides rigorous theoretical guarantees and estimated hotspots with meaningful topology, while yielding performance as good as and in many cases better than existing methods.
