| Abstract: |
| Given an image that primarily consists of noise, one may wish to perform segmentation of the image into regions of signal deemed ``hotspots``. Of equal importance is quantifying the statistical signficance of each of these estimated hotspots, also known as peaks or regions of interest. In this paper, we develop a topological data analysis method---which we deem ``imphr``---to sequentially estimate hotspots and assess the statistical significance of each subsequent noise hypothesis in the image domain outside the union of the iteratively identified regions of interest. Our method employs newly developed advanced statistical methodology from the sequential testing and selective inference literatures to ensure both a highly rigorous and computationally efficient algorithm. We apply said algorithm to simulated data, and compare it with various methods for hotspot detection and spatial clustering in the literature; we also demonstrate its performance on real-world vibrothermography and fMRI data. In sum, the imphr algorithm not only provides rigorous theoretical guarantees and estimated hotspots with meaningful topology, but also yields performance as good and in many cases better than existing methods. |
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