arXiv subjects

Andrew Xie

Publications and source records attributed to Andrew Xie.

3 recordsLinked to original sources

arXiv2026

Discrimination of Dynamic Data via Curvature Sets

Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuroscience. While early algorithms leveraged efficient updates to persistence diagrams for dynamic data, they struggled to distinguish behaviors that are isometric at each fixed time but differ qualitatively. This limitation was addressed by Kim and M\'emoli, who introduced a spatiotemporal persistence framework for dynamic metric spaces, resulting in multiparameter persistence modules. However, these modules pose computational challenges. To address this, we build on insights from G\'omez and M\'emoli, who observed that the homology of Rips complexes over size $(2k+2)$ point subsets of a metric space--termed principal curvature sets--is both tractable and informative. We extend this idea to dynamic settings by introducing dynamic curvature-set persistent homology, applying the spatiotemporal framework of Kim and M\'emoli to curvature sets. We prove that the resulting multiparameter persistence modules are interval-decomposable: in fact, they possess a stronger property we term antichain-decomposable. Utilizing this property, we present a new algorithm to efficiently compute the erosion distance $d_E$ (due to Patel) between arbitrary antichain-decomposable modules (including, but not limited to modules produced by our construction). Additionally, our construction is stable with respect to a generalized Gromov-Hausdorff distance between time-dependent datasets proposed by Kim and M\'emoli. This enables a robust computational pipeline for distinguishing dynamic data, as demonstrated in experiments with the Boids model, where we successfully detect parameter changes.

math.AT↗

arXiv2025

Neural Inverse Rendering from Propagating Light

We present the first system for physically based, neural inverse rendering from multi-viewpoint videos of propagating light. Our approach relies on a time-resolved extension of neural radiance caching -- a technique that accelerates inverse rendering by storing infinite-bounce radiance arriving at any point from any direction. The resulting model accurately accounts for direct and indirect light transport effects and, when applied to captured measurements from a flash lidar system, enables state-of-the-art 3D reconstruction in the presence of strong indirect light. Further, we demonstrate view synthesis of propagating light, automatic decomposition of captured measurements into direct and indirect components, as well as novel capabilities such as multi-view time-resolved relighting of captured scenes.

cs.CV↗

arXiv2024

Deep Learning-Based Correction and Unmixing of Hyperspectral Images for Brain Tumor Surgery

Hyperspectral Imaging (HSI) for fluorescence-guided brain tumor resection enables visualization of differences between tissues that are not distinguishable to humans. This augmentation can maximize brain tumor resection, improving patient outcomes. However, much of the processing in HSI uses simplified linear methods that are unable to capture the non-linear, wavelength-dependent phenomena that must be modeled for accurate recovery of fluorophore abundances. We therefore propose two deep learning models for correction and unmixing, which can account for the nonlinear effects and produce more accurate estimates of abundances. Both models use an autoencoder-like architecture to process the captured spectra. One is trained with protoporphyrin IX (PpIX) concentration labels. The other undergoes semi-supervised training, first learning hyperspectral unmixing self-supervised and then learning to correct fluorescence emission spectra for heterogeneous optical and geometric properties using a reference white-light reflectance spectrum in a few-shot manner. The models were evaluated against phantom and pig brain data with known PpIX concentration; the supervised model achieved Pearson correlation coefficients (R values) between the known and computed PpIX concentrations of 0.997 and 0.990, respectively, whereas the classical approach achieved only 0.93 and 0.82. The semi-supervised approach's R values were 0.98 and 0.91, respectively. On human data, the semi-supervised model gives qualitatively more realistic results than the classical method, better removing bright spots of specular reflectance and reducing the variance in PpIX abundance over biopsies that should be relatively homogeneous. These results show promise for using deep learning to improve HSI in fluorescence-guided neurosurgery.

eess.IV↗