Publications

We introduce Topological Neural Operators (TNOs), a framework for operator learning on cell complexes that lifts neural operators from points and edges to topological domains. Using Discrete Exterior Calculus, TNOs decouple where information flows (fixed topological operators) from how it is transformed (learned), and the hierarchical variant (HTNOs) propagates long-range, topology-dependent information — improving accuracy across PDE benchmarks including irregular-geometry flows.

We introduce DisPOSE, a self-supervised framework that approximates the discrete multi-view person-assignment problem as a generative diffusion process over polystochastic tensors, using differentiable Sinkhorn projections to guide solutions toward valid assignments from 2D image priors — retaining 99% of its performance with only 10% of the pseudo-labels and remaining nearly agnostic to camera arrangement.

We introduce Collapsed Effective Operators, which condense higher-order degrees of freedom into a single vertex-level operator via Schur complementation of a graded Laplacian. The resulting operator encodes long-range, topology-mediated interactions, preserves positive semi-definiteness with a strict spectral bound relative to the Hodge Laplacian, and improves spectral clustering, signal smoothing, and topological positional encodings in neural networks.

Deep functional maps underpin non-rigid 3D shape matching but rely on solvers that process spectral systems serially, a bottleneck at higher resolution. We introduce a vectorized reformulation that solves them in a single kernel call for up to a 33x speedup with identical results, document a previously unnoticed divergence in DiffusionNet’s spatial-gradient features, and revisit overlap metrics for partial-to-partial matching. These improvements ship in DeepShapeMatchingKit, an open-source toolkit that standardizes training, evaluation, and data pipelines for common deep shape matching methods.

We model the surgical operating room as a multi-modal topological complex, introducing TopoOR, a unified scene representation that captures higher-order relationships between staff, instruments, and patient across imaging, audio, and spatial modalities for holistic surgical scene understanding.

This state-of-the-art report surveys modern techniques for matching deformed 3D shapes, organizing the field into spectral methods based on functional maps, combinatorial formulations with discrete constraints, and deformation-based approaches for global alignment. We discuss emerging directions including zero-shot correspondence from vision foundation models and the open challenge of partial shape matching.

We reformulate multi-view 3D pose estimation as a hypergraph partitioning problem, introducing efficient geometric pruning to achieve up to 23% improvement in average precision over previous optimization-based methods.

We introduce copresheaf topological neural networks (CTNNs), a powerful and unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data. The framework aims to address challenges in representation learning by using concepts from algebraic topology.

We study rotational forecasting on the manifold SO(3). This leads to the proposed Savitzky-Golay Neural Controlled Differential Equations which learn continuous data-driven priors on the manifold and excel at extrapolating rotational states.

We achieve generalizable re-identification and tracking for surgical operating rooms (OR). This enables our proposed staff-centric surgical domain models, the first concept for personalized intelligent systems in the OR.

We present BeCoS, the first comprehensive benchmark and evaluation framework for the challenging but widely applicable problem setting of partial shape correspondence.

We develop a new theoretical framework using algorithmic stability and topological data analysis to establish generalization bounds without complex mutual information calculations.

We show that 3D point cloud sequences capture robust biometric information for surgical personnel recognition, avoiding the appearance-based shortcuts that cause RGB models to fail in real clinical settings.

We present TrackOR, a robust tracking framework for personalized intelligent operating rooms that enables consistent personnel identification across surgical procedures.

We combine Neural Controlled Differential Equations with Savitzky-Golay path guidance to model continuous-time rotational dynamics on SO(3), achieving improved long-term forecasting of rotational motion.

We propose a hybrid approach for estimating functional maps that leverage the strengths of basis functions originating from different operators overcoming limitations of previous approaches for non-isometric deformations.

We propose an unsupervised method for statistical shape model (SSM) construction that utilizes functional correspondences to learn shape structures across population anatomies, demonstrating robustness to noisy and potentially scaling to larger patient populations without manual annotations.

SegmentOR is a weakly-supervised 3D semantic segmentation method for operating room environments that leverages temporal consistency in 4D point cloud sequences to significantly reduce the annotation burden. We demonstrate the utility of the resulting segmentation maps for improving downstream surgical workflow analysis.

DisguisOR improves the robustness of operating room video anonymization by leveraging multi-view data to accurately localize and anonymize individuals’ faces in 3D, resulting in geometrically consistent privacy protection across all camera views.