Multi-dimensional Persistent Sheaf Laplacians for Image Analysis

TL;DR

This paper introduces a multi-dimensional persistent sheaf Laplacian framework for image analysis that leverages topological spectral representations across multiple scales and dimensions, improving stability and classification accuracy.

Contribution

It presents a novel multi-dimensional persistent sheaf Laplacian method that captures multiscale topological features for images, enhancing stability over traditional PCA-based approaches.

Findings

Provides more stable performance across various reduced dimensions.

Achieves consistent improvements over PCA baselines.

Effective on COIL20 and ETH80 datasets.

Abstract

We propose a multi-dimensional persistent sheaf Laplacian (MPSL) framework on simplicial complexes for image analysis. The proposed method is motivated by the strong sensitivity of commonly used dimensionality reduction techniques, such as principal component analysis (PCA), to the choice of reduced dimension. Rather than selecting a single reduced dimension or averaging results across dimensions, we exploit complementary advantages of multiple reduced dimensions. At a given dimension, image samples are regarded as simplicial complexes, and persistent sheaf Laplacians are utilized to extract a multiscale localized topological spectral representation for individual image samples. Statistical summaries of the resulting spectra are then aggregated across scales and dimensions to form multiscale multi-dimensional image representations. We evaluate the proposed framework on the COIL20 and ETH80 image datasets using standard classification protocols. Experimental results show that the proposed method provides more stable performance across a wide range of reduced dimensions and achieves consistent improvements to PCA-based baselines in moderate dimensional regimes.