Gabor frames and higher dimensional boundaries in signal analysis on manifolds

TL;DR

This paper introduces a method to construct Gabor frames for signals on curved manifolds, enabling detection of higher-dimensional boundaries, with applications in robotics and visual cortex analysis.

Contribution

It generalizes Gabor frame construction to higher-dimensional manifolds, capturing local linearizations and boundary features in complex signal domains.

Findings

Effective encoding of local manifold structures

Detection of higher-dimensional boundaries in signals

Application to robotics configuration spaces

Abstract

We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the manifold signal. We describe an application in configuration spaces in robotics with sharp constrains. The construction is a higher-dimensional generalization of the geometric setting developed for the study of signal analysis in the visual cortex.