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

Gabor frames and higher dimensional boundaries in signal analysis on manifolds