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.

翻译：我们提出了一种Gabor框架的构造方法，该方法能够编码任意维光滑弯曲流形上检测到的信号的局部线性化，其Gabor滤波器可检测流形信号中高维边界的存在。我们描述了该构造在机器人学中具有严格约束的构型空间中的应用。这一构造是针对视觉皮层信号分析研究中所建立的几何框架的高维推广。