Decoupling spatial pattern and its movement via complex factorization over orthogonal filter pairs

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Variations between related images (e.g. due to motions) can caused by different independent factors. A qualified representation can decouple the underlying explanatory factors rather than keeping them mixed. After decoupling, each factor lies in a lower dimension abstract space. Different computer vision tasks can be done in different abstract spaces more efficiently than in the original pixel space. For example, conducting object recognition in appearance space can result in an invariant recognition; estimating object motion in location space yields a result regardless of the object itself. In this paper, we propose an algorithm to decouple object appearance and location to amplitude and phase in static images by using complex factorization over orthogonal filter pairs. In particular, we show that, i) Orthogonal filter pairs can be learned in an unsupervised manner from multiple consecutive frames; ii) Object movement is encoded in the factorized phase gradient between frames over time. As a proof of concept, we present experiments on the application of our framework to the recovery of the optical flow. Here object movement is successfully captured by phase gradient.

, 9 pages

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