Energy Tensors: Quadratic, Phase Invariant Image Operators

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In this paper we briefly review a not so well known quadratic, phase invariant image processing operator, the energy operator, and describe its tensor-valued generalization, the energy tensor. We present relations to the real-valued and the complex valued energy operators and discuss properties of the three operators. We then focus on the discrete implementation for estimating the tensor based on Teager’s algorithm and frame theory. The kernels of the real-valued and the tensor-valued operators are formally derived. In a simple experiment we compare the energy tensor to other operators for orientation estimation. The paper is concluded with a short outlook to future work.

This work has been supported by EC Grant IST-2002-002013 MATRIS and by EC Grant IST-2003-004176 COSPAL. However, this paper does not necessarily represent the opinion of the European Community, and the European Community is not responsible for any use which may be made of its contents.