3D autoregressive model with proper transformation property under rotation

Masaru Tanaka

doi:10.1117/12.216413

11 August 1995 3D autoregressive model with proper transformation property under rotation

Masaru Tanaka

Proceedings Volume 2573, Vision Geometry IV; (1995) https://doi.org/10.1117/12.216413
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

For pattern recognition and image understanding, it is important to take invariance and/or covariance of features extracted from given data under some transformation into consideration. This makes various problems in pattern recognition and image understanding clear and easy. In this article, we present two autoregressive models which have proper transformation properties under rotations: one is a 2D autoregressive model (2D AR model) which has invariance under any 2D rotations and the other is a 3D autoregressive model (3D AR model) which has covariance under any 3D rotations. Our 2D AR model is based on a matrix representation of complex number. It is shown that our 2D AR model is equivalent to Otsu's complex AR model. On the other hand, our 3D autoregressive model is based on the representation theory of rotation group such as the fundamental representation of Lie algebra of SU(2)(Special Unitary group in 2D which includes rotation group), which is called Pauli's matrices.

Citation Download Citation

Masaru Tanaka "3D autoregressive model with proper transformation property under rotation", Proc. SPIE 2573, Vision Geometry IV, (11 August 1995); https://doi.org/10.1117/12.216413

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