Invariants from the three-dimensional vector autoregressive model

Jun Fujiki; Yasuhiko Kiuchi; Masaru Tanaka; Taketoshi Mishima

doi:10.1117/12.447269

2 November 2001 Invariants from the three-dimensional vector autoregressive model

Jun Fujiki, Yasuhiko Kiuchi, Masaru Tanaka, Taketoshi Mishima

Proceedings Volume 4476, Vision Geometry X; (2001) https://doi.org/10.1117/12.447269
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

The invariance and covariance of extracted features from an object under certain transformation play quite important roles in the fields of pattern recognition and image understanding. For instance, in order to recognize a three dimentional object, we need specific features extracted from a given object. These features should be independent of the pose and the location of an object. To extract such feature, The authors have presented the three dimensional vector autoregressive model (3D VAR model). This 3D VAR model is constructed on the quaternion, which is the basis of SU(2) (the rotation group in two dimensional complex space). Then the 3D VAR model is defined by the external products of 3D sequential data and the autoregressive(AR) coefficients, unlike the usual AR models. Therefore the 3D VAR model has some prominent features. For example, The AR coefficients of the 3D VAR model behave like vectors under any three dimensional rotation. In this paper, we derive the invariance from 3D VAR coefficients by inner product of each 3D VAR coefficient. These invariants make it possible to recognize the three dimensional curves.

Citation Download Citation

Jun Fujiki, Yasuhiko Kiuchi, Masaru Tanaka, and Taketoshi Mishima "Invariants from the three-dimensional vector autoregressive model", Proc. SPIE 4476, Vision Geometry X, (2 November 2001); https://doi.org/10.1117/12.447269

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