23 September 1999 Properties of the three-dimensional vector autoregressive model
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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 dimensional (3D) 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, one of the authors has presented the 3D vector autoregressive (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 conventional 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 present the recursive computation of 2D VAR coefficients and 3D VAR coefficients. This method reduce the cost of computation of VAR coefficients. We also define the partial correlation (PARCOR) vectors for the 2D VAR model and 3D VAR model from the point of view of data compression and pattern recognition.
© (1999) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jun Fujiki, Masaru Tanaka, "Properties of the three-dimensional vector autoregressive model", Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); doi: 10.1117/12.364097; https://doi.org/10.1117/12.364097

Autoregressive models

3D modeling

Data modeling



Pattern recognition



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