CARMA Model method of two-dimensional shape classification: An eigensystem approach vs. the LP norm

Because of periodicity of the time series derived from the N angularly equispaced radii, the correlation matrix has an invariant feature under rotation, translation, and scaling. The periodic characteristics possessed by the time series can be utilized to obtain improvement for texture boundary detection. A new circular ARMA (CARMA) model is introduced to represent the time series obtained for shape classification. This model is compared with a regular ARMA model and its high resolution and accuracy is tested for several two dimensional objects. Singular value decomposition (SVD) is used to calculate the insensitive features for shape classification and boundary reconstruction. The invariant right singular vectors of the correlation matrix are used as an orthogonal basis for the solution space. The dimension of the spanned space (model order) is calculated from a new nullity algorithm. To show the high resolution of the eigensystem approach, L
1
and classical L
2
solutions are compared.