Multiple template matching using the expansion filter

The paper describes a multiple-template generalization of a newly developed approach for template matching by signal expansion into a set of non-orthogonal template-similar basis functions. The single-template method is proven to be equivalent to "restoration" of undegraded images using the Wiener filter and optimizes a new and more practically defined matching quality criterion that the authors call discriminative signal-to-noise ratio (DSNR). Compared to the widely used matched filtering approach (also known as correlation matching) which is based an projection, expansion matching is based on decomposition and is shown to be more robust in conditions of noise, superposition and severe occlusion. In the paper, the authors extend the DSNR optimization approach to include more than one template. The generalized expansion filter presented is optimal in terms of DSNR and can be designed to elicit any desired response for each of the templates, while optimizing the DSNR criterion. The approach considers additive noise as a parameter and leads to a general formulation, of which many previous approaches (such as the synthetic discriminant function) form special cases. In the case of a single template, the formulation reverts to the previously mentioned Wiener restoration filter. >

[1]  R. Kallman.  Construction of low noise optical correlation filters. , 1986, Applied optics.

[2]  A Mahalanobis,et al.  Alternate interpretation for minimum variance synthetic discriminant functions. , 1986, Applied optics.

[3]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[4]  D Casasent,et al.  Unified synthetic discriminant function computational formulation. , 1984, Applied optics.

[5]  Charles D. Hendrix,et al.  Tradeoffs in the design of correlation filters , 1992, Other Conferences.

[6]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[7]  Jezekiel Ben-Arie.  Multi-Dimensional Linear Lattice for Fourier and Gabor Transforms, Multiple-Scale Gaussian Filtering, and Edge Detection , 1992 .

[8]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[9]  Jezekiel Ben-Arie,et al.  Restoration with equivalence to nonorthogonal image expansion for feature extraction and edge detection , 1992, Other Conferences.

[10]  K.R. Rao,et al.  Lattice architectures for signal expansion by Gaussian set wavelets with applications to recognition , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[11]  D. Casasent,et al.  Correlation synthetic discriminant functions. , 1986, Applied optics.

[12]  Jezekiel Ben-Arie,et al.  Image expansion by non-orthogonal wavelets for optimal template matching , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol. III. Conference C: Image, Speech and Signal Analysis,.

[13]  K.R. Rao,et al.  Signal representation by generalized nonorthogonal Gaussian wavelet groups using lattice networks , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[14]  D. Casasent,et al.  Minimum average correlation energy filters. , 1987, Applied optics.

[15]  K. Raghunath Rao,et al.  A novel approach for template matching by nonorthogonal image expansion , 1993, IEEE Trans. Circuits Syst. Video Technol..

[16]  B. V. Vijaya Kumar,et al.  Minimum-variance synthetic discriminant functions , 1986 .