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Generalized convolution for extraction of image features in the primary domain

Korohoda P., Dąbrowski A.

Machine Graphics and Vision

2008

Vol. 17, No. 3

279-297

In this paper, a class of techniques for flexible extraction of image features is proposed. These techniques are based on the convolution type filtering in the primary domain. The mentioned flexibility results from the fact that any discrete transform suitable for the analysis of desired image features (as, e.g., the Karhunen-Loeve transform) may be designed and the filter with the assumed transform-domain properties may be applied straightforwardly in the image (i.e., primary) domain. The proposed solution creates an entirely new approach to image filtering. After recalling the concept referred to by the authors as generalized convolution and extending it to the 2-dimensional case, the theoretical results are illustrated with several examples based on filtering of the test image with filters designed in the Haar, Hadamard and the DCT II domains. Finally, it is explained how the proposed approach indicates several possible ways for further developments towards the design of image-and-feature based tools.

Discrete symplectic transforms and their fast algorithms

Chernov V. M.

Machine Graphics and Vision

2000

Vol. 9, No. 1/2

363-368

In the article the new class of the discrete transforms associated with the anti-symmetric blinear form is intriduced. Also the invariance relations similar to the Perseval equality and fast algorithms for discrete symmetric transforms calculation are considered.