Ding, Tao (The Pennsylvania State Univ.), Sznaier, Mario (Penn State Univ.), Camps, Octavia (Penn State Univ.)

Finite Horizon Model Reduction of Periodic 2-D Systems with Applications to Texture Synthesis and Classification.

Scheduled for presentation during the Regular Session "Model reduction" (MoP05), Monday, July 24, 2006, 17:25−17:50, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

Abstract

This paper addresses the problem of finite--horizon model reduction of 2-D discrete linear shift invariant systems that have a periodic impulse response. This situation arises in the context of many practical problems from widely dissimilar areas, ranging from image processing to sensor arrays. Motivated by some well known results on realization theory and some earlier related work on model reduction of 2-D systems, we propose a new model reduction method based on working directly with two Hankel matrices obtained from the impulse response data of the system under consideration. Since the impulse response is periodic, these matrices are circulant and structural properties can then be exploited to obtain balanced realizations in an efficient way. Direct truncation of these balanced realizations provides an approximation of the original operator that retains its period structure, as well as a bound on the finite horizon approximation error. In the second portion of the paper we apply these tools to the non--trivial problems of texture synthesis and classification. The main idea is to model images as the (periodic) impulse response of a non-necessarily causal shift--invariant 2-D system and use the proposed method to identify the corresponding model. Partial images can be expanded and additional realizations of the same texture can be obtained by simply driving the corresponding model with a suitable input. Texture classification can be accomplished by recasting the problem into a 2-D model (in)validation form.