Adaptive image processing by means of polynomial transforms

Jean-Bernard Martens

doi:10.1117/12.135974

27 August 1992 Adaptive image processing by means of polynomial transforms

Jean-Bernard Martens

Proceedings Volume 1666, Human Vision, Visual Processing, and Digital Display III; (1992) https://doi.org/10.1117/12.135974
Event: SPIE/IS&T 1992 Symposium on Electronic Imaging: Science and Technology, 1992, San Jose, CA, United States

Abstract

Previous work at the Institute for Perception Research has resulted in a new model for representing images, called a polynomial transform. This transform is perceptually relevant since it mimics properties of the early stages of human vision such as localization and decomposition of luminance changes into specific basic patterns, i.e., localized polynomials. The transform also has interesting signal processing properties, some of which will be illustrated in this paper. Image interpolation is an example of how polynomial transforms can be used for image restoration. It is derived that the polynomial transform coefficients of a blurred and sampled image are related by a linear transformation to the polynomial transform coefficients of the original image. By inverting this transformation, we can obtain deblurring and interpolation. This inversion is based on the assumption that the image can be locally approximated by a low-order polynomial description. By adopting a fixed degree for this a priori polynomial description, we obtain non-adaptive interpolation algorithms. The performance of the algorithm can be further improved by varying the degree of this a priori polynomial description depending on whether the image region is locally uniform or non- uniform. Especially in the presence of noise, this adaptivity is usually very important. It is shown how such space-variant image processing can be easily described and implemented using polynomial transforms. Subjective evaluation of the image interpolation technique aims at optimizing the parameter values of the algorithm, as well as comparing the new algorithm to existing interpolation techniques. Some results of this evaluation are presented.

Citation Download Citation

Jean-Bernard Martens "Adaptive image processing by means of polynomial transforms", Proc. SPIE 1666, Human Vision, Visual Processing, and Digital Display III, (27 August 1992); https://doi.org/10.1117/12.135974

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