Moment Invariance For Perspective Transformations

Kyounq T. Park; Ernest L. Hall

doi:10.1117/12.941321

14 October 1987 Moment Invariance For Perspective Transformations

Kyounq T. Park, Ernest L. Hall

Proceedings Volume 0804, Advances in Image Processing; (1987) https://doi.org/10.1117/12.941321
Event: Fourth International Symposium on Optical and Optoelectronic Applied Sciences and Engineering, 1987, The Hague, Netherlands

Abstract

The purpose of this paper is to consider the moment invariants of known forms for perspective transformation. These are important for machine vision systems because every lens system induces a perspective transformation. This approach considers the non-linear perspective transformation in a higher dimensional, homogeneous space. The perspective transformation is linear in this homogeneous space. Algebraic invariant theory used to determine absolute algebraic and moment invariants. By using the theory of conics, the known forms may be constructed and the general form may be reduced to the standard form. The cross ratio is a well known perspective invariant. The cross ratio, which is a geometrical feature independent of the perspective transformation, is expressed in terms of the absolute invariant. New moment invariants corresponding to the perspective transformation are also derived. Examples are presented to demonstrate the theoretical approach. The significance of this work lies in increasing the understanding of object recognition for human and machine vision.

Citation Download Citation

Kyounq T. Park and Ernest L. Hall "Moment Invariance For Perspective Transformations", Proc. SPIE 0804, Advances in Image Processing, (14 October 1987); https://doi.org/10.1117/12.941321

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