Generalized moment functions and conformal transforms

Shoude Chang; Chander Prakash Grover

doi:10.1117/12.452345

21 November 2002 Generalized moment function and conformal transform

Shoude Chang, Chander Prakash Grover

Proceedings Volume 4790, Applications of Digital Image Processing XXV; (2002) https://doi.org/10.1117/12.452345
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

We propose a new class of generalized moment functions (GMFs) that scan the object with different probing functions. Using the GMF, it is possible to extract a unique geometric point within the object, called the generalized centroid (G-centroid). We can obtain a set of discrete G-centroids from the same object by using different GMFs. The GMFs, which are similar to traditional moment functions, can also be used to describe the global shape of the object, including symmetry and fullness. However, the GMFs, along with the G-centroids, can further serve to construct a feature vector of the object, which is critical to the process of image registration and pattern recognition. Conformal transforms (C-transforms) are another tool used to probe the object by rearranging the latter's mass distribution, without distorting its shape. Using the C-transformed object, it is possible to detect a new mass centroid and G-centroid. More distinguishing feature points can be extracted from the same object by changing the combination of different GMFs and C-transforms. As GMF and centroid detection can be performed by convolution, the centroid and G-centroid can be detected optically in real time. It is also possible to optically implement some of the C-transforms. We present the results of GMF and C-transform applications, including image registration and pattern recognition.

Citation Download Citation

Shoude Chang and Chander Prakash Grover "Generalized moment function and conformal transform", Proc. SPIE 4790, Applications of Digital Image Processing XXV, (21 November 2002); https://doi.org/10.1117/12.452345

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KEYWORDS

Transform theory

Pattern recognition

Convolution

Image registration

Feature extraction

Fourier transforms

Image processing

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