Abstract
The orthogonal moments have recently achieved outstanding predictive performance, and become an indispensable tool in a wide range of pattern recognition applications, including the image classification and object detection. Using the orthogonal Lagrange polynomials, we present in this paper three new sets of discrete orthogonal moments and their invariants to translation, scaling and rotation (TSR) for image representation and recognition: the orthogonal Lagrange-Fourier moments (LFMs) for the gray-scale images, the multi-channel orthogonal Lagrange-Fourier moments (MLFMs) and the quaternion orthogonal Lagrange-Fourier moments (QLFMs) for the color images. These orthogonal moments are presented in polar coordinates. We present a set of numerical experiments in the field of classification and pattern recognition to evaluate the performance of the proposed invariant moments. From a comparative study with the recent orthogonal invariant moments, we conclude that our approach is very promising in the pattern recognition field and image analysis.
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