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Translation and scale invariants of Tchebichef moments. (English) Zbl 1120.68094
Summary: Discrete orthogonal moments such as Tchebyshev moments have been successfully used in the field of image analysis. However, the invariance property of these moments has not been studied mainly due to the complexity of the problem. Conventionally, the translation and scale invariant functions of Tchebyshev moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments. In this paper, we present a new approach that is directly based on Tchebyshev polynomials to derive the translation and scale invariants of Tchebyshev moments. Both derived invariants are unchanged under image translation and scale transformation. The performance of the proposed descriptors is evaluated using a set of binary characters. Examples of using the Tchebyshev moments invariants as pattern features for pattern classification are also provided.

##### MSC:
 68T10 Pattern recognition, speech recognition 68U10 Computing methodologies for image processing
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##### References:
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