Determination of the Appropriate Geometric Moment Invariant Functions for Object Recognition

Objectives: Moment invariants have been largely deployed to solve object recognition problems often without analyzing their appropriateness. This paper presents a heuristic method to determine the most appropriate geometric moment invariant functions for object recognition. Methods: The mathematical structure of the moment invariant functions was studied. The elements in the functions that contribute to amplification of noise in the images were identified through derivations. The moment invariant functions were then classified into noise susceptible and noise resilient categories. Sample functions from each of these categories were applied over standard images subjected to different types of noises to appraise the performance of the moment invariant functions. Findings: Research work accomplished using geometric moment invariant functions always showed evidence of false positives and false negatives due to the inherent weakness of some of the moment invariant functions. Most or all of the works using geometric moment invariant functions used only the first seven Hu moment invariants. Upon expansion of the moment invariant functions, it became essential to effectively choose the functions. Existing research explains that the higher the order of the moment functions the more susceptible are they to noise in the images. The research accomplished in this paper proves that not all higher order functions are susceptible to noise. This paper proves that there are higher order geometric functions with smaller exponents which are highly resilient to noise. Applications/Improvements: The research contributed towards identifying the most suitable moment invariant functions for object recognition. This approach helps to minimize false positives and false negatives and choose noise resilient moment invariant functions.