Analysis of moment invariants and its uses for the retrieval of trademark images

Abstract

Derived from the general theory of moments, moment invariants have been frequently used as features for shape recognition and classification. Moments can provide characteristics of an object and uniquely represent its shape. Moment invariants are proven to be invariant under object translation, scaling and rotation. They are useful because they define a simple and fast set of seven elements. In this research, an intensive study has been carried out to analyze the physical meaning of Hu moment invariants. From the second-order moments, the concept of best-fit ellipse has been formulated. This formulation is confirmed by both theoretical analysis and experimental work. The ratio of major and minor axes from the best-fit ellipse can be applied to describe the global characteristic of the object. An analysis of quantization effects due to scaling and rotation of both regular and irregular objects is presented. The scaling errors for all approaches are large when the scaling factor is smaller than 0.5. Moreover, the rotational errors are big for the objects rotated other than the multiples of 90o. Besides, this error analysis has been applied to object searching using a threshold selection scheme. A new shape descriptor, called Multi-Layer Shape Descriptor (MLSD), making use of recursive sub-division technique on the basis of the best-fit ellipse concept has also been proposed. This local descriptor is invariant to translation, scaling and rotation. In our practical work, two-stage mechanism has been used to design a trademark image retrieval system. The first step acquires the global characteristic, i.e. the ratio of major and minor axes of the best-fit ellipse; while the second step obtains the local characteristics, i.e. MLSD. The system enhances 13.96% of the retrieval accuracy and improves the computational efficiency by reducing the average number of comparison to 55.55% of that required by the other approaches.