Best-fit Ellipse Concept from the Second Order Moments for Object Retrieval

Hu moment invariants are a popular tool for shape description in areas such as object identification and character recognition. The original formulation consists of a set of seven moment invariants for characterizing object features, which are independent of translation, scale, and rotation. In order to provide a meaningful description of object shape, it is important to understand the meaning of these moments. However, there are few pertinent studies. This paper firstly provides an interpretation of the second order-based moment invariants using the best-fit ellipse formulation. Then a new formulation is suggested for image retrieval. Our theoretical analysis shows that the first invariant measures the total spread of the shape relative to its area square while the second invariant measures the degree of elongation of a best-fit ellipse on the shape. Six different shapes and objects with Gaussian noise were used to confirm the findings. The ratio of major and minor axes from the best-fit ellipse were applied for describing the global information of the shape. Results of the experimental work show that this is an efficient framework for object searching and the computational complexity can be significantly reduced.