Disconnectedness: A new moment invariant for multi-component shapes

Abstract

In this paper we further develop the recent concept of multi-component shapes, which is applicable to image processing and image analysis tasks. The domain of multi-component shapes is very diverse and includes shapes that correspond to a group of objects that act together (e.g. a fish shoal), natural components of a segmented object (e.g. cells in embryonic tissues), a set of shapes corresponding to the same object appearing at different times (e.g. human gait in an image sequence), and many more. So far, there are few methods for numerically evaluating multi-component shapes. In this paper we introduce one such method: a disconnectedness measure, that naturally corresponds to multi-component shapes, and has no analogue in single-component shape measures. The new measure depends on the number of shape components, the whole shape but also the shape of its components, on the relative size of the shape's components and their mutual position. All these are natural requirements for a “disconnectedness” multi-component shape measure. In addition, the new measure is invariant with respect to translation, rotation and scaling transformations. The measure is simple and fast to compute. The disconnectedness measure introduced here is a generic image analysis tool. It has not been developed for a specific application. As such, it can be applied to a variety of applications. Several of them are provided in the paper, as well as synthetic examples that support a better understanding of the behavior of the new measure.