Compact union of disjoint boxes: An efficient decomposition model for binary volumes

This paper presents in detail the Compact Union of Disjoint Boxes (CUDB), a decomposition model for binary volumes that has been recently but briefly introduced. This model is an improved version of a previous model called Ordered Union of Disjoint Boxes (OUDB). We show here, several desirable features that this model has versus OUDB, such as less unitary basic elements (boxes) and thus, a better efficiency in some neighborhood operations. We present algorithms for conversion to and from other models, and for basic computations as area (2D) or volume (3D). We also present an efficient algorithm for connected-component labeling (CCL) that does not follow the classical two-pass strategy. Finally we present an algorithm for collision (or adjacency) detection in static environments. We test the efficiency of CUDB versus existing models with several datasets.