A Graph Formalism for Time and Memory Efficient Morphological Attribute-Space Connected Filters

Attribute-space connectivity has been put forward as a means of improving image segmentation in the case of overlapping structures. Its main drawback is the huge memory load incurred by mapping a N-dimensional image to an \((N + \dim (A))\)-dimensional volume, with \(\dim (A)\) the dimensionality of the attribute vectors used. In this theoretical paper we introduce a more space and time efficient scheme, by representing attribute spaces for analysis of binary images as a graph rather than a volume. Introducing a graph formalism for attribute-space connectivity opens up the possibility of using attribute-space connectivity on 3D volumes or using more than one attribute dimension, without incurring huge memory costs. Furthermore, the graph formalism does not require quantization of the attribute values, as is the case when representing attribute spaces in terms of \((N + \dim (A))\)-dimensional discrete volumes. Efficient processing of high dimensional data produced by multi-sensor detection systems is another advantage of application of our formalism.