Classification of 3D Surface Data Using the Concept of Vertex Unique Labelled Subgraphs

An overview is presented on the use of the concept of Vertex Unique Labelled Sub graph (VULS) mining for the use of localised classification of regions in 3D surfaces represented in terms of grid graphs. A VULS is a sub graph within some larger graph G that has a unique ("one-of") vertex labelling associated with it. Given a 3D surface represented as a grid graph, we can identify a number of different forms of VULS that may be discovered: (i) all, (ii) minimal, (iii) frequent and (iv) frequent minimal. Algorithms for discovering (mining) these are presented in the paper. The paper also presents the Backward Match Voting (BMV) algorithm for predicting (classifying) vertex labels associated with an "unseen\´ graph using a given collection of VULS. The operation of the VULS mining algorithms, and the BMV algorithm, is fully described and evaluated. The evaluation is conducted using satellite image data where the ground surface is represented as a 3D surface with the z dimension describing grey scale value. The idea is to predict vertex labels describing ground type. A statistical analysis of the results, using the Friedman test, is also presented so as to demonstrate the statistical significance of the VULS based 3D surface regional classification idea. The results indicate that the VULS concept is well suited to the task of 3D surface regional classification.