Multispectral image segmentation based on Cartesian complexes and their associated oriented matroids

Abstract

A number of strategies have been used to include spatial and topological properties in the image segmentation stage. It is generally accepted that grouping of nearby pixels by modelling neighbourhood relationships as (a, b) connected graphs may lead to meaningful image objects. In such approach, however, topological concepts may suffer from ambiguity since image elements (pixels) are two dimensional entities. This paper evaluates whether an alternative representation of digital images based both on Cartesian complexes and oriented matroids may improve multispectral image segmentation by enforcing topological and geometric properties and then be used in the classification stage. A conceptual model is defined, using Cartesian complexes, in order to link combinatorial properties of axiomatic locally finite spaces and their associated oriented matroids for involving topological properties. The proposed approach uses a layered architecture going from a physical level, going next through logical geospatial abstraction level and then through the Cartesian complex logical level. Additionally, there is a layer of oriented matroids composed by conceptual elements in terms of combinatorics for encoding relevant features to multispectral image segmentation. First, it is conducted an edge detection task, next an probability contour map using a Cartesian complex space rather than the conventional image space and finally, an image classification using random forest method. A computational solution including several components was developed using a framework for parallel computing. The performance of this solution was assessed using a small subset of GEOBIA2016 benchmark dataset. It is shown that the usage of a partial implementation of Cartesian complexes and associated oriented matroids is computationally but does not increase classification accuracy.