A Combinatorial Approach for Hyperspectral Image Segmentation

José Antonio Valero Medina, Pablo Andrés Arbeláez Escalante, Iván Alberto Lizarazo Salcedo

Abstract: A common strategy in high spatial resolution image analysis is to define coarser geometric space elements, i.e. superpixels, by grouping near pixels based on (a, b)–connected graphs as neighborhood definitions. Such an approach, however, cannot meet some topological axioms needed to ensure a correct representation of connectedness relationships. Superpixel boundaries may present ambiguities because one-dimensional contours are represented by pixels, which are two-dimensional. Additionally, the high spatial resolution available today has increased the volume of data that must be processed during image segmentation even after data reduction phases such as principal component analysis. The inherent complexity of segmentation algorithms, including texture analysis, along with the aforementioned volume of data, demands considerable computing resources. In this paper, we propose a novel way for segmenting hyperspectral imagery data by defining a computational framework based on Axiomatic Locally Finite Spaces (ALFS) provided by Cartesian complexes, which provide a geometric space that complies with the \(T_{0}\) digital topology. Our approach links also oriented matroids to geometric space representations and is implemented on a parallel computational framework. We evaluated quantitatively our approach on a subset of hyperspectral remote sensing scenes. Our results show that, by departing from the conventional pixel representation, it is possible to segment an image based on a topologically correct digital space, while simultaneously taking advantage of combinatorial features of their associated oriented matroids.