Development of an alternative method for multispectral image segmentation based on cartesian complexes and its associated oriented matroids

Abstract

In digital image analysis, a strategy used to address spatial and topological properties is to define image objects, as they are known in the remote sensing community, grouping pixels as coarser geometric space elements or super pixels. This process is known as image segmentation. In this process it is common to group 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. Super pixel boundaries may present ambiguities because one-dimensional contours are represented by pixels, which are 2-dimensional. The inherent complexity of segmentation algorithms along with the high volume of data of the high resolution images, demand considerable computing resources. Because of the above, geometric algorithms traditionally used for image segmentation work on 2-dimensional entities (i.e., there are neither 0-dimensional nor 1-dimensional entities to build boundaries on) and, therefore, take decisions based on topological relationships ambiguously represented. This research managed to conceptually design and computationally implement an alternative method for multispectral image segmentation based on axiomatic locally finite spaces (ALFS) provided by cartesian complexes, which take into account topological and geometric properties. This alternative representation model provides a geometric space that complies with the T 0 digital topology free of topological ambiguities, on which a novel way for segmenting imagery data is built. Proposed model is developed and implemented in such a way that the required subset of geometrical characteristics are transformed into combinatorial structures encoding topological and geometric features present in combinatorial half spaces using its oriented matroid. The proposed approach uses a layered architecture going from a physical level, going next through the logical geospatial abstraction level and then through the cartesian complex logical level. Additionally, there is a layer oforiented matroids composed of conceptual elements in terms of combinatorics for encoding relevant features to multispectral image segmentation. First, it is conducted an edge detection task using a multi-scale texture analysis and oriented gradient calculation, next a spectral affinity analysis, including oriented derivative filter appliance to finally obtain a probability contour map using a cartesian complex space rather than the pixel conventional image representation. Therefore, a computational framework by which it is possible the representation of a multispectral digital image in a way that explicitly takes into account topological properties in order to better conduct image segmentation was produced. Accuracy assessment of boundaries produced by proposing approach was carried out through two validation strategies: (1) segment scale generalization to the scale of the available segmentation ground truth and (2) proposed approach versus conventional pixel boundary detection benchmarking. The 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. Even though the precision produced from cartesian complexes still does not exceed that obtained from the conventional approach based on pixels, the approach here proposed does achieve a better recall and average precision. This permits to affirm that the model proposed and implemented as part of the research here presented constitutes a reliable alternative for the segmentation of multispectral images. It was possible to confirm that the usage of axiomatic locally finite spaces and their associated matroids enables image topological-geometric segmentation.