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Resumen El presente artículo propone un nuevo enfoque de clasificación de imágenes que utiliza como representación del espacio complejos cartesianos libre de ambigüedad en las relaciones topológicas. El enfoque propuesto comprende seis fases: (i) conversión de la imagen convencional al espacio de complejos cartesianos; (ii) transformación a niveles de grises; (iii) producción de super-píxeles basada en la transformada de cuenca; (iv) producción del espacio de textura aprovechando elementos inter-pixel 1-dimensionales; (v) clasificación mediante máquinas de soporte vectorial; y (vi) evaluación de los resultados. Aunque la exactitud temática de la clasificación a partir del nuevo enfoque mejora la exactitud obtenida con una representación convencional del espacio, la prueba de confianza indica que esa mejoría no es estadísticamente significativa. Sin embargo, el nuevo enfoque puede ser fortalecido en el futuro mediante la incorporación de técnicas para mejorar la definición de límites entre cuencas utilizando valores de probabilidad y espacios de textura multiescala. Abstract This article proposes a new approach to image classification using a space representation as a Cartesian complex free of ambiguity in the topological relationships of adjacency, connectivity, and boundary. The proposed model comprises six phases: (i) image conversion from the conventional space into the Cartesian complex space; (ii) greyscale transformation, (iii) super-pixel space production based on watershed transform, (iv) texture space production taking advantage of 1-dimensional interpixel elements, (v) classification using support vector machines and (vi) results quality assessment. Although global accuracy of the proposed classification improves accuracy of results obtained with a conventional representation of space, the confidence test shows that this improvement is not statistically significant. However, the new approach can be further strengthened by incorporating techniques to improve boundaries definition between watersheds based on probability values as well as using spaces of multiscale texture.

To preserve geometric features, GEOBIA-based image classification first segments a scene grouping geometrically near pixels in superpixels, with the additional benefit of meaningfully decreasing the number of spatial units to be classified. This grouping is usually based on neighbourhood definitions that use (a,b)-connected pixel graphs. Such an approach aims to find object boundaries, which are one-dimensional, from pixels, which are two-dimensional. However, this is practically impossible since topological axioms needed to ensure a correct representation of connectedness relationships cannot be satisfied by (a,b)-connected pixel graphs. The purpose of this paper is to test a novel image segmentation approach from unidimensional space elements based on axiomatic locally finite spaces (ALFS) and their linked oriented matroids. The proposed approach comprises the following stages: (i) multi-scale texture analysis using Gaussian derivative filter kernels; multi-scale gradient calculation for both multispectral image and , spectral affinity analysis and watershed transform were also used in boundary texture analysis image; geometric strength boundary; (iv) affinity analysis-based spectral strength boundary; (v) global strength boundary; (vi) watershed transform definition; (vii) directional filtering response and (viii) support vector machine (SVM) classification. We tested the proposed approach classifying a small subset of GEOBIA2016 benchmark dataset over the town of Potsdam (Germany). For the test, both the ALFS-based and conventional image segments were classified using the support vector machine (SVM) algorithm and compared their results. The use of ALFS-based watershed transform using multiscale texture and multispectral gradients and affinity analysis favoured the proper definition of super pixels resulting in a classification overall accuracy improvement. On the other hand, the general accuracy value of the classification was also improved when the directional filtering response channel was used. However, the increase is small since this response is scale dependent and therefore, resulting classes are mixed depending on the combination of objects with different scales and texture patterns. It is the case of Low vegetation and Building classes which were the two classes that became confused in both conventional and ALFS representations. Results from this study show that the ALFS-based image classification allows to improve the overall accuracy. Results also suggest that the inclusion of additional, directionally filtered bands, not always improve thematic accuracy due to the scale dependence of directional filtering. The availability of an underlying ALFS provides a topologically correct affinity analysis since, in contrast to the conventional representation based only on pixels, available inter-pixel elements allows an adequate affinity assessment along a connecting line whose representation is made from unidimensional elements. While results of the experiments show that the benefits of the inclusion of an underlying space based on ALFS are not significant, the possibility to fulfil topological requirements suggest that the ALFS-based image analysis framework is worth of further development. Authors will explore options to reformulate several processing tasks based on Cartesian complexes to produce better outcomes. This includes fitting cylindrical parabolas to elliptical patches at each unidimensional space element after computing oriented gradient to counteract the phantom order effect (i.e. to avoid producing borders which do not exist).

Segmentation of Remotely Sensed Imagery: Moving from Sharp Objects to Fuzzy Regions

Geographic Object-Based Image Analysis (GEOBIA) aims to better exploit earth remotely sensed imagery by focusing on building image-objects resembling the real-world objects instead of using raw pixels as basis for classification. Due to the recentness of the field, concurrent and sometimes competing methods, terminology, and theoretical approaches are evolving. This risk of babelization has been identified as one of the central threats for GEOBIA, as it could hinder scientific discourse and the development of a generally\ud accepted theoretical framework. This paper contributes to the definition of such ontology by proposing a general functional model of the remote sensing image analysis. The model compartmentalizes the remote sensing process into six stages: (i) sensing the earth surface in order to derive pixels which represent incomplete data about real-world objects; (ii) pre-processing the pixels in order to remove\ud atmospheric, geometric, and radiometric distortions; (iii) grouping the pre-processed pixels (prixels) to produce image-objects (grouped pixels or grixels) at one or several scales; (iv) feature analysis to examine and measure relevant spectral, geometric and contextual properties and relationships of grixels in order to produce feature vectors (vexcels) and decision rules for subsequent discrimination;\ud (v) assignation of grixels to pre-defined qualitative or quantitative land cover classes, thus producing pre-objects (preliminary objects); and (vi) post-processing to refine the previous results and output the geographic objects of interest. The grouping stage may be analized from two different perpectives: (i) discrete segmentation which produces well-defined image-objects, and (ii) continuous segmentation which produces image-fields with indeterminate boundaries. The proposed generic model is applied to analyze two specific GEOBIA software implementations. A functional decomposition of discrete segmentation is also discussed and tested. It is concluded that the proposed framework enhances the evaluation and comparison of different GEOBIA approaches and by this is helping to establish a generally accepted ontology.