Integration of SAR and DEM data: Geometrical considerations

General principles for integrating data from different sources are derived from the experience of registration of SAR images with digital elevation models (DEM) data. The integration consists of establishing geometrical relations between the data sets that allow us to accumulate information from both data sets for any given object point (e.g., elevation, slope, backscatter of ground cover, etc.). Since the geometries of the two data are completely different they cannot be compared on a pixel by pixel basis. The presented approach detects instances of higher level features in both data sets independently and performs the matching at the high level. Besides the efficiency of this general strategy it further allows the integration of additional knowledge sources: world knowledge and sensor characteristics are also useful sources of information. The SAR features layover and shadow can be detected easily in SAR images. An analytical method to find such regions also in a DEM needs in addition the parameters of the flight path of the SAR sensor and the range projection model. The generation of the SAR layover and shadow maps is summarized and new extensions to this method are proposed

Contains and Inside relationships within combinatorial Pyramids

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular pyramid framework encode different types of relationships between regions. This paper compares different graph models used within the irregular pyramid framework according to a set of relationships between regions. We also define a new algorithm based on a pyramid of combinatorial maps which allows to determine if one region contains the other using only local calculus.Comment: 35 page

Open Issues and Chances for Topological Pyramids

High resolution image data require a huge amount of computational resources. Image pyramids have shown high performance and flexibility to reduce the amount of data while preserving the most relevant pieces of information, and still allowing fast access to those data that have been considered less important before. They are able to preserve an existing topological structure (Euler number, homology generators) when the spatial partitioning of the data is known at the time of construction. In order to focus on the topological aspects let us call this class of pyramids “topological pyramids”. We consider here four open problems, under the topological pyramids context: The minimality problem of volumes representation, the “contact”-relation representation, the orientation of gravity and time dimensions and the integration of different modalities as different topologies.Austrian Science Fund P20134-N13Junta de Andalucía FQM–296Junta de Andalucía PO6-TIC-0226

Image = Structure + Few Colors

Topology plays an important role in computer vision by capturing the structure of the objects. Nevertheless, its potential applications have not been sufficiently developed yet. In this paper, we combine the topological properties of an image with hierarchical approaches to build a topology preserving irregular image pyramid (TIIP). The TIIP algorithm uses combinatorial maps as data structure which implicitly capture the structure of the image in terms of the critical points. Thus, we can achieve a compact representation of an image, preserving the structure and topology of its critical points (maxima, the minima and the saddles). The parallel algorithmic complexity of building the pyramid is O(log d) where d is the diameter of the largest object.We achieve promising results for image reconstruction using only a few color values and the structure of the image, although preserving fine details including the texture of the image

Invariant Representative Cocycles of Cohomology Generators using Irregular Graph Pyramids

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns `quantities' to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. An extension to obtain scanning and rotation invariant cocycles is given.Comment: Special issue on Graph-Based Representations in Computer Visio

Characterizing Configurations of critical points through LBP Extended Abstract

In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) is given using combinatorial maps and a method for obtaining a representative LBP image is developed based on merging regions and Minimum Contrast Algorithm. The LBP code characterizes the topological category (max, min, slope, saddle) of the 2D gray level landscape around the center region. We extend the result studying how to merge non-singular slopes with one of its neighbors and how to extend the results to nonwell formed images/maps. Some ideas related to robust LBP and isolines are also given in last section

Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators

An algorithm to compute a minimal length basis of representative cocycles of cohomology generators for 2D images is proposed. We based the computations on combinatorial pyramids foreseeing its future extension to 3D objects. In our research we are looking for a more refined topological description of deformable 2D and 3D shapes, than they are the often used Betti numbers. We define contractions on the object edges toward the inner of the object until the boundaries touch each other, building an irregular pyramid with this purpose. We show the possible use of the algorithm seeking the minimal cocycles that connect the convex deficiencies on a human silhouette. We used minimality in the number of cocycle edges in the basis, which is a robust description to rotations and noise

Characterizing obstacle-avoiding paths using cohomology theory

Abstract. In this paper, we investigate the problem of analyzing the shape of obstacle-avoiding paths in a space. Given a d-dimensional space with holes, representing obstacles, we ask if certain paths are equivalent, informally if one path can be continuously deformed into another, within this space. Algebraic topology is used to distinguish between topologically different paths. A compact yet complete signature of a path is constructed, based on cohomology theory. Possible applications include assisted living, residential, security and environmental monitoring. Numerical results will be presented in the final version of this paper

3D-Voronoi Diagramme zur quantitativen Bildanalyse in der Interphase-Cytogenetik

Um die Anordnung von Chromosomen in Zellkernen der Interphase zu untersuchen, wurde ein Verfahren aus der Computergeometrie adaptiert. Dieser Ansatz basiert auf der Zerlegung von dreidimensionalen Bildvolumen mithilfe des Voronoi-Diagramms in konvexe Polyeder. Die graphenorientierte, geometrische Struktur dieses Verfahrens ermöglicht sowohl eine schnelle Extraktion von Objekten im Bildraum als auch die Berechnung morphologischer Parameter wie Volumina, Oberflächen und Rundheitsfaktoren. In diesem Beitrag wird exemplarisch die dreidimensionale Morphologie von XChromosomen in weiblichen Interphasezellkernen mithilfe dieser drei Parameter untersucht. Um diese Zellkerne mit lichtoptischen Methoden zu untersuchen, wurden die Territorien der X-Chromosomen mit einem molekularcytogenetischen Verfahren fluoreszierend dargestellt. Zur Unterscheidung des aktiven und inaktiven X-Chromosoms wurde das Barr-Körperchen zusätzlich markiert und mithilfe eines Epifluoreszenzmikroskops, ausgerüstet mit einer CCD-Kamera, aufgenommen. Anschließend wurden 1 2 - 2 5 äquidistante, lichtoptische Schnitte der X-Chromosomenterritorien mit einem konfokalen Laser Scanning Mikroskop (CLSM) aufgenommen. Diese lichtoptischen Schnitte wurden mithilfe des Voronoi-Verfahrens segmentiert und analysiert. Methoden aus der Computergraphik wurden zur Visualisierung der Ergebnisse eingesetzt. Es konnte gezeigt werden, daß mithilfe des Voronoi-Verfahrens Chromosomen- Territorien anhand der morphologischen Parameter zuverlässig beschrieben werden können