Incremental spectral clustering and its application to topological mapping

This paper presents a novel use of spectral clustering algorithms to support cases where the entries in the affinity matrix are costly to compute. The method is incremental – the spectral clustering algorithm is applied to the affinity matrix after each row/column is added – which makes it possible to inspect the clusters as new data points are added. The method is well suited to the problem of appearance-based, on-line topological mapping for mobile robots. In this problem domain, we show that we can reduce environment-dependent parameters of the clustering algorithm to just a single, intuitive parameter. Experimental results in large outdoor and indoor environments show that we can close loops correctly by computing only a fraction of the entries in the affinity matrix. The accompanying video clip shows how an example map is produced by the algorithm

Topomap: Topological Mapping and Navigation Based on Visual SLAM Maps

Visual robot navigation within large-scale, semi-structured environments deals with various challenges such as computation intensive path planning algorithms or insufficient knowledge about traversable spaces. Moreover, many state-of-the-art navigation approaches only operate locally instead of gaining a more conceptual understanding of the planning objective. This limits the complexity of tasks a robot can accomplish and makes it harder to deal with uncertainties that are present in the context of real-time robotics applications. In this work, we present Topomap, a framework which simplifies the navigation task by providing a map to the robot which is tailored for path planning use. This novel approach transforms a sparse feature-based map from a visual Simultaneous Localization And Mapping (SLAM) system into a three-dimensional topological map. This is done in two steps. First, we extract occupancy information directly from the noisy sparse point cloud. Then, we create a set of convex free-space clusters, which are the vertices of the topological map. We show that this representation improves the efficiency of global planning, and we provide a complete derivation of our algorithm. Planning experiments on real world datasets demonstrate that we achieve similar performance as RRT* with significantly lower computation times and storage requirements. Finally, we test our algorithm on a mobile robotic platform to prove its advantages.Comment: 8 page

Hierarchical growing neural gas

“The original publication is available at www.springerlink.com”. Copyright Springer.This paper describes TreeGNG, a top-down unsupervised learning method that produces hierarchical classification schemes. TreeGNG is an extension to the Growing Neural Gas algorithm that maintains a time history of the learned topological mapping. TreeGNG is able to correct poor decisions made during the early phases of the construction of the tree, and provides the novel ability to influence the general shape and form of the learned hierarchy

Generalized fuzzy topographic topological mapping

Fuzzy Topographic Topological Mapping (FTTM) is a model for solving neuromagnetic inverse problem. FTTM consists of four topological spaces which are connected by three homeomorphisms. FTTM 1 and FTTM 2 were designed to present 3-D view of an unbounded single current and bounded multicurrent sources, respectively. It has been showed that FTTM 1 and FTTM 2 are homeomorphic and this homeomorphism will generate another 14 FTTM. There is a conjecture stated that if there exist n numbers of FTTM, then they will generate another n4 ? n new FTTM. In this thesis, the conjecture is proven by using geometrical features of FTTM. In the process, several definitions such as sequence of FTTM, sequence of polygon, sequence of cube with combination of two, three and four FTTM are developed. Some geometrical and algebraic properties of sequences of FTTM are identified and proven. A new conjecture is also proposed in this thesis which states that the number of generating Fkn if there are k components and n models of Fk is nk ? n . Surprisingly, the nonzero sequence of cube with combination of two, three and four FTTM appeared in Pascal’s Triangle

DNA Mapping Algorithms: Topological Mapping

There are several basic approaches that can be used in attempting to produce high-resolution DNA restriction maps. A standard approach is the match/merge approach in which first the topology of the map units being mapped together is suppressed and lists of potential matches between fragments are generated, and second the topology is introduced to eliminate matchlists which are inconsistent with the topology. This technical report documents a different approach to DNA mapping, known as topological mapping. In topological mapping the precedence of the two criteria are reversed, i.e., the topology of the two map units is used as the primary search constraint and only those fragments within specific topologically constrained bounds are considered for a potential match. In this approach, the primary topological constraint reduces the number of fragment comparisons that must be considered, in comparison to the match/merge approach. The more topological structure is present in each map unit, the greater the reduction. The conceptual approach is discussed in general. Specific mechanisms for implementing the ideas are presented, and the structure of the software based in these mechanisms is described. Heuristic approaches which can be used for pre- and post-processing are suggested and analyzed. Execution results are given for the application of the software to a number of laboratory generated mapping problems, which were provided by the Olson laboratory

Designing compression structures by topological mapping

Congreso celebrado en la Escuela de Arquitectura de la Universidad de Sevilla desde el 24 hasta el 26 de junio de 2015.The Force Density Method has been traditionally employed to seek the equilibrium shape of tension structures. Recently, the use of a process based on topology has been introduced to provide a first network in which the Force Density Method can be applied. Compression-only structures such as vaults and domes can also be modelled by means of the former approach if this is modified to get a design process similar to the Gaudí’s one based on hanging models. The conjunction of Topological Mapping and the Forced Density Method is first explained in the form-finding process of tension structures and, later on, the modifications to that approach are introduced so that an iterative procedure is obtained to get equilibrium shapes of compression-only structures. The versatility of this novel approach is presented by means of the analysis of some representative examples

Incremental topological mapping using omnidirectional vision

This paper presents an algorithm that builds topological maps, using omnidirectional vision as the only sensor modality. Local features are extracted from images obtained in sequence, and are used both to cluster the images into nodes and to detect links between the nodes. The algorithm is incremental, reducing the computational requirements of the corresponding batch algorithm. Experimental results in a complex, indoor environment show that the algorithm produces topologically correct maps, closing loops without suffering from perceptual aliasing or false links. Robustness to lighting variations was further demonstrated by building correct maps from combined multiple datasets collected over a period of 2 month