Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces meet--as well as a topology on these objects. Existing algorithms encode this information in designated data structures, but require that these data structures fit entirely in Random Access Memory (RAM). Today, 3D images with several billion voxels are acquired, e.g. in structural neurobiology. Since these large volumes can no longer be processed with existing methods, we present a new algorithm which performs geometry and topology extraction with a runtime linear in the number of voxels and log-linear in the number of faces and curves. The parallelizable algorithm proceeds in a block-wise fashion and constructs a consistent representation of the entire volume image on the hard drive, making the structure of very large volume segmentations accessible to image analysis. The parallelized C++ source code, free command line tools and MATLAB mex files are avilable from this http URL
were introduced in image analysis in @cite_5 and are used as data structures, e.g. in @cite_13 as well as in some algorithms of the Computational Geometry Algorithms Library (CGAL) www.cgal.org . The extension of combinatorial maps to higher dimensions is involved but possible @cite_14 @cite_3 and has facilitated the development of the 3-dimensional topological map @cite_18 @cite_4 . This map captures not only the topology of a segmentation but also its embedding into the segmented space, i.e. containment relations and orders of objects @cite_14 @cite_1 . It is therefore more expensive to construct and manipulate than a data structure that encodes only the topology.
@cite_18 @cite_14 @cite_4 @cite_1 @cite_3 @cite_5 @cite_13
2020141201 2073401105 2623510711 2470820246
We introduce a novel projection-based visualization method for high-dimensional data sets by combining concepts from MDS and the geometry of the hyperbolic spaces. This approach hyperbolic multi-dimensional scaling (H-MDS) is a synthesis of two important concepts for explorative data analysis and visualization: (i) multi-dimensional scaling uses proximity or pair distance data to generate a low-dimensional, spatial presentation of the data; (ii) previous work on the "hyperbolic tree browser" demonstrated the extraordinary advantages for an interactive display of graph-like data in the two-dimensional hyperbolic space (H2).In the new approach, H-MDS maps proximity data directly into the H2. This removes the restriction to "quasihierarchical", graph-based data--a major limitation of (ii). Since a suitable distance function can convert all kinds of data to proximity (or distance-based) data, this type of data can be considered the most general.We review important properties of the hyperbolic space and, in particular, the circular Poincare model of the H2. It enables effective human-computer interaction: by mouse dragging the "focus", the user can navigate in the data without loosing the context. In H2 the "fish-eye" behavior originates not simply by a non-linear view transformation but rather by extraordinary, non-Euclidean properties of the H2. Especially, the exponential growth of length and area of the underlying space makes the H2 a prime target for mapping hierarchical and (now also) high-dimensional data.Several high-dimensional mapping examples including synthetic and real-world data are presented. Since high-dimensional data produce "ring"-shaped displays, we present methods to enhance the display by modulating the dissimilarity contrast. This is demonstrated for an application for unstructured text: i.e., by using multiple film critiques from news:rec.art.movies.reviews and www.imdb.com, each movie is placed within the H2--creating a "space of movies" for interactive exploration. In this paper, we define the three-dimensional topological map, a model which represents both the topological and geometrical information of a three-dimensional labeled image. Since this model describes the image's topology in a minimal way, we can use it to define efficient image processing algorithms. The topological map is the last level of map hierarchy. Each level represents the region boundaries of the image and is defined from the previous level in the hierarchy, thus giving a simple constructive definition. This model is an extension of the similar model defined for 2D images. Progressive definition based on successive map levels allows us to extend this model to higher dimension. Moreover, with progressive definition, we can study each level separately. This simplifies the study of disconnection cases and the proofs of topological map properties. Finally, we provide an incremental extraction algorithm which extracts any map of the hierarchy in a single image scan. Moreover, we show that this algorithm is very efficient by giving the results of our experiments made on artificial images. In this paper, we propose a novel appearance-based approach for topological mapping based on a hierarchical decomposition of the environment. In our map, images with similar visual properties are grouped together in nodes, which are represented by means of an average global descriptor and an index of binary features based on a bag-of-words online approach. Each image is represented by means of a global descriptor and a set of local features, and this information is used in a two-level loop closure approach, where first global descriptors are employed to obtain the most likely nodes of the map and then binary image features are used to retrieve the most likely images inside these nodes. This hierarchical scheme enables us to reduce the search space when recognizing places, maintaining high accuracy when creating a map. Our approach is validated using several public datasets and compared against several state-of-the-art techniques. The accuracy and the sparsity of the generated maps are also discussed. The wide availability of affordable RGB-D sensors changes the landscape of indoor scene analysis. Years of research on simultaneous localization and mapping (SLAM) have made it possible to merge multiple RGB-D images into a single point cloud and provide a 3D model for a complete indoor scene. However, these reconstructed models only have geometry information, not including semantic knowledge. The advancements in robot autonomy and capabilities for carrying out more complex tasks in unstructured environments can be greatly enhanced by endowing environment models with semantic knowledge. Towards this goal, we propose a novel approach to generate 3D semantic maps for an indoor scene. Our approach creates a 3D reconstructed map from a RGB-D image sequence firstly, then we jointly infer the semantic object category and structural class for each point of the global map. 12 object categories (e.g. walls, tables, chairs) and 4 structural classes (ground, structure, furniture and props) are labeled in the global map. In this way, we can totally understand both the object and structure information. In order to get semantic information, we compute semantic segmentation for each RGB-D image and merge the labeling results by a Dense Conditional Random Field. Different from previous techniques, we use temporal information and higher-order cliques to enforce the label consistency for each image labeling result. Our experiments demonstrate that temporal information and higher-order cliques are significant for the semantic mapping procedure and can improve the precision of the semantic mapping results.