In order to interactively investigate large-scale 3D data sets, we propose an improved hierarchical data structure for structured grids and an original hierarchical data structure for unstructured grids. These multi-tiered implementations allow the user to interactively control both the local and global density of the mesh. Therefore, the user can interactively refine areas of interest and decimate peripheral regions. By controlling the density of the mesh throughout the volume, the user controls where computational cycles are spent and gains a deeper insight into the geometric structure of the mesh. i 1 Introduction Computational scientists and engineers are producing ever larger sets of volume data. While the specific application problems encountered by computational scientists vary widely across (as well as within) disciplines, the computational structure of the collected data varies remarkably little and is usually represented in the form of discrete approximations of scalar and ...

This paper introduces a spatial indexing structure that adjusts itself so as to provide faster access to spatially referenced data most in demand. The structure is a hybrid of a splay tree and a quadtree. The quadtree is a well-known spatial data structure that successively segments a spatial data area into quadrants, preserving the spatial arrangement of the data. Access to data is based on a traversal of the tree according to a featureÕs containment within a specific quadrant. The splay tree, on the other hand, is a binary search tree that adjusts itself through the use of a splay operation to promote frequently accessed data to the top of the tree where it can be more quickly accessed during future operations. Because users of spatial data tend to concentrate on a specific area for querying, the combination of features from both of these data structures should provide efficient access time to the region of interest. The research includes an object-oriented implementation of the structure as part of the Object Vector Product Format (OVPF) project. This paper examines the data structure and associated operations, and gives an outline of the object-oriented implementation and preliminary experimental results.

An overview is presented of object-based and image-based representations of objects by their interiors. The representations are distinguished by the manner in which they can be used to answer two fundamental queries in database applications: (1) Feature query: given an object, determine its constituent cells (i.e., their locations in space). (2) Location query: given a cell (i.e., a location in space), determine the identity of the object (or objects) of which it is a member as well as the remaining constituent cells of the object (or objects). Regardless of the representation that is used, the generation of responses to the feature and location queries is facilitated by building an index (i.e., the result of a sort) either on the objects or on their locations in space, and implementing it using an access structure that correlates the objects with the locations. Assuming the presence of an access structure, implicit (i.e., image-based) representations are described that are good for finding the objects associated with a particular location or cell (i.e., the location query), while requiring that all cells be examined when determining the locations associated with a particular object (i.e., the feature query). In contrast, explicit (i.e., object-based) representations are good for the feature query,

A region quadtree representation of an image can be normalized thereby yielding a quadtree that contains the least number of nodes in O(s 2 log2 s) time where s is the length of the grid. A new algorithm is proposed whose asymp-totic time bound is the same but whose first part only takes O(s2). It is shown empirically to be able to produce the normalized quadtrees for a number of images in real applications.

Cmnputing surface and/or object intersections is a cornerstone of many al- gorithms in Geometric Modelling and Computer Graphics, for example Set Operations between solids, or surfaces Ray Casting displav. We present an object centered, information preserving, hierarchical representation for polyhedra called Prism Tree. We use the representation to decompose the intersection algorithms into two steps: the localization of intersections, and their processing. When dealing with polyhedra with many faces (typically more than one thousand), the first step is by far the most expensive. The Prism Tree structure is used to compute efficiently this localization step. A preliminary implementation of the Set Operations and Ray Casting algorithms has been constructed.

This dissertation presents a new and efficient next-best-view algorithm for 3D reconstruction of indoor environments using active range sensing. A major challenge in range acquisition for 3D reconstruction is an efficient automated view planning algorithm to determine a sequence of scanning locations or views such that a set of acquisition constraints and requirements is satisfied and the object or environment of interest can be satisfactorily reconstructed. Due to the intractability of the view planning problem and the lack of global geometric information, a greedy approach is adopted to approximate the solution. A practical view metric is formulated to include many real-world acquisition constraints and reconstruction quality requirements. This view metric is flexible to allow trade-offs between different requirements of the reconstruction quality. A major contribution of this work is the application of a hierarchical approach to greatly accelerate the evaluation of the view metric

eral categories, there are geometric representations in terms of points, lines, and surfaces; symbolic representations in terms of primitive components and their spatial relationships; and functional representations in terms of functional parts and their functional relationships. We will begin with a survey of the most common methods for representing 3D objects and then proceed to the representations required by the most common types of object recognition algorithms. 14.1 Survey of Common Representation Methods Computer vision began with the work of Roberts in 1965 on recognition of polyhedral objects, using simple wire-frame models and matching to straight line segments extracted from images. Line-segment-based models have remained popular even today, but there are also a number of alternatives that attempt to more closely represent the data from objects that can have curved and even free-form surfaces. In this section, we will look at mesh models, surface-edge-vertex models,

ition. In general categories, there are geometric representations in terms of points, lines, and surfaces; symbolic representations in terms of primitive components and their spatial relationships; and functional representations in terms of functional parts and their functional relationships. We will begin with a survey of the most common methods for representing 3D objects and then proceed to the representations required by the most common types of object recognition algorithms. 14.1 Survey of Common Representation Methods Computer vision began with the work of Roberts in 1965 on recognition of polyhedral objects, using simple wire-frame models and matching to straight line segments extracted from images. Line-segment-based models have remained popular even today, but there are also a number of alternatives that attempt to more closely represent the data from objects that can have curved and even free-form surfaces. In this section, we will look at mesh models, surfa

In this paper we present a method of partitioning feature space of given data into a number of hypercuboids. Each data point is allocated to one of the hypercuboids using an allocation rule based on spatial distances of a point in n dimensional space from the cuboid coordinates. For each partition or cell in our instance, we measure the degree of complexity of the classification problem based on the local probability distributions. We derive the overall complexity of the classification problem as a weighted sum of the hypercube's separability measure and the number of elements present in them. On a total of eight Gaussian distributions and two UCI pattern recognition benchmarks, we quantify the complexity of the classification problem. Also, we discuss how our approach can be used to solve a range of pattern recognition problems in a non-conventional but highly effective manner.

The ability of classifiers to learn decision boundaries in data space depends on the data distribution overlaps across given class categories. Accurate estimates of classification complexity are needed to rank data problems in terms of difficulties with learning data and for appropriate feature and classifier selection to improve classification results. In this paper we compare our proposed novel data resolution dependent separability measures including purity, kNN separability and collective entropy, with five well-known standard probabilistic distance measures. The proposed measures make no assumptions on the normality of distribution. Data resolution is defined by the extent of data space partitioning into cells or hypercuboids. The separability measures are computed for data in each cell separately and the final measurements are aggregated over all resolutions. Our results on nine tasks from the University of California-Irvine repository show that data resolution based separability measures convincingly outperform the probability based distance measures in terms of their superior correlation with the training and test errors on three chosen classifiers.