Data structures for retrieval on integer grids

A family of data structures is presented for retrieval of the sum of values of points within a half-plane or polygon, given that the points are on integer coordinates in the plane. Fredman has shown that the problem has a lower bound of Ω(N^2/3) for intermixed updates and retrievals. Willard has shown an upper bound of O(N^2log6^4) for the case where the points are not restricted to integer coordinates.We have developed families of related data structures for retrievals of half-planes or polygons. One of the data structures permits intermixed updates and half-plane retrievals in O(N^2/3log N) time, where N is the size of the grid.We use a technique we call "Rotation" to permit a better match of a portion of the data structure to the particular problem. Rotations appear to be an effective method for trading-off storage redundancy against retrieval time for certain classes of problems

Investigating the use of semantic technologies in spatial mapping applications

Semantic Web Technologies are ideally suited to build context-aware information retrieval applications. However, the geospatial aspect of context awareness presents unique challenges such as the semantic modelling of geographical references for efficient handling of spatial queries, the reconciliation of the heterogeneity at the semantic and geo-representation levels, maintaining the quality of service and scalability of communicating, and the efficient rendering of the spatial queries' results. In this paper, we describe the modelling decisions taken to solve these challenges by analysing our implementation of an intelligent planning and recommendation tool that provides location-aware advice for a specific application domain. This paper contributes to the methodology of integrating heterogeneous geo-referenced data into semantic knowledgebases, and also proposes mechanisms for efficient spatial interrogation of the semantic knowledgebase and optimising the rendering of the dynamically retrieved context-relevant information on a web frontend

Multi-view Convolutional Neural Networks for 3D Shape Recognition

A longstanding question in computer vision concerns the representation of 3D shapes for recognition: should 3D shapes be represented with descriptors operating on their native 3D formats, such as voxel grid or polygon mesh, or can they be effectively represented with view-based descriptors? We address this question in the context of learning to recognize 3D shapes from a collection of their rendered views on 2D images. We first present a standard CNN architecture trained to recognize the shapes' rendered views independently of each other, and show that a 3D shape can be recognized even from a single view at an accuracy far higher than using state-of-the-art 3D shape descriptors. Recognition rates further increase when multiple views of the shapes are provided. In addition, we present a novel CNN architecture that combines information from multiple views of a 3D shape into a single and compact shape descriptor offering even better recognition performance. The same architecture can be applied to accurately recognize human hand-drawn sketches of shapes. We conclude that a collection of 2D views can be highly informative for 3D shape recognition and is amenable to emerging CNN architectures and their derivatives.Comment: v1: Initial version. v2: An updated ModelNet40 training/test split is used; results with low-rank Mahalanobis metric learning are added. v3 (ICCV 2015): A second camera setup without the upright orientation assumption is added; some accuracy and mAP numbers are changed slightly because a small issue in mesh rendering related to specularities is fixe

An Algorithm for Data Reorganization in a Multi-dimensional Index

In spatial databases, data are associated with spatial coordinates and are retrieved based on spatial proximity. A spatial database uses spatial indexes to optimize spatial queries. An essential ingredient for efficient spatial query processing is spatial clustering of data and reorganization of spatial data. Traditional clustering algorithms and reorganization utilities lack in performance and execution. To solve this problem we have developed an algorithm to convert a two dimensional spatial index into a single dimensional value and then a reorganization is done on the spatial data. This report describes this algorithm as well as various experiments to validate its effectiveness

A quick-retrieval high-speed digital framing camera

A new high-speed digital framing camera is described. The design is built around a rotating polygon mirror that provides a framing rate of 24 000 frames/s. The camera electronics digitizes an image into a 32×104 grid of pixels, where the second dimension of the grid can be varied and is determined by the 8 bit computer-aided measurement and control digitizer sampling rate. Available digitizer memory provides for 314 frames at this horizontal resolution. The advantages over other available high-speed framing cameras are (1) low cost of the system provided the digitizers are available, (2) rapid retrieval of a recorded event, and (3) the ease with which the system can be used. Sample results from an application in high-power arc photography are given to illustrate the system's spatial and temporal resolution

Neural 3D Mesh Renderer

For modeling the 3D world behind 2D images, which 3D representation is most appropriate? A polygon mesh is a promising candidate for its compactness and geometric properties. However, it is not straightforward to model a polygon mesh from 2D images using neural networks because the conversion from a mesh to an image, or rendering, involves a discrete operation called rasterization, which prevents back-propagation. Therefore, in this work, we propose an approximate gradient for rasterization that enables the integration of rendering into neural networks. Using this renderer, we perform single-image 3D mesh reconstruction with silhouette image supervision and our system outperforms the existing voxel-based approach. Additionally, we perform gradient-based 3D mesh editing operations, such as 2D-to-3D style transfer and 3D DeepDream, with 2D supervision for the first time. These applications demonstrate the potential of the integration of a mesh renderer into neural networks and the effectiveness of our proposed renderer

Voronoi-Based Region Approximation for Geographical Information Retrieval with Gazetteers

Gazetteers and geographical thesauri can be regarded as parsimonious spatial models that associate geographical location with place names and encode some semantic relations between the names. They are of particular value in processing information retrieval requests in which the user employs place names to specify geographical context. Typically the geometric locational data in a gazetteer are confined to a simple footprint in the form of a centroid or a minimum bounding rectangle, both of which can be used to link to a map but are of limited value in determining spatial relationships. Here we describe a Voronoi diagram method for generating approximate regional extents from sets of centroids that are respectively inside and external to a region. The resulting approximations provide measures of areal extent and can be used to assist in answering geographical queries by evaluating spatial relationships such as distance, direction and common boundary length. Preliminary experimental evaluations of the method have been performed in the context of a semantic modelling system that combines the centroid data with hierarchical and adjacency relations between the associated place names