In this paper, a fast path planning method by optimization of a path graph for both efficiency and accuracy is proposed. A conventional quadtree-based path planning approach is simple, robust, and efficient. However, it has two limitations. The first limitation is that many small cells are required to represent obstacles because the positions and shapes of the cells are not object-dependent and...

This paper presents an efficient simplification method for regular meshes obtained with a binary subdivision scheme. Our mesh connectivity is constrained with a quadtree data structure. We propose a quadtree built especially for this class of meshes having a constant-time traversal property. We introduce a rate-distortion (RD) framework to decimate the mesh and build a progressive representatio...

The imaging of subsurface targets, such as landmines, using Ground Penetrating Radar (GPR) is becoming an increasingly important area of research. Conventional image formation techniques expend large amounts of computational resources on fully resolving a region, even if there is a large amount of clutter. For example, standard backprojection algorithms require O(N). However, by using multi-res...

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract Any binary image can be represented by a quadtree. Therefore random quadtrees correspond to bounded random sets in the plane. We discuss various possibilities for randomizing the quadtree. The most natural randomization yields Mandelbrot percolation.

This paper presents a rate-distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed in this kind of image, giving a toy model for a non-linear adaptive coding technique, and its rate-distortion behavior is studied. The effect of refining the quadtree decomposition in the Rate-Distortion decay is also studied.

A formula is provided to compute the number of new blocks resulting from the decomposition induced by a shift of a single quadtree node of arbitrary size by an arbitrary amount. A precise calculation is also presented for the average number of BLACK nodes required to represent a square of width 2 m in a region quadtree.

We present a new I/O-efficient index structure for storing planar subdivisions. This so-called guard-quadtree is a compressed linear quadtree, which is provably efficient for map overlay, point location, and range queries in low-density subdivisions. In particular, we can preprocess a lowdensity subdivision with n edges, in O(sort(n)) I/Os, to build a guard-quadtree that allows us to: (i) compu...

Title of dissertation: DYNAMIC DATA STRUCTURES FOR GEOMETRIC SEARCH AND RETRIEVAL Eunhui Park, 2013 Dissertation directed by: Professor David M. Mount Department of Computer Science Data structures for geometric search and retrieval are of significant interest in areas such as computational geometry, computer graphics, and computer vision. The focus of this dissertation is on the design of effi...