Subset Warping: Rubber Sheeting with Cuts

Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself

On the Detection of Visual Features from Digital Curves using a Metaheuristic Approach

In computational shape analysis a crucial step consists in extracting meaningful features from digital curves. Dominant points are those points with curvature extreme on the curve that can suitably describe the curve both for visual perception and for recognition. Many approaches have been developed for detecting dominant points. In this paper we present a novel method that combines the dominant point detection and the ant colony optimization search. The method is inspired by the ant colony search (ACS) suggested by Yin in [1] but it results in a much more efficient and effective approximation algorithm. The excellent results have been compared both to works using an optimal search approach and to works based on exact approximation strateg

Near-Shortest Path Routing in Hybrid Communication Networks

Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA\u2720] introduced the HYBRID model, which is based on the concept of synchronous message passing and uses two fundamentally different principles of communication: a local mode, which allows every node to exchange one message per round with each neighbor in a local communication graph; and a global mode where any pair of nodes can exchange messages, but only few such exchanges can take place per round. A sizable portion of the previous research for the HYBRID model revolves around basic communication primitives and computing distances or shortest paths in networks. In this paper, we extend this study to a related fundamental problem of computing compact routing schemes for near-shortest paths in the local communication graph. We demonstrate that, for the case where the local communication graph is a unit-disc graph with n nodes that is realized in the plane and has no radio holes, we can deterministically compute a routing scheme that has constant stretch and uses labels and local routing tables of size O(log n) bits in only O(log n) rounds

An Overview of Rendering from Volume Data --- including Surface and Volume Rendering

Volume rendering is a title often ambiguously used in science. One meaning often quoted is: `to render any three volume dimensional data set'; however, within this categorisation `surface rendering'' is contained. Surface rendering is a technique for visualising a geometric representation of a surface from a three dimensional volume data set. A more correct definition of Volume Rendering would only incorporate the direct visualisation of volumes, without the use of intermediate surface geometry representations. Hence we state: `Volume Rendering is the Direct Visualisation of any three dimensional Volume data set; without the use of an intermediate geometric representation for isosurfaces'; `Surface Rendering is the Visualisation of a surface, from a geometric approximation of an isosurface, within a Volume data set'; where an isosurface is a surface formed from a cross connection of data points, within a volume, of equal value or density. This paper is an overview of both Surface Rendering and Volume Rendering techniques. Surface Rendering mainly consists of contouring lines over data points and triangulations between contours. Volume rendering methods consist of ray casting techniques that allow the ray to be cast from the viewing plane into the object and the transparency, opacity and colour calculated for each cell; the rays are often cast until an opaque object is `hit' or the ray exits the volume

Collision-free path planning

Motion planning is an important challenge in robotics research. Efficient generation of collision-free motion is a fundamental capability necessary for autonomous robots;In this dissertation, a fast and practical algorithm for moving a convex polygonal robot among a set of polygonal obstacles with translations and rotations is presented. The running time is O(c((n + k)N + nlogn)), where c is a parameter controlling the precision of the results, n is the total number of obstacle vertices, k is the number of intersections of configuration space obstacles, and N is the number of obstacles, decomposed into convex objects. This dissertation exploits a simple 3D passage-network to incorporate robot rotations as an alternative to complex cell decomposition techniques or building passage networks on approximated 3D C-space obstacles;A common approach in path planning is to compute the Minkowski difference of a polygonal robot model with the polygonal obstacle environment. However such a configuration space is valid only for a single robot orientation. In this research, multiple configuration spaces are computed between the obstacle environment and the robot at successive angular orientations spanning [pi] . Although the obstacles do not intersect, each configuration space may contain intersecting configuration space obstacles (C-space obstacles). For each configuration space, the algorithm finds the contour of the intersected C-space obstacles and the associated passage network by slabbing the collision-free space. The individual configuration spaces are then related to one another by a heuristic called proper links that exploit spatial coherence. Thus, each level is connected to the adjacent levels by proper links to construct a 3D network. Dijkstra\u27s algorithm is used to search for the shortest path in the 3D network. Finally, the path is projected onto the plane to show the final locus of the path