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375
Edge Detection with Embedded Confidence
 IEEE Trans. Pattern Anal. Machine Intell
, 2001
"... Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework well known artifacts of the gradient based edge dete ..."
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Cited by 70 (1 self)
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Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework well known artifacts of the gradient based edge detectors, such as large spurious responses can be explained quantitatively. It is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model. The widely used threestep edge detection procedure: gradient estimation, nonmaxima suppression, hysteresis thresholding; is generalized to include the information provided by the confidence measure. The additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges. Keywords: edge detection, performance assessment, gradient estimation, window operators 1
Viewdependent displacement mapping
 ACM Transactions on Graphics
, 2003
"... Displacement mapping was originally created as a rendering tool to provide smallscale modulation of an underlying smooth surface. However, it has now emerged as a sculpting tool, to the extent that complex geometry can effectively be added to a scene at rendering time. The attendant complexity of d ..."
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Cited by 68 (1 self)
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Displacement mapping was originally created as a rendering tool to provide smallscale modulation of an underlying smooth surface. However, it has now emerged as a sculpting tool, to the extent that complex geometry can effectively be added to a scene at rendering time. The attendant complexity of displacement maps is placing increased demands on rendering systems, from quality, performance, and memory perspectives. While adequate solutions exist within scanline rendering architectures, good general solutions have been difficult to come by in raytraced or hardwarebased environments, or in situations in which a complete displaced surface is desired. We present an approach to the rendering of displacement mapped surfaces that scales with the complexity of the displacement map, with an eye to minimizing the amount of additional geometry generated by the mapping process. We perform a feature analysis of displacement maps, aggregate these features, and map them onto geometry in space. This approach affords a significant degree of complexity control, it permits featurebased tessellation of surfaces, and it is amenable to use in raytraced, scanline, or hardware accelerated settings. This kind of feature analysis naturally applies to other classes of texture mapping as well. 1
OutputSensitive Results on Convex Hulls, Extreme Points, and Related Problems
, 1996
"... . We use known data structures for rayshooting and linearprogramming queries to derive new outputsensitive results on convex hulls, extreme points, and related problems. We show that the f face convex hull of an npoint set P in a fixed dimension d # 2 can be constructed in O(n log f + (nf) ..."
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Cited by 66 (13 self)
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. We use known data structures for rayshooting and linearprogramming queries to derive new outputsensitive results on convex hulls, extreme points, and related problems. We show that the f face convex hull of an npoint set P in a fixed dimension d # 2 can be constructed in O(n log f + (nf) 11/(#d/2#+1) log O(1) n) time; this is optimal if f = O(n 1/#d/2# / log K n) for some sufficiently large constant K . We also show that the h extreme points of P can be computed in O(n log O(1) h + (nh) 11/(#d/2#+1) log O(1) n) time. These results are then applied to produce an algorithm that computes the vertices of all the convex layers of P in O(n 2# ) time for any constant #<2/(#d/2# 2 + 1). Finally, we obtain improved time bounds for other problems including levels in arrangements and linear programming with few violated constraints. In all of our algorithms the input is assumed to be in general position. 1. Introduction Let P be a set of n points in ddimen...
Voronoi Diagram and Convex Hull Based Geocasting and Routing in Wireless Networks
, 1999
"... A broad variety of location dependent services will become feasible in the near future due to the use of the Global Position System (GPS), which provides location information (latitude, longitude and possibly height) and global timing to mobile users. Routing is a problem of sending a message from a ..."
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Cited by 61 (11 self)
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A broad variety of location dependent services will become feasible in the near future due to the use of the Global Position System (GPS), which provides location information (latitude, longitude and possibly height) and global timing to mobile users. Routing is a problem of sending a message from a source to a destination. Geocasting is the problem of sending a message to all nodes located within a region (e.g. circle or square). Recently, several localized GPS based routing and geocasting protocols for a mobile ad hoc network were reported in literature. In directional (DIR) routing and geocasting methods, node A (the source or intermediate node) transmits a message m to all neighbors located between the two tangents from A to the region that could contain the destination. It was shown that memoryless directional methods may create loops in routing process. In two other proposed methods (proven to be loopfree), geographic distance (GEDIR) or most forward progress within radius (MFR)...
CInDeR: Collision and Interference Detection in Realtime using Graphics Hardware
, 2003
"... Collision detection is a vital task in almost all forms of computer animation and physical simulation. It is also one of the most computationally expensive, and therefore a frequent impediment to efficient implementation of realtime graphics applications. We describe how graphics hardware can be us ..."
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Cited by 54 (0 self)
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Collision detection is a vital task in almost all forms of computer animation and physical simulation. It is also one of the most computationally expensive, and therefore a frequent impediment to efficient implementation of realtime graphics applications. We describe how graphics hardware can be used as a geometric coprocessor to carry out the bulk of the computation involved with collision detection. Hardware frame buffer operations are used to implement a raycasting algorithm which detects static interference between solid polyhedral objects. The algorithm is linear in both the number of objects and number of polygons in the models. It also requires no preprocessing or special data structures.
Voronoi Diagrams in Higher Dimensions under Certain Polyhedral Distance Functions
, 1995
"... The paper bounds the combinatorial complexity of the Voronoi diagram of a set of points under certain polyhedral distance functions. Specifically, if S is a set of n points in general position in R^d, the maximum complexity of its Voronoi diagram under the L1 metric, and also under a simplicial dist ..."
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Cited by 54 (24 self)
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The paper bounds the combinatorial complexity of the Voronoi diagram of a set of points under certain polyhedral distance functions. Specifically, if S is a set of n points in general position in R^d, the maximum complexity of its Voronoi diagram under the L1 metric, and also under a simplicial distance function, are both shown to be \Theta(n dd=2e ). The upper bound for the case of the L1 metric follows from a new upper bound, also proved in this paper, on the maximum complexity of the union of n axisparallel hypercubes in R^d. This complexity is \Theta(n dd=2e ), for d 1, and it improves to \Theta(n bd=2c ), for d 2, if all the hypercubes have the same size. Under the L 1 metric, the maximum complexity of the Voronoi diagram of a set of n points in general position in R³ is shown to be \Theta(n 2 ). We also show that the general position assumption is essential, and give examples where the complexity of the diagram increases significantly when the points are in d...
A High Accuracy Volume Renderer for Unstructured Data
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... This paper describes a volume rendering system for unstructured data, especially finite element data, that creates images with very high accuracy. The system will currently handle meshes whose cells are either linear or quadratic tetrahedra. Compromises or approximations are not introduced for the s ..."
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Cited by 53 (6 self)
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This paper describes a volume rendering system for unstructured data, especially finite element data, that creates images with very high accuracy. The system will currently handle meshes whose cells are either linear or quadratic tetrahedra. Compromises or approximations are not introduced for the sake of efficiency. Whenever possible, exact mathematical solutions for the radiance integrals involved and for interpolation are used. The system will also handle meshes with mixed cell types: tetrahedra, bricks, prisms, wedges, and pyramids, but not with high accuracy. Accurate semitransparent shaded isosurfaces may be embedded in the volume rendering. For very small cells, subpixel accumulation by splatting is used to avoid sampling error. A revision to an existing accurate visibility ordering algorithm is described which includes a correction and a method for dramatically increasing its efficiency. Finally, hardware assisted projection and compositing are extended from tetrahedra to arbit...
The Crust and the BetaSkeleton: Combinatorial Curve Reconstruction
 Graphical Models and Image Processing
, 1998
"... We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraneous edges. The required sampling density varies with the Local Feature Size on the cur ..."
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Cited by 50 (0 self)
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We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraneous edges. The required sampling density varies with the Local Feature Size on the curve, so that areas of less detail can be sampled less densely. We give two different graphs that, in this sense, reconstruct smooth curves: a simple new construction which we call the crust, and the fiskeleton, using a specific value of fi. 1 Introduction There are many situations in which a set of sample points lying on or near a surface is used to reconstruct a polygonal approximation to the surface. In the plane, this problem becomes a sort of unlabeled version of connectthedots: we are given a set of points and asked to connect them into the most likely polygonal curve. We show that under fairly generous and welldefined sampling conditions either of two proximitybased graphs defined ...
Simplifying Polygonal Models Using Successive Mappings
, 1997
"... We present the use of mapping functions to automatically generate levels of detail with known error bounds for polygonal models. We develop a piecewise linear mapping function for each simplification operation and use this function to measure deviation of the new surface from both the previous leve ..."
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Cited by 48 (9 self)
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We present the use of mapping functions to automatically generate levels of detail with known error bounds for polygonal models. We develop a piecewise linear mapping function for each simplification operation and use this function to measure deviation of the new surface from both the previous level of detail and from the original surface. In addition, we use the mapping function to compute appropriate texture coordinates if the original map has texture coordinates at its vertices. Our overall algorithm uses edge collapse operations. We present rigorous procedures for the generation of local planar projections as well as for the selection of a new vertex position for the edge collapse operation. As compared to earlier methods, our algorithm is able to compute tight error bounds on surface deviation and produce an entire continuum of levels of detail with mappings between them. We demonstrate the effectiveness of our algorithm on several models: a Ford Bronco consisting of over 300 ...
Randomized PursuitEvasion in a Polygonal Environment
, 2004
"... This paper contains two main results: First, we revisit the wellknown visibility based pursuitevasion problem and show that, in contrast to deterministic strategies, a single pursuer can locate an unpredictable evader in any simplyconnected polygonal environment using a randomized strategy. The ..."
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Cited by 48 (7 self)
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This paper contains two main results: First, we revisit the wellknown visibility based pursuitevasion problem and show that, in contrast to deterministic strategies, a single pursuer can locate an unpredictable evader in any simplyconnected polygonal environment using a randomized strategy. The evader can be arbitrarily faster than the pursuer and it may know the position of the pursuer at all times but it does not have prior knowledge of the random decisions made by the pursuer. Second, using the randomized algorithm together with the solution to a problem called the "lion and man problem" [2] as subroutines, we present a strategy for two pursuers (one of which is at least as fast as the evader) to quickly capture an evader in a simplyconnected polygonal environment. We show how this strategy can be extended to obtain a strategy for (i) a polygonal room with a door, (ii) two pursuers who have only lineofsight communication, and (iii) a single pursuer (at the expense of increased capture time).