13 results for Klette, Reinhard, Report, 2007

Shortest Path Algorithms for Sequences of Polygons
Li, Fajie; Klette, Reinhard (2007)
Report
The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original MI_tech website http://www.mi.auckland.ac.nz/index.php?option=com_content&view=article&id=91&Itemid=76 . All other rights are reserved by the author(s). In both English and Chinese Given a sequence k simple polygons in a plane, and a start point p, a target point q. We approximately compute a shortest path that starts at p, then visits each of the polygons in the specified order, and finally ends at q. So far no solution was known if the polygons are disjoint and nonconvex. By applying a rubberband algorithm, we give an approximative algorithm with time complexity in κ(ε) · σ(n),where n is the total number of vertices of the given polygons, and function κ(ε) is as κ(ε)=(LoL)=/ε where Lo is the length of the initial path, and L is the true (i.e., optimum) path length. The given rubberband algorithm can also be applied to solve approximately three NPcomplete or NPhard 3D Euclidean shortest path (ESP) problems in time κ(ε)·σ(k), where k is the number of layers in a stack which contains the defined obstacles.
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An Approximate Algorithm for Solving the Watchman Route Problem
Li, Fajie; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original MI_tech website http://www.mi.auckland.ac.nz/index.php?option=com_content&view=article&id=91&Itemid=76 . All other rights are reserved by the author(s). The watchman route problem (WRP) was first introduced in 1988 and is defined as follows: How to calculate a shortest route completely contained inside a simple polygon such that any point inside this polygon is visible from at least one point on the route? So far the best known result for the WRP is an σ(n3logn) runtime algorithm (with inherent numerical problems of its implementation). This paper gives an κ(ε)·σ(kn) approximate algorithm for WRP by using a rubberband algorithm, where n is the number of vertices of the simple polygon, k a number of essential cuts and ε the chosen accuracy constant.
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Border and Surface Tracing  Theoretical Foundations
Brimkov, Valentin; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). In this paper we define and study digital manifolds of arbitrary dimension, and provide (in particular) a general theoretical basis for curve or surface tracing in picture analysis. The studies involve properties such as onedimensionality of digital curves and (n1)dimensionality of digital hypersurfaces that makes them discrete analogs of corresponding notions in continuous topology. The presented approach is fully based on the concept of adjacency relation and complements the concept of dimension as common in combinatorial topology. This work appears to be the first one on digital manifolds based on a graph theoretical definition of dimension. In particular, in the ndimensional digital space, a digital curve is a onedimensional object and a digital hypersurface is an (n1)dimensional object, as it is in the case of curves and hypersurfaces in the Euclidean space. Relying on the obtained properties of digital hypersurfaces, we propose a uniform approach for studying good pairs defined by separations and obtain a classification of good pairs in arbitrary dimension. We also discuss possible applications of the presented definitions and results.
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Understanding Human Motion: A Historic Review
Klette, Reinhard; Tee, Garry (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Understanding human motion is based on analyzing global motion patterns, rather than on studying local patterns such as hand gestures or facial expressions. This report reviews briefly (by selection, not by attempting to cover developments, and with a focus on Western History) people and contributions in science, art, and technology which contributed to the field of human motion understanding. This review basically stops at the time when advanced computing technology became available for performing motion studies based on recorded image data or extensive (modelbased) calculations or simulations.
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Segmentation of Scanned Insect Footprints Using ART2 for Threshold Selection
Shin, BokSuk; Cha, EuiYoung; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). In a process of insect footprint recognition, footprint segments need to be extracted from scanned insect footprints in order to find out appropriate features for classification. In this paper, we use a clustering method in a preprocessing stage for extraction of insect footprint segments. In general, sizes and strides of footprints may be different according to type and size of an insect for recognition. Therefore we propose a method for insect footprint segment extraction using an improved ART2 algorithm regardless of size and stride of footprint pattern. In the improved ART2 algorithm, an initial threshold value for clustering is determined automatically using the contour shape of the graph created by accumulating distances between all the spots within a binarized footprint pattern image. In the experimental results, applying the proposed method to two kinds of insect footprint patterns, we illustrate that clustering is accomplished correctly.
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Approximate ESPs on Surfaces of Polytopes Using a Rubberband Algorithm
Li, Fajie; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Let p and q be two points on the surface of a polytope P . This report provides a rubberband algorithm for computing a Euclidean shortest path between p and q (surface ESP) that is contained on the surface of P . The algorithm has k1(e) · k2(e) · O(n^2) time complexity, where n is the number of vertices of P , ki(e) = (L0i  Li )/e, for the true length Li of some shortest path with initial (polygonal path) length L0i (used when approximating this shortest path), for i = 1, 2. Rubberband algorithms follow a straightforward design strategy, and the proposed algorithm is easy to implement and thus of importance for applications, e.g. when analyzing 3D ob jects in 3D image analysis (such as in biomedical or industrial image analysis, using 3D image scanners).
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On Depth Recovery from Gradient Vector Fields
Wei, Tiangong; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Depth recovery from gradient vector fields is required when reconstructing a surface (in threedimensional space) from its gradients. Such a reconstruction task results, for example, for techniques in computer vision aiming at calculating surface normals (such as shape from shading, photometric stereo, shape from texture, shape from contours and so on). Surprisingly, discrete integration has not been studied very intensively so far. This chapter presents three classes of methods for solving problems of depth recovery from gradient vector fields: a twoscan method, a Fouriertransform based method, and a wavelettransform based method. These methods extend previously known techniques, and related proofs are given in a short but concise form. The twoscan method consists of two different scans through a given gradient vector field. The final surface height values can be determined by averaging these two scans. Fouriertransform based methods are noniterative so that boundary conditions are not needed, and their robustness to noisy gradient estimates can be improved by choosing associated weighting parameters. The wavelettransform based method overcomes the disadvantage of the Fouriertransform based method, which implicitly require that a surface height function is periodic. Experimental results using synthetic and real images are also presented.
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Euclidean Shortest Paths in Simple Polygons
Li, Fajie; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Let p and q be two points in a simple polygon P. This chapter provides two rubberband algorithms for computing a shortest path between p and q that is contained in P. The two algorithms are based on previously known results on triangular or trapezoidal decompositions of simple polygons, and have either kappa(epsilon) times O(n) or kappa(epsilon) times O(n log n) time complexity, where kappa(epsilon) = (L0  L)/epsilon, for the true length L of the shortest path and length L0 of a used initial polygonal path. Rubberband algorithms follow a straightforward design strategy, and the proposed algorithms ar easy to implement (after having the decompositions at hand).
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Touring Polygons, Parts Cutting, and qRectangles
Li, Fajie; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Given a sequence of k simple polygons in a plane, a start point p, and a target point q. We approximately compute a shortest path that starts at p, then visits each of the polygons in the specified order, and finally ends at q. So far no solution was known if the polygons are pairwise disjoint and nonconvex. By applying a rubberband algorithm, we give an approximative algorithm with time complexity in kappa(epsilon) times O(n), where n is the total number of vertices of the given polygons, and function kappa(epsilon) is as follows: kappa(epsilon) = (L_0  L)/epsilon, where L_0 is the length of the initial path, and L is the true (i.e., optimum) path length. The given rubberband algorithm can also be applied to solve approximately three NPcomplete or NPhard 3D Euclidean shortest path (ESP) problems in time kappa(epsilon) times O(k), where k is the number of layers in a stack which contains the defined obstacles.
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Decomposing a Simple Polygon into Trapezoids
Li, Fajie; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). Chazelle's triangulation \cite{BC1991} forms today the common basis for lineartime Euclidean shortest path (ESP) calculations (where start and end point are given within a simple polygon). This paper provides an alternative method for subdividing a simple polygon into ``basic shapes'', using trapezoids instead of triangles. The authors consider the presented method as being substantially simpler than the lineartime triangulation method. However, it requires a sorting step (of a subset of vertices of the given simple polygon); all the other subprocesses are linear time.
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Euclidean Shortest Paths in Simple Cube Curves at a Glance
Li, Fajie; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cubecurve with arbitrary accuracy, defined by epsilon >0, and in time complexity kappa(epsilon) O(n), where kappa(epsilon) is the length difference between the path used for initialization and the minimumlength path, divided by epsilon. A runtime diagram also illustrates this lineartime behavior of the implemented ESP algorithm.
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Zooming Optical Flow Computation
Ohnishi, Naoya; Imiya, Atsushi; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original CITR web site; http://citr.auckland.ac.nz/techreports/ under terms that include this permission. All other rights are reserved by the author(s). This paper introduces a new algorithm for computing multiresolution optical flow, and compares this new hierarchical method with the traditional combination of the LucasKanade method with a pyramid transform. The paper shows that the new method promises convergent optical flow computation. Aiming at accurate and stable computation of optical flow, the new method propagates results of computations from low resolution images to those of higher resolution. The resolution of images increases this way for the sequence of images used in those calculations. The given input sequence of images defines the maximum of possible resolution.
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BeliefPropagation on Edge Images for Stereo Analysis of Image Sequences
Guan, Shushi; Klette, Reinhard (2007)
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The University of Auckland LibraryYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (fortyfive) days from the most recent time that you verified that this technical report is still available from the original MI_tech website http://www.mi.auckland.ac.nz/index.php?option=com_content&view=article&id=91&Itemid=76 . All other rights are reserved by the author(s). The history of stereo analysis of images dates back more than one hundred years, but stereo analysis of image sequences is a fairly recent subject. Sequences allow timepropagation of results, but also come with particular characteristics such as being of lower resolution, or with less contrast. This article discusses the application of belief propagation (BP), which is widely used for solving various lowlevel vision problems, for the stereo analysis of nightvision stereo sequences. For this application it appears that BP often fails on the original frames for objects with blurry borders (trees, clouds, . . . ). In this paper, we show that BP leads to more accurate stereo correspondence results if it is applied on edge images, where we have decided for the Sobel edge operator, due to its time efficiency. We present the applied algorithm and illustrate results (without, or with prior edge processing) on seven, geometrically rectified nightvision stereo sequences (provided by Daimler AG, Germany).
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