133 results for Klette, Reinhard, Report

  • Height data from gradient fields

    Klette, Reinhard; Schluns, Karsten (1996-08)

    Report
    The University of Auckland Library

    The paper starts with a review of integration techniques for calculating height maps from dense gradient fields. There exist a few proposals of local integration methods (Coleman/Jain 1982, Healey/Jain 1984, Wu/Li 1988, Rodehorst 1993), and two proposals for global optimization (Horn/Brooks 1986 and Frankot/ Chellappa 1988). Several experimental evaluations of such integration techniques are discussed in this paper. The examined algorithms received high markings on curved objects but low markings on polyhedral shapes. Locally adaptive approaches are suggested to cope with complex shapes in general.

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  • Evaluation of Algorithms for Linear Shape from Shading

    Kozera, Ryszard; Klette, Reinhard (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). We analyse different sequential algorithms for the recovery of object shape from a single shading pattern generated under the assumption of a linear reflectance map. The algorithms are based on the finite difference approximation of the derivatives. They operate on a rectangular discrete image (or part of it) and use the height of the sought-after surface along a curve in the image (image boundary) as initial data. The evaluation of different numerical schemes is achieved by comparing stability, convergence, and domains of influence of each scheme in question. The relative difficulty of handling a linear case indicates that the case of non-linear reflectance maps is far from being trivial.

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  • Euclidean Shortest Paths in Simple Polygons

    Li, Fajie; Klette, Reinhard (2007)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 q-Rectangles

    Li, Fajie; Klette, Reinhard (2007)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 non-convex. 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 NP-complete or NP-hard 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)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 linear-time 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 linear-time 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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  • Analysis of the Rubberband Algorithm

    Li, Fajie; Klette, Reinhard (2006)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). We consider simple cube-curves in the orthogonal 3D grid of cells. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve's length is defined to be that of the minimum-length polygonal curve (MLP) contained and complete in the tube of the curve. Only one general algorithm, called rubberband algorithm, was known for the approximative calculation of such an MLP so far. An open problem in KLE_ROS_2004 is related to the design of algorithms for the calculation of the MLP of a simple cube-curve: Is there a simple cube-curve such that none of the nodes of its MLP is a grid vertex? This paper constructs an example of such a simple cube-curve, and we also characterize the class of all of such cube-curves. This study leads to a correction in Option 3 of the rubberband algorithm (by adding one missing test). We also prove that the rubber-band algorithm has linear time complexity ${\cal O}(m)$ where $m$ is the number of critical edges of a given simple cube curve, which solves another open problem in the context of this algorithm.

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  • Minimum-Length Polygons of First-Class Simple Cube-Curves

    Li, Fajie; Klette, Reinhard (2005)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). We consider simple cube-curves in the orthogonal 3D grid. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve's length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far only one general algorithm called rubber-band algorithm was known for the approximative calculation of such an MLP. A proof that this algorithm always converges to the correct curve, is still an open problem. This paper proves that the rubber-band algorithm is correct for the family of first-class simple cube-curves.

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  • Understanding Human Motion: A Historic Review

    Klette, Reinhard; Tee, Garry (2007)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 (model--based) calculations or simulations.

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  • A Comparison of Property Estimators in Stereology and Digital Geometry

    Huang, Yuman; Klette, Reinhard (2004)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). We consider selected geometric properties of 2D or 3D sets, given in form of binary digital pictures, and discuss their estimation. The properties examined are perimeter and area in 2D, and surface area and volume in 3D. We evaluate common estimators in stereology and digital geometry according to their multiprobe or multigrid convergence properties, and precision and efficiency of estimations.

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  • A New Algorithm for Gradient Field Integration

    Wei, Tiangong; Klette, Reinhard (2001)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 proposes two improvements for reflectance based shape recovery. First, it is shown that albedo-independent photometric stereo allows albedo computation. This computation is based on photometric equations that relate surface normals to triplets of the image irradiances. Second, the paper also presents as the main result a new algorithm for depth recovery from surface normals. In order to improve the accuracy and robustness and to strengthen the relation between the depth map and surface normals, two new constraints are added into the associated cost function. They constrain the behavior of high-order change rate between the variables. Therefore, the changes of depth maps will be more regular. The Frankot-Chellappa-algorithm is a special case of our algorithm in the sense that it uses a subset of constraints only.

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  • Interactions between Number Theory and Image

    Klette, Reinhard; Zunic, Jovisa (2000)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). The conceptual design of many procedures used in image analysis starts with models which assume as an input sets in Euclidean space which we regard as real objects. However, the application finally requires that the Euclidean (real) objects have to be modelled by digital sets, i.e. they are approximated by their corresponding digitizations. Also "continuous" operations (for example integrations or differentiations) are replaced by "discrete" counterparts (for example summations or differences) by assuming that such an replacement has only a minor impact on the accuracy or efficiency of the implemented procedure. This paper discusses applications of results in number theory with respect to error estimations, accuracy evalua- tions, correctness proofs etc. for image analysis procedures. Knowledge about digitization errors or approximation errors may help to suggest ways how they can be kept under required limits. Until now have been only minor impacts of image analysis on developments in number theory, by defining new problems, or by specifying ways how existing results may be discussed in the context of image analysis. There might be a more fruitful exchange between both disciplines in the future.

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  • Approximate ESPs on Surfaces of Polytopes Using a Rubberband Algorithm

    Li, Fajie; Klette, Reinhard (2007)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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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  • Digital Visibility and Visualisation of Magnetic Resonance Imaging Series

    Yip, Ben; Klette, Reinhard (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 two new approaches to visualise the three-dimensional object that is depicted by a MR (Magnetic Resonance) imaging series. The exterior of the object is visualised with a surface rotation approach, which is based on the concept of digital visibility. The interior of the object is visualised with a cut and view approach, which is based on a special solution for resampling. After image data pre-processing, the surface rotation approach allows the user to rotate and visualise the object in any angle of view; while the cut and view approach let the user see the interior of the object by creating a planar cut onto the three dimensional object and then visualise the cross-section. These two approaches complement each other. Together, they provide a simple, fast processing method for the medical experts to visualise the MR imaging series. The time complexity and the quality of the outcome are satisfactory even it is processed with Intel 486 processor.

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  • Multiresolution Surface Reconstruction: Edge Collapsing + Simplification Envelopes

    Zhou, Shao-zheng; Klette, Reinhard (1997)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). Multiresolution surfaces are especially useful for fast rendering, real-time display, and progressive transmission. This paper reviews major surface simplification techniques and multiresolution surface reconstruction approaches. Based on comparison among various approximation algorithms we propose an appropriate measure for surface approximation accuracy and essential concepts for multiresolution surface reconstruction. Having analyzed the surface simplification process, we propose our solution for multiresolution surface reconstruction - combination of the edge collapsing operation and simplification envelopes, which can generate continuous multiresolution surfaces with globally-guaranteed approximation errors.

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  • The Class of Simple Cube-Curves Whose MLPs Cannot Have Vertices at Grid Points

    Li, Fajie; Klette, Reinhard (2004)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). We consider simple cube-curves in the orthogonal 3D grid of cells. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve's length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far only one general algorithm called rubber-band algorithm was known for the approximative calculation of such a MLP. There is an open problem which is related to the design of algorithms for calculation a 3D MLP of a cube-curve: Is there a simple cube-curve such that none of the vertices of its 3D MLP is a grid vertex? This paper constructs an example of such a simple cube-curve. We also characterize this class of cube-curves.

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  • Curves, Hypersurfaces, and Good Pairs of Adjacency Relations

    Brimkov, Valentin; Klette, Reinhard (2004)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 report we propose several equivalent definitions of digital curves and hypersurfaces in arbitrary dimension. The definitions involve properties such as one-dimensionality of curves and (n ? 1)-dimensionality of hypersurfaces that make them discrete analogs of corresponding notions in topology. Thus this work appears to be the first one on digital manifolds where the definitions involve the notion of dimension. In particular, a digital hypersurface in nD is an (n?1)-dimensional object, as it is in the case of continuous hypersurfaces. 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.

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  • Combinatorics on Incidence Pseudographs

    Klette, Reinhard (2003)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). Incidence pseudographs (or the dual model of complexes based on a bounded-by relation) are popular models for pixels or voxels and relations between these. They allow a definition of a topological space, and combinatorial formulas characterize open and closed sets in this topology. K. Voss characterized in 1993 open regions in incidence pseudographs. This article reviews these results and provides also combinatorial formulas for closed regions.

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  • Recovery of Coloured Surface Reflectances Using the Photometric Stereo Method

    Chen, Chia-Yen; Klette, Reinhard; Chen, Chi-Fa (2002)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). We discuss a fast and efficient method to estimate the surface reflectance values with respect to different wavelength of light. Qualitative and quantitative evaluations show that surfaces rendered using surface reflectances obtained by the proposed method are more realistic when compared with conventional rendering methods.

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  • Analysis of Finite Difference Algorithms for Linear Shape from Shading

    Wei, Tiangong; Klette, Reinhard (2000)

    Report
    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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 presents and analyzes four explicit, two implicit and four semi-implicit finite difference algorithms for the linear shape from shading problem. Comparisons of accuracy, solvability, stability and convergence of these schemes indicate that the weighted semi-implicit scheme and the box scheme are better than the other ones because they can be calculated more easily, they are more accurate, faster in convergence and unconditionally stable.

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  • Towards Experimental Studies of Digital Moment Convergence

    Klette, Reinhard; Zunic, Jovisa (2000)

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    The University of Auckland Library

    You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) 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). Digital moments approximate real moments where the accuracy depends upon grid resolution. There are theoretical results about the speed of convergence. However, there is a lack of more detailed studies with respect to selected shapes of regions, or with respect to experimental data about convergence. This paper discusses moments for specific shapes of regions, and provides some initial experimental data about measured convergence of digital moments.

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