133 results for Klette, Reinhard, Report

  • Surface Area Estimation for Digitized Regular Solids

    Kenmochi, Yukiko; 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). Regularly gridded data in Euclidean 3-space are assumed to be digitizations of regular solids with respect to a chosen grid resolution. Gauss and Jordan introduced different digitization schemes, and the Gauss center point scheme is used in this paper. The surface area of regular solids can be expressed finitely in terms of standard functions for specific sets only, but it is well defined by triangulations for any regular solid. We consider surface approximations of regularly gridded data characterized to be polyhedrizations of boundaries of these data. The surface area of such a polyhedron is well defined, and it is parameterized by the chosen grid resolution. A surface area measurement technique is multigrid convergent for a class of regular solids iff it holds that for any set in this class the surface areas of approximating polyhedra of the digitized regular solid converge towards the surface area of the regular solid if the grid resolution goes to infinity. Multigrid convergent volume measurements have been studied in mathematics for more than one hundred years, and surface area measurements had been discussed for smooth surfaces. The problem of multigrid convergent surface area measurement came with the advent of computer-based image analysis. The paper proposes a classification scheme of local and global polyhedrization approaches which allows us to classify different surface area measurement techniques with respect to the underlying polyhedrization scheme. It is shown that a local polyhedrization technique such as marching cubes is not multigrid convergent towards the true value even for elementary convex regular solids such as cubes, spheres or cylinders. The paper summarizes work on global polyhedrization techniques with experimental results pointing towards correct multigrid convergence. The class of general ellipsoids is suggested to be a test set for such multigrid convergence studies.

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  • Digital Straightness

    Rosenfeld, Azriel; 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). A digital arc is called `straight' if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970's, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.

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  • Minimum-Length Polygon of a Simple Cube-Curve in 3D Space

    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 a"rubber-band algorithm" is known to compute such a curve approximately. We provide an alternative iterative algorithm for the approximative calculation of the MLP for curves contained in a special class of simple cube-curves (for which we prove the correctness of our alternative algorithm), and the obtained results coincide with those calculated by the rubber-band algorithm.

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  • On Digitization Effects on Reconstruction of Geometric Properties of regions

    Klette, Reinhard; Zunic, Jovisa (1999)

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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). Representations of real regions by corresponding digital pictures cause an inherent loss of information. there are infinitely many different real regions with and identical corresponding digital picture. So, there are limitations in the reconstruction of the originals and their properties from digital pictures. The problem which will be studied here is what is the impact of a digitization process on the efficiency in the reconstruction of the basic geometric properties

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  • Shape from Shading and Photometric Stereo Methods

    Klette, Reinhard; Kozera, Ryszard (1998)

    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 TR is a review of shading based shape recovery (i.e. shape from shading, and photometric stereo methods). It reports about advances in applied work and about results in theoretical fundamentals.

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  • Navigation Using Optical Flow Fields: An Application of Dominant Plane Detection

    Kawamoto, Kazuhiko; Yamada, Daisuke; Klette, Reinhard (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). Video sequences capturing real scenes may be interpreted with respect to a dominant plane which is a planar surface covering 'a majority' of pixels in an image of a video sequence, i.e. that planar surface which is represented in the image by a maximum number of pixels. In this paper, we propose an algorithm for the detection of dominant planes from optical flow fields caused by camera motion in a static scene. We, in particular, intend to adopt this algorithm as a module for obstacle detection in vision-based navigation of autonomous robots.

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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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  • Shortest Paths in a Cuboidal World

    Li, Fajie; Klette, Reinhard (2006)

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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). Since 1987 it is known that the Euclidean shortest path problem is NP-hard. However, if the 3D world is subdivided into cubes, all of the same size, defining obstacles or possible spaces to move in, then the Euclidean shortest path problem has a linear-time solution, if all spaces to move in form a simple cube-curve. The shortest path through a simple cube-curve in the orthogonal 3D grid is a minimum-length polygonal curve (MLP for short). So far only one general and linear (only with respect to measured run times) algorithm, called the {\it rubberband algorithm}, was known for an approximative calculation of an MLP. The algorithm is basically defined by moves of vertices along critical edges (i.e., edges in three cubes of the given cube-curve). A proof, that this algorithm always converges to the correct MLP, and if so, then always (provable) in linear time, was still an open problem so far (the authors had successfully treated only a very special case of simple cube-curves before). In a previous paper, the authors also showed that the original rubberband algorithm required a (minor) correction. This paper finally answers the open problem: by a further modification of the corrected rubberband algorithm, it turns into a provable linear-time algorithm for calculating the MLP of any simple cube-curve. The paper also presents an alternative provable linear-time algorithm for the same task, which is based on moving vertices within faces of cubes. For a disticntion, we call the modified original algorithm now the {\it edge-based rubberband algorithm}, and the second algorithm is the {\it face-based rubberband algorithm}; the time complexity of both is in ${\cal O}(m)$, where $m$ is the number of critical edges of the given simple cube-curve.

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  • 3D Reconstruction Using Shape from Photometric Stereo and Contours

    Chen, Chia-Yen; 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). In this work, we further discuss an approach to 3D shape recovery by combining photometric stereo and shape from contours methods. Surfaces recovered by photometric stereo are aligned, adjusted and merged according to a preliminary 3D model obtained by shape from contours. Comparisons are conducted to evaluate the performances of different methods. It has been found that the proposed combination provides more accurate shape recovery than using either photometric stereo or shape from contours alone.

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  • A Silhouette Based Human Motion Tracking System

    Rosenhahn, Bodo; Kersting, Uwe; Andrew, Smith; Brox, Thomas; Klette, Reinhard; Seidel, Hans-Peter (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). This paper proposes a system for model based human motion estimation. We start with a human model generation system, which uses a set of input images to automatically generate a free-form surface model of a human upper torso. We subsequently determine joint locations automatically and generate a texture for the surface mesh. Following this, we present morphing and joint transformation techniques to gain more realistic human upper torso models. An advanced model such as this is used in a system for silhouette based human motion estimation. The presented motion estimation system contains silhouette extraction based on level set functions, a correspondence module, which relates image data to model data and a pose estimation module. This system is used for a variety of experiments: Different camera setups (between one to four cameras) are used for the experiments and we estimate the pose configurations of a human upper torso model with 21 degrees of freedom at two frames per second. We also discuss degenerated cases for silhouette based human motion estimation. Next, a comparison of the motion estimation system with a commercial marker based tracking system is performed to gain a quantitative error analysis. The results show the applicability of the system for marker-less human movement analysis. Finally we present experimental results on tracking leg models and show the robustness of our algorithms even for corrupted image data.

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  • Analysis of Finite Difference Algorithms for Linear Shape from Shading

    Wei, Tiangong; Klette, Reinhard (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). 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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  • Wide-Angle Image Acquisition, Analysis and Visualisation

    Klette, Reinhard; Gimel'farb, Georgy (2001)

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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). Recent camera technology provides new solutions for wide-angle image acquisition. Multi- or single-line cameras have been designed for spaceborne and airborne scanners to provide high resolution imagery. Line cameras may also work as panorama scanners, and models of these have already been studied in computer vision for a few years. These cameras or models require studies in calibration, registration and epipolar geometry to ensure accurate imaging and stereo analysis. The resulting images or depth maps also allow new approaches in 3D scene visualisation. The paper informs about line camera models and camera hardware, the historic background in photogrammetry and aerial mapping, calibration of line cameras, registration of captured images, epipolar geometry for along-track and panoramic stereo, stereo matching with a focus on dynamic programming, and visualisation. The paper illustrates sketched concepts using a few of the high-resolution aerial and panoramic image data.

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  • Length Estimation for Curves with Different Samplings

    Noakes, Lyle; Kozera, Ryszard; Klette, Reinhard (2001)

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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). This paper looks at the problem of approximating the length of the unknown parametric curve ⋎ [0,1] → IRⁿ from points qᵢ = ⋎ (tᵢ), where the parameters ti are not given. When the tᵢ are uniformly distributed Lagrange interpolation by piecewise polynomials provides efficient length estimates, but in other cases this method can behave very badly [15]. In the present paper we apply this simple algorithm when the tᵢ are sampled in what we call an ε-uniform fashion, where 0 ≤ ε ≤ 1. Convergence of length estimates using Lagrange interpolants is not as rapid as for uniform sampling, but better than for some of the examples of [15]. As a side-issue we also consider the task of approximating ⋎ up to parameterization, and numerical experiments are carried out to investigate sharpness of our theoretical results. The results may be of interest in computer vision, computer graphics, approximation and complexity theory, digital and computational geometry, and digital image analysis.

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  • Digital Curves in 3D Sapce and a Linear-Time Length Estimation Algorithm

    Bülow, Thomas; Klette, Reinhard (1999)

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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). We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional euclidian space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far no algorithm was known for the calculation of such a shortest polygonal curve. This paper provides an iterative algorithmic solution, including a presentation of its foundations and of experimental results.

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  • Height data from gradient fields

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

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    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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  • Multigrid Convergence of Surface Approximations

    Klette, Reinhard; Wu, Feng (1998)

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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). This report deals with multigrid approximations of surfaces. Surface area and volume approximations are discussed for regular grids (3D objects), and surface reconstruction for irregular grids (terrain surfaces). Convergence analysis and approximation error calculations are emphasized.

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  • Topologies on the Planar Orthogonal Grid

    Klette, Reinhard (2001)

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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). This paper discusses different topologies on the planar orthogonal grid and shows homeomorphy between cellular models. It also points out that graph-theoretical topologies exist defined by planar extensions of the 4-adjacency graph. All these topologies are potential models for image carriers.

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  • Dominant Plane Estimation

    Kawamoto, Kazuhiko; Klette, Reinhard (2001)

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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). Video sequences capturing real scenes may be interpreted with respect to a dominant plane which is a planar surface covering more than 50% of a frame, or being that planar surface which is represented in the image with the largest number of pixels. This note shows a possible way for estimating the surface normal of this plane if just camera rotation is allowed.

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  • Albedo Recovery Using a Photometric Stereo Method

    Chen, Chia-Yen; Klette, Reinhard (2001)

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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). This paper describes a method for the calculation of surface reflectance values via photometric stereo. Experimental results show that surfaces rendered with reflectance values calculated by the proposed method have more realistic appearances than those with constant albedo.

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