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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  • Topologies on the Planar Orthogonal Grid

    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 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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  • A Comparative Evaluation of Length Estimators

    Coeurjolly, David; 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). The paper compares previously published length estimators having digitized curves as input. The evaluation uses multigrid convergence (theoretical results and measured speed of convergence) and further measures as criteria. The paper also suggests a new gradient-based method for length estimation.

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  • Experience with Optical Flow in Colour Video Image Sequences

    Barron, John; 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). The paper studies optical flow methods on colour frames captured by a digital video camera. The paper reviews related work,specifies some new colour optical flow constraints and reports on experimental evaluations for one image sequence.

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  • Albedo Recovery Using a Photometric Stereo Method

    Chen, Chia-Yen; 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 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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  • 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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  • Dominant Plane Estimation

    Kawamoto, Kazuhiko; 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). 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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  • Length Estimation for Curves with Different Samplings

    Noakes, Lyle; Kozera, Ryszard; 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 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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  • Decomposition Method for the Linear Schrödinger Equation

    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). The Schrödinger equation is solved by using the decomposition method. A rapidly convergent series solution is achieved. The accuracy of the results obtained indicates the superiority of the decomposition methods over the existing numerical methods that were applied to this equation.

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  • 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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  • Towards Experimental Studies of Digital Moment Convergence

    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). 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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  • Cell Complexes through Time

    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). The history of cell complexes is closely related to the birth and development of topology in general. Johann Benedict Listing (1802-1882) introduced the term "topology" into mathematics in a paper published in 1847, and he also defined cell complexes for the first time in a paper published in 1862. Carl Friedrich Gauss (1777-1855) is often cited as the one who initiated these ideas, but he did not publish either on topology or on cell complexes. The pioneering work of Leonhard Euler (1707-1783) on graphs is also often cited as the birth of topology, and Euler's work was cited by Listing in 1862 as a stimulus for his research on cell complexes. There are different branches in topology which have little in common: point set topology, algebraic topology, differential topology etc. Confusion may arise if just "topology" is specied, without clarifying the used concept. Topological subjects in mathematics are often related to continuous models, and therefore quite irrelevant to computer based solutions in image analysis. Compared to this, only a minority of topology publications in mathematics addresses discrete spaces which are appropriate for computer-based image analysis. In these cases, often the notion of a cell complex plays a crucial role. This paper briefly reports on a few of these publications, which might be helpful or at least of interest for recent studies in topological issues in image analysis. It is not a balanced review, due to a certain randomness in the selection process of cited work. This paper is also not intended to cover the very lively progress in cell complex studies within the context of image analysis during the last two decades. Basically it stops its historic review at the time when this subject in image analysis research gained speed in 1980-1990. As a general point of view, the paper indicates that image analysis contributes to a fusion of two topological concepts, the geometric or abstract cell complex approach and point set topology, which leads to an in-depth study of topologies defined on geometric or abstract cell complexes.

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  • On Errors in Calculated Moments of Convex Sets Using Digital Images

    Klette, Reinhard; Zunic, Jovisa (1999)

    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). Moments have been widely used in shape recognition and identification. In general, the (k,l)-moment, denoted by mk,l(S), of a planar measurable set S is defined by mk,l(S) = sxkyl dx dy We assume situations in image analysis and pattern recognition where real objects are acquired (by thresholding, segmentation etc.) as binary images D(S), i.e. as digital sets or digital regions. For a set S, in this paper its digitization is defined to be the set of all grid points with integer coordinates which belong to the region occupied by the given set S. Since in image processing applications, the exact values of the moments mk,l(S) remain unknown, they are usually approximated by discrete moments µk,l(S) where µk,l(S) = S(i,j)D(S)ik.jl = Si,jareintegers(i,j)S ik.jl. Moments of order up to two (i.e. k + l 2) are frequently used and our attention is focused on them, i.e. on the limitation in their estimation from the corresponding digital picture. In this paper it is proved that mk,l(S)-1/rk+l+2.µµ,l(r.S)=O(1/r15/11+e) O (1/r1.363636...) for k + l = 2, where S is a convex set in the plane with a boundary having continuous third derivative and positive curvature at every point, r is the number of pixels per unit (i.e. 1/r is the size of the pixel), while r S denotes the dilation of S by factor r.

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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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  • Linear Time Calculation of 2D Shortest Polygonal Jordan Curves

    Yang, Nan; Klette, Reinhard (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). The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this report we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed one-dimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for finding the shortest polygonal Jordan curve is introduced, and its correctness and complexity is discussed.

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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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  • A Comparative Study on 2D Curvature Estimators

    Hermann, Simon; 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). Curvature is a frequently used property in two-dimensional (2D) shape analysis, directly or for derived features such as corners or convex and concave arcs. This paper presents curvature estimators which follow approaches in differential geometry. Digital-straight segment approximation (as known from digital geometry) is used in those estimators. Results of multigrid experiments are evaluated leading to a comparative performance analysis of several curvature estimators.

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

    Li, Fajie; Klette, Reinhard (2004)

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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 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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  • Improved Fusion of Photometric Stereo and Shape from Contours

    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 reports about a method for merging shape data, obtained via photometric stereo and shape from contours, into a 3D model.

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  • Angle Counts for Isothetic Polygons and Polyhedra

    Yip, Ben; 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). In the case of isothetic simple polyhedra there are only six different types of 3D angles. This article states and proofs a formula about counts of these angles. This complements formulas in combinatorial topology such as Euler's polyhedron formula, or the previously known formula on angle counts for isothetic polygons. The latter formula and the shown equality for angle counts of isothetic simple polyhedra are useful formulas for analyzing isothetic boundaries in 2D digital images (e.g. classification into inner (boundary of a hole) or outer boundaries, see [5]) and isothetic surfaces in 3D digital images (e.g. necessary condition for a complete surface scan).

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