194 results for Klette, Reinhard

  • Surface Area Estimation for Digitized Regular Solids

    Kenmochi, Yukiko; 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). 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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  • Cell Complexes through Time

    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). 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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  • The Length of Digital Curves

    Klette, Reinhard; Yip, Ben (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). The paper discusses one of the elementary subjects in image analysis: how to measure the length of a digital curve? A digital curve in the plane is defined to be a cycle given either as an alternating sequence of vertices and edges, or an alternating sequence of edges and squares. The paper reports about two length estimators, ones based on the partition of a frontier of a simply-connected isothetic polygon into digital straight segments, and one based on calculating the minimum-length polygon within an open boundary of a simply-connected isothetic polygon. Both techniques are known to be implementations of convergent estimators of the perimeter of bounded, polygonal or smooth convex sets in the euclidean plane. For each technique a linear-time algorithm is specified, and both algorithms are compared with respect to convergence speed and number of generated segments. The experiments show convergent behavior also for perimeters of non-convex bounded subsets of the euclidean plane.

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  • Evaluation of Curve Length Measurements

    Klette, Reinhard; Yip, Ben (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). This paper compares two techniques for measuring the length of a digital curve. Both techniques (digital straight segment approximation, minimum length polygon) are known to be convergent estimators. Theoretical convergence result are cited. The main focus is on experimental evaluation: several measures are defined, applied and discussed. Test sets are digitized for consecutive resolutions.

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

    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). 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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  • Reconstruction of Multiresolution Terrain Surfaces

    Zhou, Shao-zheng; Klette, Reinhard (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). Multiresolution surfaces are especially useful for fast rendering, real-time display and interactive manipulation of large and dense terrain surface models. This paper reviews major multiresolution terrain surface reconstruction techniques and analyses the corresponding data structures. We have proposed and implemented, based on Delaunay retriangulation, a greedy refinement algorithm with a straightforward data structure to reconstruct multiresolution terrain surfaces. Our greedy refinement algorithm is a multi-pass algorithm, having the complexity of O(n 2 ) if using global error metric and O(n log n) if using local error metric.

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  • Gravity Centers of Smooth Planar Convex Regions from Digital Pictures

    Klette, Reinhard; Zunic, Jovisa (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). Representations of real objects by corresponding digital pictures cause an inherent loss of information. There are infinitely many different real shapes with an identical corresponding digital picture. The problem we are interested in is how effciently the gravity center (or centroid) of a planar convex region whose boundary has a continuos third derivative and positive curvature (at every point) can be reconstructed from its digital picture. We derive an absolute upper error bound if such a smooth planar convex region is represented in a binary picture with resolution r, where r is the number of pixels per unit. This result can be extended to regions which may be obtained from smooth planar convex regions by finite applications of unions, intersections or set differences. The upper error bound remains the same which converges to zero with increase in grid resolution.

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  • Segmentation of Scanned Insect Footprints Using ART2 for Threshold Selection

    Shin, Bok-Suk; Cha, Eui-Young; Klette, Reinhard (2007)

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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 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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  • Structure from Motion in the Presence of Noise

    Liu, Gang; Klette, Reinhard (2005)

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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). Structure from Motion (SfM) is one of the most attractive approaches within computer vision which aims on estimating 3D structure from 2D image sequences. This paper focuses on a stability analysis and studies the error propagation of image noise. To stabilize SfM, we further present two optimization schemes by using a priori knowledge of the scene.

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  • Surface Visualisation and 3D Feature Analysis in Confocal Microscopy Images

    Fong, Fu; Klette, Reinhard; Hon, Man (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). Chondrons form the fundamental biomechanical and metabolic unit of articular cartilage. But there is no accurate description of chondron volume which is known to change when articular cartilage is functionally loaded. This report discusses the 3D feature analysis of the confocal microscopy images of chondrons. The basic principle of confocal microscopy is described. The segmentation problem of confocal images is also discussed. Two different reconstruction algorithms, Marching Cubes and Dividing Cubes are also illustrated and their respectively ways of calculating volume and surface area are also discussed. The results of calculating 3D features of sperical polysterene beads using Marching Cubes algorithms are also given

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  • Footprint Recognition of Rodents and Insects

    Hasler, Nils; Klette, Reinhard; Agnew, Warren (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). In today s pest control operations large numbers of tracking tunnels are used to estimate the number of rodents present in the target area, providing a basis for planning the required amount of poison. The marks left in the tunnels have to be interpreted by trained experts. This article introduces two methods that make a step towards automating the process of recognizing footprints of rodents and insects. Furthermore two classification methods (Principal Component Analysis, a simple Na¨?ve Bayes classifier) are studied to distinguish the four examined insect species. Here, a combination of both classifiers proved superior to using just one method.

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  • Evaluation of an Adaptive Composite Gaussian Model in Video Surveillance

    Zang, Qi; Klette, Reinhard (2002)

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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 surveillance systems seek to automatically identify events of interest in a variety of situations. Extracting a moving object from background is the most important step of the whole system. There are many approaches to track moving objects in a video surveillance system. These can be classified into three main groups: feature-based tracking, background subtraction, and optical flow techniques. Background subtraction is a region-based approach where the objective is to identify parts of the image plane that are significantly different to the background. In order to avoid the most common problems introduced by gradual illumination changes, waving trees, shadows, etc., the background scene requires a composite model. A mixture of Gaussian distributions is most popular. In this paper, we classify and discuss several recently proposed composite models. We have chosen one of these for implementation and evaluate its performance. We also analyzed its benefits and drawbacks, and designed an improved version of this model based on our experimental evaluation. One stationary camera has been used.

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

    Kawamoto, Kazuhiko; Yamada, Daisuke; Klette, Reinhard (2002)

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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 '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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  • Zooming Optical Flow Computation

    Ohnishi, Naoya; Imiya, Atsushi; Klette, Reinhard (2007)

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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 introduces a new algorithm for computing multi-resolution optical flow, and compares this new hierarchical method with the traditional combination of the Lucas-Kanade 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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  • Understanding Human Motion: A Historic Review

    Klette, Reinhard; Tee, Garry (2007)

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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). 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 Scale Invariant Surface Curvature Estimator

    Rugis, John; 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). In this paper we introduce a new scale invariant curvature measure, similarity curvature. We define a similarity curvature space which consists of the set of all possible similarity curvature values. An estimator for the similarity curvature of digital surface points is developed. Experiments and results applying similarity curvature to synthetic data are also presented.

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  • Surface Registration Markers from Range Scan Data

    Rugis, John; 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). We introduce a data processing pipeline designed to generate registration markers from range scan data. This approach uses curvature maps and template histograms to identify local surface features. The noise associated with real-world scans is addressed using a (common) Gauss filter and expansion segmentation. Experimental results are presented for data from The Digital Michelangelo Project.

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  • Analysis of the Rubberband Algorithm

    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). 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)

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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. 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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  • Two Approximative Algorithms for Calculating Minimum-Length Polygons in 3D Space

    Li, Fajie; Klette, Reinhard (2005)

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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. 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 no provable general algorithm is known for the approximative calculation of such an MLP. This paper presents two approximative algorithms for computing the MLP of a general simple cube-curve in $O(n^4)$ time, where $n$ is the total number of critical edges of the given simple cube-curve.

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