Approximating polygonal curves in two and three dimensions

Eu, David; Toussaint, Godfried T.

doi:10.1117/12.142160

Cited by 7 publications

(15 citation statements)

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“…We call the solution fixed in the former case and free otherwise. From the form of the expressions in (7), (8) we deduce the following simple observation. If the joint is on the line x = x q+1 , we can regard it as a solution for the partition into S 1 (q + 1) = S 1 (q) ∪ {p q+1 } and S 2 (q + 1) = S 2 (q) \ {p q+1 }.…”

Section: Fitting a 1-joint Polylinementioning

confidence: 96%

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Polyline Fitting of Planar Points Under Min-sum Criteria

Aronov

Asano

Katoh

et al. 2004

Algorithms and Computation

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Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum criteria with respect to L 1 -and L 2 -metrics, which are more appropriate measures than uniform and Hausdorff metrics in statistical context. We present efficient algorithms for the 1-joint versions of the problem and fully polynomial-time approximation schemes for the general k-joint versions.

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Section: Fitting a 1-joint Polylinementioning

confidence: 96%

“…Indeed, we can classify the solution into two types: (a) An inequality in (7), (8) holds with equality. (b) All of the inequalities in (7), (8) are strict. We call the solution fixed in the former case and free otherwise.…”

Section: Fitting a 1-joint Polylinementioning

confidence: 99%

Polyline Fitting of Planar Points Under Min-sum Criteria

Aronov

Asano

Katoh

et al. 2004

Algorithms and Computation

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“…Several algorithms have been proposed for approximating polygonal chains [5,9,17,20,26,32]. Most optimal algorithms take Ω(n 2 ) time to find approximations in R 2 , but some algorithms are faster for certain error criteria.…”

Section: Algorithmmentioning

confidence: 99%

A Computational-Geometry Approach to Digital Image Contour Extraction

Jiang

Tejada

2011

Transactions on Computational Science XIII

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We present a method for extracting contours from digital images, using techniques from computational geometry. Our approach is different from traditional pixel-based methods in image processing. Instead of working directly with pixels, we extract a set of oriented feature points from the input digital images, then apply classical geometric techniques, such as clustering, linking, and simplification, to find contours among these points. Experiments on synthetic and natural images show that our method can effectively extract contours, even from images with considerable noise; moreover, the extracted contours have a very compact representation.(176 pages) iv Acknowledgments Many thanks to my advisor, Dr. Minghui Jiang, for his encouragement and support, and for getting me interested in the field of computational geometry. His concern for me as a student and his advice have been a great help. He introduced me to the practice of doing research, and his many comments have helped me become a better researcher.

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“…The process stops when no further edge elimination occurs. Similar to (Kégl and Krzyzak, 2002), a method presented by (Eu and Toussaint, 1994) was used to smooth the skeleton graph. This refinement step was performed with the objective to simplify the skeleton graph by reducing redundant vertices that do not contribute to its main shape features.…”

Section: Skeletonization Of Componentsmentioning

confidence: 99%

Automatic reconstruction of skeletal structures from TLS forest scenes

Schilling

Maas

2014

ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Detailed information about 3D forest structure is vital in forest science for analyzing the spatio-temporal development of plants as well as precise harvest forecasting in forest industry. Up to now, the majority of methods focus on complete structural reconstruction of trees from multiple scans, which might not be a suitable starting point with respect to modeling forest scenes over larger areas. For this reason, we propose a strategy to obtain skeletal structures of trees from single scans following a divide-and-conquer approach well-known from computer science. First, we split the range image into components representing surface patches and trace each component's boundary, which is essential for our skeleton retrieval method. Therefore, we propose an extension to standard boundary tracing that takes a component's interior depth discontinuities into account. Second, each component is processed separately: A 2D skeleton is obtained via the Voronoi Diagram and refined. Subsequently, a component is segmented into subsets of points depending on their proximity to skeleton nodes. Afterwards, the skeleton is split into paths and a Principal Curve is computed from each path's point cluster in order to retrieve the component shape as a set of 3D polygonal lines. Our method retrieves the intricate branching structure of components representing tree crown parts reliably and efficiently. The results are fitting with respect to a visual inspection. At present, results are fragments of tree skeletons, but it opens an attractive perspective to complete tree skeletons from skeletal parts, which we currently regard as future work.

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Approximating polygonal curves in two and three dimensions

Cited by 7 publications

References 0 publications

Polyline Fitting of Planar Points Under Min-sum Criteria

Polyline Fitting of Planar Points Under Min-sum Criteria

A Computational-Geometry Approach to Digital Image Contour Extraction

Automatic reconstruction of skeletal structures from TLS forest scenes

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