Computing a compact spline representation of the medial axis transform of a 2D shape

Zhu, Yanshu; Sun, Feng; Choi, Yi-King; Jüttler, Bert; Wang, Wenping

doi:10.1016/j.gmod.2014.03.007

Cited by 20 publications

(8 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With a large number of nodes, a large amount computation would be caused to prevent practical use of curve skeletons in applications. To address this, we may adopt spline curves to approximate branches using very few control points, and so reduce computation, as suggested in [ZSC*14]. This is an important issue for our future work.…”

Section: Resultsmentioning

confidence: 99%

Contracting Medial Surfaces Isotropically for Fast Extraction of Centred Curve Skeletons

Wang

2017

Computer Graphics Forum

View full text Add to dashboard Cite

Curve skeletons, which are a compact representation for three‐dimensional shapes, must be extracted such that they are high quality, centred and smooth. However, the centredness measurements in existing methods are expensive, lowering the extraction efficiency. Although some methods trade quality for acceleration, their generated low‐quality skeletons are not suitable for applications. In this paper, we present a method to quickly extract centred curve skeletons. It operates by contracting the medial surface isotropically to the locus of the centres of its maximal inscribed spheres, which are spheres that have their centres on the medial surface and cannot be further enlarged while remaining the boundary of their intersections with the medial surface composed of only the points on the sphere surfaces. Thus, the centred curve skeleton can be extracted conveniently. For fast extraction, we develop novel measures to quickly generate the medial surface and contract it layer by layer, with every layer contracted isotropically using spheres of equal radii to account for every part of the medial surface boundary. The experimental results show that we can stably extract curve skeletons with higher centredness and at much higher speeds than existing methods, even for noisy shapes.

show abstract

Section: Resultsmentioning

confidence: 99%

Contracting Medial Surfaces Isotropically for Fast Extraction of Centred Curve Skeletons

Wang

2017

Computer Graphics Forum

View full text Add to dashboard Cite

show abstract

“…Yushkevich et al [ 17 ] first proposed to fit the MAT with cubic B-splines for statistical shape analysis. Zhu et al improved this by automatically computing a compact spline representation of the MAT of a 2D binary shape [ 18 ]. However, this approach handles only vector shape representations, i.e., only works with the Voronoi-based MAT method of [ 19 ].…”

Section: Related Workmentioning

confidence: 99%

Spline-Based Dense Medial Descriptors for Lossy Image Compression

2021

View full text Add to dashboard Cite

Medial descriptors are of significant interest for image simplification, representation, manipulation, and compression. On the other hand, B-splines are well-known tools for specifying smooth curves in computer graphics and geometric design. In this paper, we integrate the two by modeling medial descriptors with stable and accurate B-splines for image compression. Representing medial descriptors with B-splines can not only greatly improve compression but is also an effective vector representation of raster images. A comprehensive evaluation shows that our Spline-based Dense Medial Descriptors (SDMD) method achieves much higher compression ratios at similar or even better quality to the well-known JPEG technique. We illustrate our approach with applications in generating super-resolution images and salient feature preserving image compression.

show abstract

“…[FEC02] proved that all Voronoi vertices are also MA points (refer to Figure ). More recent techniques generate the MA by minimizing the quadric error [LWS*15] or one‐sided Hausdorff distance [ZSC*14] between the input shapes and the medial spheres. The research on MA computation from defect laden point clouds is still active, e.g.…”

Section: Related Workmentioning

confidence: 99%

Incremental Labelling of Voronoi Vertices for Shape Reconstruction

Peethambaran

Parakkat

Tagliasacchi

et al. 2018

Computer Graphics Forum

View full text Add to dashboard Cite

We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves. The proposed framework has been thoroughly evaluated for its usefulness using various test data. Results indicate that even sparsely and non‐uniformly sampled curves with outliers or collection of curves are faithfully reconstructed by the proposed algorithm.

show abstract

Computing a compact spline representation of the medial axis transform of a 2D shape

Cited by 20 publications

References 34 publications

Contracting Medial Surfaces Isotropically for Fast Extraction of Centred Curve Skeletons

Contracting Medial Surfaces Isotropically for Fast Extraction of Centred Curve Skeletons

Spline-Based Dense Medial Descriptors for Lossy Image Compression

Incremental Labelling of Voronoi Vertices for Shape Reconstruction

Contact Info

Product

Resources

About