Generating genus‐<i>n</i>‐to‐<i>m</i> mesh morphing using spherical parameterization

Lee, Tong‐Yee; Yao, Chih‐Yuan; Chu, Hung‐Kuo; Tai, Ming-Jen; Chen, Cheng‐Chieh

doi:10.1002/cav.146

Cited by 18 publications

(13 citation statements)

References 26 publications

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“…In recent years Reeb graphs have been used as a search key in shape databases [18], as well as to characterize complex scientific data [6]. They provide a surface based method for genus reduction [28,23,35] that does not require conversion of input models as in volumetric approaches [36,34,27]. The notion of persistence was introduced in [10] and is used to rank the importance of topological features [17,2].…”

Section: Related Workmentioning

confidence: 99%

“…Meshes of arbitrary genus can be mapped to the plane [15,3] or to a topologically equivalent base domain [20,21,30]. Recent work [23] maps meshes of arbitrary genus γ to a series of γ + 1 spherical domains. One of these domains represents a positive surface while the remaining γ are negative surfaces.…”

Section: Related Workmentioning

confidence: 99%

“…The methods of [5] and [23] allow for maps between meshes of different genus. [5] requires the user to manually specify control meshes with the same number of faces for both the source and target.…”

Section: Related Workmentioning

confidence: 99%

“…[5] requires the user to manually specify control meshes with the same number of faces for both the source and target. The recent work of [23] parameterizes meshes of genus γ via a single "positive" spherical parameterization and γ "negative" spherical parameterizations. The approach works well in many cases, however suffers from several key issues.…”

Section: Related Workmentioning

confidence: 99%

“…If a face is both a valid parent and child we split the face as in 6 (c). Although the size of the mesh near Jacobi loops increases, we avoid the reduction of detail that can occur in previous methods [23].…”

Section: Robust Cross Parameterizationmentioning

confidence: 99%

See 4 more Smart Citations

Genus Oblivious Cross Parameterization: Robust Topological Management of Inter-Surface Maps

House

Singh²

2007

15th Pacific Conference on Computer Graphics and Applications (PG'07)

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We consider the problem of generating a map between two triangulated meshes, M and M ', with arbitrary and possibly differing genus. This problem has rarely been tackled in its generality. Early schemes considered only topological spheres. Recent algorithms allow inputs with an arbitrary number of tunnels but require M and M ' to have equal genus, mapping tunnel to tunnel. Other schemes which allow more general inputs are not guaranteed to work and the authors do not provide a characterization of the input meshes that can be processed successfully. Moreover, the techniques have difficulty dealing with coarse meshes with many tunnels.In this paper we present the first robust approach to build a map between two meshes of arbitrary unequal genus. We also provide a simplified method for setting the initial alignment between M and M ', reducing reliance on landmarks and allowing the user to select "landmark tunnels" in addition to the standard landmark vertices. After computing the map, we automatically derive a continuous deformation from M to M ' using a variational implicit approach to describe the evolution of non-landmark tunnels.Overall, we achieve a cross parameterization scheme that is provably robust in the sense that it can map M to M ' without constraints on their relative genus or on the density of the triangulation with respect to the number of tunnels. To demonstrate the practical effectiveness of our scheme we provide a number of examples of inter-surface parameterizations between meshes of different genus and shape.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Robust Cross Parameterizationmentioning

confidence: 99%

See 3 more Smart Citations

Genus Oblivious Cross Parameterization: Robust Topological Management of Inter-Surface Maps

House

Singh²

2007

15th Pacific Conference on Computer Graphics and Applications (PG'07)

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Compatible quadrangulation by sketching

Yao¹,

Chu²,

Ju³

et al. 2009

Computer Animation & Virtual

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Mesh quadrangulation has received increasing attention in the past decade. While previous works have mostly focused on producing a high quality quad mesh of a single model, the connectivity of the quadrangulation is typically difficult to control and varies among models even with similar shapes. In this paper, we propose a novel interactive framework for quadrangulating a set of models collectively with compatible connectivity. Furthermore, we demonstrate its application to 3D mesh morphing. In our approach, the user interactively sketches a skeleton within each model, and our method automatically computes compatible base domains for all models from these skeletons, on which the models are parameterized. With this novel parameterization, it is very easy to generate a pleasing and smooth 3D morphing sequence among these compatible models. The method yields quadrangulation with comparable quality to existing approaches, but greatly simplifies compatible re-meshing among a group of topologically equivalent models, in particular characters and animals models, with direct applications in shape blending and morphing.

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A graph‐based shape matching scheme for 3D articulated objects

Chao

Lin

Chang

et al. 2011

Computer Animation & Virtual

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In this paper, a novel graph-based shape matching scheme for three-dimensional articulated objects is introduced. The underlying graph structure of a given 3D model is composed of its topological skeleton and local geometric features. Matching two graph structures is generally an NP-hard combinatorial optimization problem. To reduce computation cost, two graphs are embedded on a high-dimensional space, and then matched based on an extension of Earth Mover's Distance (EMD). Furthermore, the symmetric components of an articulated object are determined by a voting algorithm with a selfmatching strategy to refine the matching correspondences. Experimental results show that the proposed approach is robust, even when the models are under the surface disturbances of noise addition, smoothing, simplification, similarity transformation, and pose deformation. In addition, the proposed approach is capable of handling both global and partial shape matching.

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Generating genus‐n‐to‐m mesh morphing using spherical parameterization

Cited by 18 publications

References 26 publications

Genus Oblivious Cross Parameterization: Robust Topological Management of Inter-Surface Maps

Genus Oblivious Cross Parameterization: Robust Topological Management of Inter-Surface Maps

Compatible quadrangulation by sketching

A graph‐based shape matching scheme for 3D articulated objects

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