Fast as-isometric-as-possible shape interpolation

Zhang, Zhibang; Li, Guiqing; Lu, Hao; Ouyang, Yaobin; Yin, Minghao; Xian, Chuhua

doi:10.1016/j.cag.2014.09.005

Cited by 15 publications

(4 citation statements)

References 42 publications

(72 reference statements)

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“…Zhang et al . [ZLL*15] created an orthogonal frame for each edge of the mesh and defined connection maps between frames of an edge and the four edges of its adjacent triangles. Based on the notion, they proposed a fast as‐isometric‐as‐possible interpolation framework.…”

Section: Related Workmentioning

confidence: 99%

Articulated‐Motion‐Aware Sparse Localized Decomposition

Wang

Zeng

et al. 2016

Computer Graphics Forum

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Compactly representing time‐varying geometries is an important issue in dynamic geometry processing. This paper proposes a framework of sparse localized decomposition for given animated meshes by analyzing the variation of edge lengths and dihedral angles (LAs) of the meshes. It first computes the length and dihedral angle of each edge for poses and then evaluates the difference (residuals) between the LAs of an arbitrary pose and their counterparts in a reference one. Performing sparse localized decomposition on the residuals yields a set of components which can perfectly capture local motion of articulations. It supports intuitive articulation motion editing through manipulating the blending coefficients of these components. To robustly reconstruct poses from altered LAs, we devise a connection‐map‐based algorithm which consists of two steps of linear optimization. A variety of experiments show that our decomposition is truly localized with respect to rotational motions and outperforms state‐of‐the‐art approaches in precisely capturing local articulated motion.

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Section: Related Workmentioning

confidence: 99%

Articulated‐Motion‐Aware Sparse Localized Decomposition

Wang

Zeng

et al. 2016

Computer Graphics Forum

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“…Moreover, our use of the strain tensor in characterizing metric distortion is closely related to the applications in various physically based deformation scenarios including [Thomaszewski et al 2009;Müller et al 2014] among many others (see also the surveys on physically based elastic deformable models [Nealen et al 2006;Rumpf and Wardetzky 2014]). Our approach is also related to the works that aim to design as-isometricas-possible shape deformations [Zhang et al 2015;Solomon et al 2011;Martinez Esturo et al 2013]. Similarly to the latter work, our framework is general and allows an arbitrary prescribed distortion, although our method works directly on surface representations and moreover enables applications such as joint deformation design.…”

Section: Related Workmentioning

confidence: 91%

Functional Characterization of Deformation Fields

Corman

Ovsjanikov

2019

ACM Trans. Graph.

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In this paper we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows to represent a deformation field in a coordinate-free way as a linear operator acting on real-valued functions defined on the shape. Such a representation both provides a way to relate deformation fields to other classical functional operators and enables analysis and processing of deformation fields using standard linear-algebraic tools. This opens the door to a wide variety of applications such as explicitly adding extrinsic information into the computation of functional maps, intrinsic shape symmetrization, joint deformation design through precise control of metric distortion, and coordinate-free deformation transfer without requiring pointwise correspondences. Our method is applicable to both surface and volumetric shape representations and we guarantee the equivalence between the operator-based and standard deformation field representation under mild genericity conditions in the discrete setting. We demonstrate the utility of our approach by comparing it with existing techniques and show how our representation provides a powerful toolbox for a wide variety of challenging problems.

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“…Somewhat more closely related to ours are data-driven and feature-based interpolation methods. These include interpolation based on hand-crafted features [18,27] or by exploring various local shape spaces obtained by analyzing a shape collection [19,51,39]. These approaches work well if the input shapes are sufficiently similar, but require triangle meshes and dense point-wise correspondences, or a single template that is fitted to all input data to build a statistical model, e.g.…”

Section: Related Workmentioning

confidence: 99%

Intrinsic Point Cloud Interpolation via Dual Latent Space Navigation

Rakotosaona,

Ovsjanikov

2020

Preprint

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We present a learning-based method for interpolating and manipulating 3D shapes represented as point clouds, that is explicitly designed to preserve intrinsic shape properties. Our approach is based on constructing a dual encoding space that enables shape synthesis and, at the same time, provides links to the intrinsic shape information, which is typically not available on point cloud data. Our method works in a single pass and avoids expensive optimization, employed by existing techniques. Furthermore, the strong regularization provided by our dual latent space approach also helps to improve shape recovery in challenging settings from noisy point clouds across different datasets. Extensive experiments show that our method results in more realistic and smoother interpolations compared to baselines.

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Fast as-isometric-as-possible shape interpolation

Cited by 15 publications

References 42 publications

Articulated‐Motion‐Aware Sparse Localized Decomposition

Articulated‐Motion‐Aware Sparse Localized Decomposition

Functional Characterization of Deformation Fields

Intrinsic Point Cloud Interpolation via Dual Latent Space Navigation

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