Geometric modeling in shape space

Kilian, Martin; Mitra, Niloy J.; Pottmann, Helmut

doi:10.1145/1275808.1276457

Cited by 153 publications

(176 citation statements)

References 31 publications

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“…Shape space modeling by Kilian et al [8] accounts for 3D shapes as points of a high-dimensional Riemannian shape space equipped with an isometric inner-product. Interpolation of two 3D shapes is then converted to find a geodesic path in the shape space.…”

Section: Related Workmentioning

confidence: 99%

“…Our method is closely related to [8,22,3]. While our method is inspired by [8], a faster performance is achieved by reformulating discrete energy terms with rotation matrices for explicit orthogonality and by decoupling the energy terms into two linear optimizations for each iteration via block-coordinates descent.…”

Section: Related Workmentioning

confidence: 99%

“…Different from the rigid motion, an isometric motion allows for non-rigid deformation that keeps the geodesic distance of any two points on the surface of a deforming object [7]. Kilian et al [8] cast the modeling of isometric motions to finding a shortest geodesic path in a high-dimensional shape space. However, their formulation is very time-consuming in optimizing the whole trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed initialization can easily be transplanted to other shape interpolation methods based on nonlinear optimization [8,10,2].…”

Section: Introductionmentioning

confidence: 99%

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Fast as-isometric-as-possible shape interpolation

Zhang

et al. 2015

Computers & Graphics

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The proposed initialization can easily be transplanted to other shape interpolation methods based on nonlinear optimization [8,10,2].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fast as-isometric-as-possible shape interpolation

Zhang

et al. 2015

Computers & Graphics

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“…In this regard, the work is more closely related to landmark based treatments of Kendall (1984), Bookstein (1989) and Kilian et al (2007) than parametric ones of Charpiat et al (2005), Michor and Mumford (2006), Mio et al (2007) and Younes (1998). The main disadvantage of the land-mark based approach is that it is highly dependent on the chosen landmarks and correspondence (Wang et al 2004).…”

Section: Shape Spacementioning

confidence: 99%

A Shape Representation with Elastic Quadratic Polynomials—Preservation of High Curvature Points under Noisy Conditions

Kubota

2008

Int J Comput Vis

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We present a new shape representation technique for a planar shape using overlapping quadratic splines. The technique refines the shape by iteratively updating each spline to reduce the cost associated with C 1 discontinuity. It consists of a series of affine commutative linear operators, producing a smooth bandpass frequency response. The primary purpose of the technique is to remove minute highcurvature points while preserving salient ones. We compare the performance of the technique against those that are based on either linear splines, cubic splines, or wavelets. We consider three criteria: sensitivity of detecting salient highcurvature points, Hausdorff distance between the representation and the original shape, and computation time. The results show that the proposed technique is highly effective in preserving salient high curvature points with a relatively small Hausdorff distance and a computational cost.

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A blendshape model that incorporates physical interaction

Wang

Fyffe

et al. 2012

Computer Animation & Virtual

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The linear blendshape technique has been intensively used for computer animation and games due to its simplicity and effectiveness. However it cannot describe rotational deformations and deformations due to self collision or scene interaction. In this paper, we present a new technique to address these two major limitations by introducing physical-based simulation to blendshapes.The proposed technique begins by constructing a mass-spring system for each blendshape target. Each system is initialized in its steady state by setting the rest length of each spring as the edge length of the corresponding target. To begin shape interpolation, we linearly interpolate the rest lengths of the springs according to a given interpolation factor α ∈ [0, 1]. The interpolated shape is then generated by computing the equilibrium of the mass-spring system with the interpolated rest lengths. Results from our technique show physically-plausible deformations even in the case of large rotations between blendshape targets. In addition, the new blendshape model is able to interact with other scene elements by introducing collision detection and handling to the mass-spring system.

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Geometric modeling in shape space

Cited by 153 publications

References 31 publications

Fast as-isometric-as-possible shape interpolation

Fast as-isometric-as-possible shape interpolation

A Shape Representation with Elastic Quadratic Polynomials—Preservation of High Curvature Points under Noisy Conditions

A blendshape model that incorporates physical interaction

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