On Linear Variational Surface Deformation Methods

By Mario Botsch, Olga Sorkine-Hornung. IEEE Transactions on Visualization and Computer Graphics, 2008

315 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/f9e0b34e65a741f97dad3b3a0e1cd28e398bf4ec

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Style-content separation by anisotropic part scales (2010, background): “Last but not least, meaningful deformation of man-made shapes, e.g., for editing [Gal et al. 2009; Xu et al. 2009], is challenging since such deformation cannot be free-form [Botsch and Sorkine 2008] and a strong emphasis on shape semantics is necessary.”
Multi-View Stereo: A Tutorial (2015, unknown): “There are little variations in the definition of regularization terms, where “Mesh Laplacian” and “Mesh Bi-Laplacian” are often used to define the regularization force [42] (See Figure 3.”
Realtime facial animation with on-the-fly correctives (2013, methodology): “tion [Botsch and Sorkine 2008] v(2)i = v(1)i + Dv(1)i using both depth and 2D facial feature constraints.”
Motion capture using joint skeleton tracking and surface estimation (2009, methodology): “Here, L is the cotangent Laplacian matrix and δ are the differential coordinates of our current mesh with vertices V [6].”
Multilinear pose and body shape estimation of dressed subjects from image sets (2010, methodology): “We refine the initial 3D mesh by Laplace deformation [4, 21] so that the 3D correspondences of the markers are located on the projection rays of their 2D image positions.”
Drag Your GAN: Interactive Point-based Manipulation on the Generative Image Manifold (2023, background): “Conventionalapproaches[Botsch and Sorkine 2007] typically convert images into meshes, and then deform the mesh subject to geometric constraints such as rigidity [Igarashi et al. 2005; Sorkine and Alexa 2007] and Laplacian smoothness [Lipman et al. 2004, 2005; Sorkine et al. 2004].”
Robust single-view geometry and motion reconstruction (2009, methodology): “For the same frame, an elastically deformed template T̃ j with vertices ṽji is created by warping Tinit to the current frame j using the linearized thin-plate energy as described in [Botsch and Sorkine 2008].”
Unrestricted Facial Geometry Reconstruction Using Image-to-Image Translation (2017, background): “where, wi,j is the weight corresponding to the biharmonic Laplacian operator (see [21, 5]), ~n(ci) is the”
Free-Viewpoint Video of Human Actors Using Multiple Handheld Kinects (2013, methodology): “Specifically, for each human actor k, we use a Laplacian deformation framework [53] to move the mesh vertices v′ in Z pv towards the corresponding point p′ in Z pv .”