Geometric modeling in shape space

By Martin Kilian, Niloy J. Mitra, Helmut Pottmann. ACM Transactions on Graphics, 2007

344 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

One Point Isometric Matching with the Heat Kernel (2010, positive): “High quality correspondences are also essential in morphing, and shape interpolation [KMP07].”
Style-content separation by anisotropic part scales (2010, background): “2005] or other creatures [Praun et al. 2001; Kilian et al. 2007].”
Learning Smooth Neural Functions via Lipschitz Regularization (2022, background): “Shape interpolation is a fundamental task and several classic meth-ods exist, such as [Solomon et al. 2015] and [Kilian et al. 2007].”
Map-based exploration of intrinsic shape differences and variability (2013, methodology): “Third, linear methods such as PCA are most often used — a notable exception being [Kilian et al. 2007] — even when it is not clear that a flat approximation to the shape space, either locally or globally is indicated.”
Interactive 3D Modeling with a Generative Adversarial Network (2017, methodology): “For example, [Kilian et al. 2007], [Allen et al. 2003], and others describe methods for interpolation between surfaces with consistent parameterizations.”
Optimization Methods on Riemannian Manifolds and Their Application to Shape Space (2012, background): “introduced a Riemannian shape space in [13], in which shapes are represented by meshes with fixed connectivity.”