This paper presents a shape-blending algorithm that interpolates between 2D and 3D polyhedrons. Shape blending, which is sometimes called shape metamorphosis or geometric morphing, has applications in such areas as entertainment and medical visualization. Our algorithm directly interpolates vertices of polyhedral source shapes by using variationally optimized subdivision surfaces. To interpolat...

An af®ne-invariant (AI) deformable contour model for object matching, called AI-EigenSnake (AI-ES), is proposed in the Bayesian framework. In AI-ES, the prior distribution of object shapes is estimated from the sample data. This distribution is then used to constrain the prototype contour, which is dynamically adjustable in the matching process. In this way, large shape deformations due to the ...

The ubiquity of the Laplace-Beltrami operator in shape analysis can be seen by observing the wide variety of applications where it has been found to be useful. Here we demonstrate a small subset of such uses with their latest developments including a scale invariant transform for general triangulated meshes, an effective and efficient method for denoising meshes using Beltrami flows via high di...

This paper concerns the abstraction of sets of functions for use in abstract interpretation. The paper gives an overview of existing methods, which are illustrated with applications to shape analysis, and formalizes a new family of relational abstract domains that allows sets of functions to be abstracted more precisely than with known approaches, while being still machine-representable.

This paper introduces a novel shape representation which performs shape analysis in a hierarchical fashion using Gaussian and Laplacian pyramids. A background on hierarchical shape analysis is given along with a detailed explanation of the hierarchical method, and results are shown on natural contours. A comparison is performed between the new method and our proposed approach using Point Distri...

Taking up and extending earlier suggestions, we show how twoand three-dimensional shapes of secondorder HBT correlations can be described in a multivariate Edgeworth expansion around Gaussian ellipsoids, with expansion coefficients, identified as the cumulants of pair momentum difference q, acting as shape parameters. Off-diagonal terms dominate both the character and magnitude of shapes. Cumul...

In this technical report we derive the analytic form of the Hessian matrix for shape matching energy. Shape matching (Fig. 1) is a useful technique for meshless deformation, which can be easily combined with multiple techniques in real-time dynamics (refer to [MHTG05, BMM15] for more details). Nevertheless, it has been rarely applied in scenarios where implicit (such as backward differentiation...

We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. This work extends the theory introduced in a previous paper (Al-Malki et al. 1999) in which scattering polarization from a spherically symmetric envelope illuminated by an anisotropic point source was considered. Here we generalize to account for the more realistic expectation of a n...

This article proposes a rigorous and realistic solution of the Lambertian Shape From Shading (SFS) problem. The power of our approach is threefolds. First, our work is based on a rigorous mathematical method: we define a new notion of weak solutions (in the viscosity sense) which does not necessarily requires boundary data (contrary to the work of [28, 27, 26, 4, 11]) and which allows to define...

People readily perceive patterns of shading as 3‐D shapes. Owing to the generalised bas‐ relief ambiguity when extracting shape from shading, people must simultaneously estimate the shape of the surface and the nature of the light source. In many cases cues in the image will be insufficient to resolve all of the ambiguities present, and in such cases the human visual system may employ one of a ...