3D shape models are often put together from several partial reconstructions. There are good algorithms available now to perform the necessary, precise registration automatically, but only after the partial reconstructions have been brought into approximate positions. This paper proposes a technique to do precisely that. Automatic `crude registration' is illustrated for Euclidean and a ne transf...

In this paper we introduce a new scale invariant curvature measure, similarity curvature. We define a similarity curvature space which consists of the set of all possible similarity curvature values. An estimator for the similarity curvature of digital surface points is developed. Experiments and results applying similarity curvature to synthetic data are also presented.

Aim. To develop a new invariant descriptor for the characterization of protein surfaces, suitable for various analysis tasks, such as protein functional classification, and search and retrieval of protein surfaces over a large database. Methods. We start with a local descriptor of selected circular patches on the protein surface. The descriptor records the distance distribution between the cent...

We study a useful numerical invariant of normal surface singularities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic Gorenstein or rational (without assuming a priori that they are Q -Gorenstein). In §2 we prove effective results (stated in terms of Kawachi’s invariant) reg...

Various applications of global surface parametrization benefit from the alignment of parametrization isolines with principal curvature directions. This is particularly true for recent parametrization-based meshing approaches, where this directly translates into a shape-aware edge flow, better approximation quality, and reduced meshing artifacts. Existing methods to influence a parametrization b...

In this work, a geometric invariant curve and surface normalization method is presented. Translation, scale and shear are normalized by Principal Component Analysis (PCA) whitening. Independent Component Analysis (ICA) and the third order moments are then employed for rotation and reflection normalization. By applying this normalization, curves and surfaces that are related by geometric transfo...

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...

We develop the theory of maximal representations of the fundamental group π1(Σ) of a compact connected oriented surface Σ with boundary ∂Σ, into the isometry group of a Hermitian symmetric space X or, more generally, a group of Hermitian type G. For any homomorphism ρ : π1(Σ) → G, we define the Toledo invariant T(Σ, ρ), a numerical invariant which is in general not a characteristic number, but ...