In this paper, we present a novel constrained texture mapping method based on the harmonic map. We first project the surface of a 3D model on a planar domain by an angle-based-flattening technique and perform a parametrization. The user then specifies interactively the constraints between the selected feature points on the parametric domain of the 3D model and the corresponding pixels on the te...

In this paper we propose a novel approach for the mapping of 3D surfaces. With the Reeb graph of Laplace-Beltrami eigenmaps, our method automatically detects stable landmark features intrinsic to the surface geometry and use them as boundary conditions to compute harmonic maps to the unit sphere. The resulting maps are diffeomorphic, robust to natural pose variations, and establish corresponden...

Conformal (Same form or shape) mapping is an important technique used in complex analysis and has many applications in different physical situations.If the function is harmonic (ie it satisfies Laplace’s equation∇f = 0 )then the transformation of such functions via conformal mapping is also harmonic. So equations pertaining to any field that can be represented by a potential function (all conse...

We review two versions of a new topology preserving mapping, the HaToM. This mapping has previously been investigated as a data visualization tool but, in this paper, we investigate empirically the quantization errors in both versions of the mapping. We show that the more model driven version does not minimise the quantization error either when it is calculated in the usual manner or when we us...

We review two versions of a topology preserving algorithm one of which we had previously [1] found to be more successful in defining smooth manifolds and tight clusters. In the context of outlier detection, however, the other is shown to be more successful. Nevertheless, we show that, by using local kernels for calculation of responsibilities, the first one can also be used in this manner.