• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.1
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• pp.149-159
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• 2008

In this paper, we propose a blind watermarking algorithm of 3d mesh model using spherical parameterization. Spherical parameterization is a useful method which is applicable to 3D data processing. Especially, orthogonal coordinate can not analyse the feature of the vertex coordination of the 3D mesh model, but this is possible to analyse and process. In this paper, the centroid center of the 3D model was set to the origin of the spherical coordinate, the orthogonal coordinate system was transformed to the spherical coordinate system, and then the spherical parameterization was applied. The watermark was embedded via addition/modification of the vertex after the feature analysis of the geometrical information and topological information. This algorithm is robust against to the typical geometrical attacks such as translation, scaling and rotation. It is also robust to the mesh reordering, file format change, mesh simplification, and smoothing. In this case, the this algorithm can extract the watermark information about $90{\sim}98%$ from the attacked model. This means it can be applicable to the game, virtual reality and rapid prototyping fields.

• Journal of Information Processing Systems
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• v.10 no.1
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.