Adaptive image sampling through establishing 3D geometrical model

Adaptive sampling for high dimensional manifold attracts much attention from related fields. The principal curvature based strategy is one of the popular methods. However, principal curvature estimation remains an open problem. Considering the relationship between geodesics and the principal curvatures of manifold, we transform the optimized sampling density computation into the problem of uniform sampling in the geodesic metric of manifold. Therefore, two well studied uniform sampling methods such as Poisson disk and farthest point strategy are used. For image sampling, a 3D geometrical metric model is built based on mean shift. Mean shift value is applied to describe the image grey information and taken as the height of this model. Uniform sampling is implemented to generate samples with blue noise properties on the 3D model surface. Then, adaptive results are obtained when these samples are projected back to the original 2D image. In contrast to previous methods, this strategy is flexible and can be easily extended to unorganized points simplification or mesh coarsening. Extensive experiments demonstrated the effectiveness of the proposed method.