Abstract-Blue noise point sampling is one of the core algorithms in computer graphics. In this paper we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including non-photorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces.

No abstract

Implicit functions have a wide range of applications in entertainment, engineering and medical imaging. A standard two-phase implicit function only represents the interior and exterior of a single object. To facilitate solid modeling of heterogeneous objects with multiple internal regions, object-space multiphase implicit functions are much desired. Multiphase implicit functions have much potential in modeling natural organisms, heterogeneous mechanical parts and anatomical atlases. In this paper, we introduce a novel class of object-space multiphase implicit functions that are capable of accurately and compactly representing objects with multiple internal regions. Our proposed multiphase implicit functions facilitate true object-space geometric modeling of heterogeneous objects with non-manifold features. We present multiple methods to create object-space multiphase implicit functions from existing data, including meshes and segmented medical images. Our algorithms are inspired by machine learning algorithms for training multicategory max-margin classifiers. Comparisons demonstrate that our method achieves an error rate one order of magnitude smaller than alternative techniques.