A Three-dimensional Error-diffusion Algorithm for Importance Sampling with Blue-noise Property

We propose a novel discrete three-dimensional sampling algorithm based on the error-diffusion method, which can generate sampling points with blue-noise property. To obtain sampling points with a high quality bluenoise spectrum in 3D domain, we introduce an effective metric for the 3D blue-noise property based on 3D Fourier transform. Then, a cost function used for the search of optimal parameters, including optimal diffusion coefficients and threshold modulation strength values, is designed to guarantee the blue-noise property of sampling points. Experiments show that our algorithm is able to generate sampling points with uniform and random distribution, which possess 3D blue-noise property, and supports importance sampling in three dimensional domain. Comparing with similar work, our algorithm can achieve sampling point distribution that possesses better isotropic properties and has lower time cost in 3D discrete domain. Several applications including volume rendering and tetrahedral meshing are also explored.