A new class of anisotropic diffusion models is proposed for image processing which can be viewed either as a novel kind of regularization of the classical Perona--Malik model or, as advocated by the authors, as a new independent model. The models are diffusive in nature and are characterized by the presence of both forward and backward regimes. In contrast to the Perona--Malik model, in the proposed model the backward regime is confined to a bounded region, and gradients are only allowed to grow up to a large but tunable size, thus effectively preventing indiscriminate singularity formation, i.e., staircasing. Extensive numerical experiments demonstrate that the method is a viable denoising/deblurring tool. The method is significantly faster than competing state-of-the-art methods and appears to be particularly effective for simultaneous denoising and deblurring. An application to satellite image enhancement is also presented.

In this paper, we present Confetti, a novel point-based rendering approach based on object-space point interpolation of densely sampled surfaces. We introduce the concept of a transformation-invariant covariance matrix of a set of points which can efficiently be used to determine splat sizes in a multiresolution point hierarchy. We also analyze continuous point interpolation in object-space and we define a new class of parameterized blending kernels as well as a normalization procedure to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on texture mapping and alpha-blending as well as programmable vertex and pixel-shaders.

We present a novel point-based rendering approach based on object-space point interpolation. We introduce the concept of a transformation-invariant covariance matrix of a set of points to efficiently determine splat sizes in a multiresolution hierarchy. We analyze continuous point interpolation in object-space, and define a new class of parametrized blending kernels to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on α-texture mapping and α-blending.