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Dataset distillation provides an effective approach to reduce memory and computational costs by optimizing a compact dataset that achieves performance comparable to the full original. However, for large-scale datasets and complex deep…

For the case of approximation of convection--diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The…

Image denoising and image segmentation play essential roles in image processing. Partial differential equations (PDE)-based methods have proven to show reliable results when incorporated in both denoising and segmentation of images. In our…

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…

We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…

An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…

We explore the problem of computationally generating special `prime' images that produce optical illusions when physically arranged and viewed in a certain way. First, we propose a formal definition for this problem. Next, we introduce…

The class-conditional image generation based on diffusion models is renowned for generating high-quality and diverse images. However, most prior efforts focus on generating images for general categories, e.g., 1000 classes in ImageNet-1k. A…

Denoising Diffusion Probabilistic models have become increasingly popular due to their ability to offer probabilistic modeling and generate diverse outputs. This versatility inspired their adaptation for image segmentation, where multiple…

One of the major open problems in computer vision is detection of features in visually impaired images. In this paper, we describe a potential solution using Phase Stretch Transform, a new computational approach for image analysis, edge…

Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of…

Our goal is to develop fine-grained real-image editing methods suitable for real-world applications. In this paper, we first summarize four requirements for these methods and propose a novel diffusion-based image editing framework with…

This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretization and continuous piecewise linear functions in the spatial…

Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements…

We introduce segmentation-free guidance, a novel method designed for text-to-image diffusion models like Stable Diffusion. Our method does not require retraining of the diffusion model. At no additional compute cost, it uses the diffusion…

The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…

In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion…

In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…

Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image…

Deep learning-based image generation has seen significant advancements with diffusion models, notably improving the quality of generated images. Despite these developments, generating images with unseen characteristics beneficial for…