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We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
Text-based image segmentation aims to delineate object boundaries within an image from text prompts, offering higher flexibility and broader application scope compared to traditional fixed-category segmentation tasks. Recent studies have…
This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…
We present Diff3F as a simple, robust, and class-agnostic feature descriptor that can be computed for untextured input shapes (meshes or point clouds). Our method distills diffusion features from image foundational models onto input shapes.…
To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence…
The video composition task aims to integrate specified foregrounds and backgrounds from different videos into a harmonious composite. Current approaches, predominantly trained on videos with adjusted foreground color and lighting, struggle…
In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…
Image sequences filtering have recently become a very important technical problem especially with the advent of new technology in multimedia and video systems applications. Often image sequences are corrupted by some amount of noise…
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…
Image segmentation is a long-standing challenge in computer vision, studied continuously over several decades, as evidenced by seminal algorithms such as N-Cut, FCN, and MaskFormer. With the advent of foundation models (FMs), contemporary…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…
Recent studies have demonstrated that the forward diffusion process is crucial for the effectiveness of diffusion models in terms of generative quality and sampling efficiency. We propose incorporating an analytical image attenuation…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
THis work is a survey of a few nonlinear PDE based models in image restoring.
Diffusion-based super-resolution (SR) models have recently garnered significant attention due to their potent restoration capabilities. But conventional diffusion models perform noise sampling from a single distribution, constraining their…
Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…