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As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation…
In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other…
Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models.…
For image inpainting, the existing Denoising Diffusion Probabilistic Model (DDPM) based method i.e. RePaint can produce high-quality images for any inpainting form. It utilizes a pre-trained DDPM as a prior and generates inpainting results…
Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the acquisition of labeled training data is very time-consuming,…
This paper presents a comprehensive derivation and implementation of the Chan-Vese active contour model for image segmentation. The model, derived from the Mumford-Shah variational framework, evolves contours based on regional intensity…
We propose a new method for the numerical solution of a PDE-driven model for colour image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data…
We propose a novel method for multi-phase segmentation of images based on high-dimensional local feature vectors. While the method was developed for the segmentation of extremely noisy crystal images based on localized Fourier transforms,…
In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…
Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…
Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models…
Second-order PDE models have been widely used for suppressing multiplicative noise, but they often introduce blocky artifacts in the early stages of denoising. To resolve this, we propose a fourth-order nonlinear PDE model that integrates…
We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a…
This work focuses on a parameter-free joint piecewise smooth image denoising and contour detection. Formulated as the minimization of a discrete Mumford-Shah functional and estimated via a theoretically grounded alternating minimization…
The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this paper, we explore a linkage between these…
How to effectively remove the noise while preserving the image structure features is a challenging issue in the field of image denoising. In recent years, fractional PDE based methods have attracted more and more research efforts due to the…
I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two…
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…
The main objective of image segmentation is to divide an image into homogeneous regions for further analysis. This is a significant and crucial task in many applications such as medical imaging. Deep learning (DL) methods have been proposed…
The space of images can be equipped with a Riemannian metric measuring both the cost of transport of image intensities and the variation of image intensities along motion lines. The resulting metamorphosis model was introduced and analyzed…