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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…
Image segmentation is to separate an image into distinct homogeneous regions belonging to different objects. It is an essential step in image analysis and computer vision. This paper compares some segmentation technologies and attempts to…
The weighted MAX k-CUT problem involves partitioning a weighted undirected graph into k subsets, or colors, to maximize the sum of the weights of edges between vertices in different subsets. This problem has significant applications across…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…
The Cahn--Hilliard equations are a versatile model for describing the evolution of complex morphologies. In this paper we present a computational pipeline for the numerical solution of a ternary phase-field model for describing the…
In the paper the optimal image segmentation by means of piecewise constant approximations is considered. The optimality is defined by a minimum value of the total squared error or by equivalent value of standard deviation of the…
In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We…
We consider the problem of scale detection in images where a region of interest is present together with a measurement tool (e.g. a ruler). For the segmentation part, we focus on the graph based method by Flenner and Bertozzi which…
Medical image segmentation plays a crucial role in various clinical applications. A major challenge in medical image segmentation is achieving accurate delineation of regions of interest in the presence of noise, low contrast, or complex…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
A numerical method is formulated for the solution of the advective Cahn-Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation…
Image segmentation aims to partition an image according to the objects in the scene and is a fundamental step in analysing very high spatial-resolution (VHR) remote sensing imagery. Current methods struggle to effectively consider land…
Connected component analysis (CCA) has been heavily used to label binary images and classify segments. However, it has not been well-exploited to segment multi-valued natural images. This work proposes a novel multi-value segmentation…
We extend previous works on the multiplicity of solutions to the Allen-Cahn system on closed Riemannian manifolds by considering an arbitrary number of phases. Specifically, we show that on parallelizable manifolds, the number of solutions…
The goal of this paper is to present a new efficient image segmentation method based on evolutionary computation which is a model inspired from human behavior. Based on this model, a four layer process for image segmentation is proposed…
An automatic image segmentation procedure is an inevitable part of many image analyses and computer vision which deeply affect the rest of the system; therefore, a set of interactive segmentation evaluation methods can substantially…
This review presents various image segmentation methods using complex networks. Image segmentation is one of the important steps in image analysis as it helps analyze and understand complex images. At first, it has been tried to classify…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
Segmentation of a colour image composed of different kinds of texture regions can be a hard problem, namely to compute for an exact texture fields and a decision of the optimum number of segmentation areas in an image when it contains…