AN IMAGE SEGMENTATION VARIATIONAL MODEL WITH FREE DISCONTINUITIES AND CONTOUR CURVATURE

2004 ◽  
Vol 14 (01) ◽  
pp. 1-45 ◽  
Author(s):  
GIOVANNI BELLETTINI ◽  
RICCARDO MARCH
Keyword(s):  
Image Segmentation ◽  
Input Image ◽  
Piecewise Smooth ◽  
Variational Model ◽  
Smooth Approximation ◽  
Different Depths ◽  
Free Discontinuities ◽  
Γ Convergence ◽  
Contour Curvature

We introduce a functional for image segmentation which takes into account the transparencies (or shadowing) and the occlusions between objects located at different depths in space. By minimizing the functional, we try to reconstruct a piecewise smooth approximation of the input image, the contours due to transparencies, and the contours of the objects together with their hidden portions. The functional includes a Mumford–Shah type energy and a term involving the curvature of the contours. The variational properties of the functional are studied, as well as its approximation by Γ-convergence. The comparison with the Nitzberg–Mumford variational model for segmentation with depth is also discussed.

Variational Problems in Image Segmentation and I-Convergance Methods

2006 ◽  
pp. 46-71
Author(s):  
Giovanni Bellettini ◽  
Riccardo Riccardo
Keyword(s):  
Image Segmentation ◽  
Variational Method ◽  
Numerical Scheme ◽  
Variational Problems ◽  
Input Image ◽  
Convergence Theory ◽  
Mathematical Framework ◽  
Smooth Approximation ◽  
Variational Models ◽  
Geometric Term

Variational models for image segmentation aim to recover a piecewise smooth approximation of a given input image together with a discontinuity set which represents the boundaries of the segmentation. In particular, the variational method introduced by Mumford and Shah includes the length of the discontinuity boundaries in the energy. Because of the presence of such a geometric term, the minimization of the corresponding functional is a difficult numerical problem. We consider a mathematical framework for the Mumford-Shah functional and we discuss the computational issue. We suggest the use of the G-convergence theory to approximate the functional by elliptic functionals which are convenient for the purpose of numerical computation. We then discuss the design of an iterative numerical scheme for image segmentation based on the G-convergent approximation. The relation between the Mumford-Shah model and the

scholarly journals Reconstruction of Multi-Temporal Satellite Imagery by Coupling Variational Segmentation and Radiometric Analysis

2021 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Nicola Case ◽  
Alfonso Vitti
Keyword(s):  
Image Segmentation ◽  
Variational Model ◽  
Great Level ◽  
Radiometric Analysis ◽  
Variational Segmentation ◽  
Landsat 7 ◽  
Multi Temporal ◽  
Original Procedure ◽  
Variational Image ◽  
Homogeneous Regions

Digital images, and in particular satellite images acquired by different sensors, may present defects due to many causes. Since 2013, the Landsat 7 mission has been affected by a well-known issue related to the malfunctioning of the Scan Line Corrector producing very characteristic strips of missing data in the imagery bands. Within the vast and interdisciplinary image reconstruction application field, many works have been presented in the last few decades to tackle the specific Landsat 7 gap-filling problem. This work proposes another contribution in this field presenting an original procedure based on a variational image segmentation model coupled with radiometric analysis to reconstruct damaged images acquired in a multi-temporal scenario, typical in satellite remote sensing. The key idea is to exploit some specific features of the Mumford–Shah variational model for image segmentation in order to ease the detection of homogeneous regions which will then be used to form a set of coherent data necessary for the radiometric reconstruction of damaged regions. Two reconstruction approaches are presented and applied to SLC-off Landsat 7 data. One approach is based on the well-known histogram matching transformation, the other approach is based on eigendecomposition of the bands covariance matrix and on the sampling from Gaussian distributions. The performance of the procedure is assessed by application to artificially damaged images for self-validation testing. Both of the proposed reconstruction approaches had led to remarkable results. An application to very high resolution WorldView-3 data shows how the procedure based on variational segmentation allows an effective reconstruction of images presenting a great level of geometric complexity.

FRACTURE MECHANICS IN PERFORATED DOMAINS: A VARIATIONAL MODEL FOR BRITTLE POROUS MEDIA

2009 ◽  
Vol 19 (11) ◽  
pp. 2065-2100 ◽  
Author(s):  
MATTEO FOCARDI ◽  
M. S. GELLI ◽  
M. PONSIGLIONE
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fracture Mechanics ◽  
Special Functions ◽  
Variational Model ◽  
Perforated Domain ◽  
Functions Of Bounded Variation ◽  
Perforated Domains ◽  
Γ Convergence ◽  
Internal Scale

This paper deals with fracture mechanics in periodically perforated domains. Our aim is to provide a variational model for brittle porous media in the case of anti-planar elasticity. Given the perforated domain Ωε ⊂ ℝN (ε being an internal scale representing the size of the periodically distributed perforations), we will consider a total energy of the type [Formula: see text] Here u is in SBV(Ωε) (the space of special functions of bounded variation), Su is the set of discontinuities of u, which is identified with a macroscopic crack in the porous medium Ωε, and [Formula: see text] stands for the (N - 1)-Hausdorff measure of the crack Su. We study the asymptotic behavior of the functionals [Formula: see text] in terms of Γ-convergence as ε → 0. As a first (nontrivial) step we show that the domain of any limit functional is SBV(Ω) despite the degeneracies introduced by the perforations. Then we provide explicit formula for the bulk and surface energy densities of the Γ-limit, representing in our model the effective elastic and brittle properties of the porous medium, respectively.

scholarly journals Shannon Wavelet Precision Integration Method for Pathologic Onion Image Segmentation Based on Homotopy Perturbation Technology

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Haihua Wang ◽  
Shu-Li Mei
Keyword(s):  
Image Segmentation ◽  
Burkholderia Cepacia ◽  
Integration Method ◽  
Interpolation Property ◽  
Variational Model ◽  
Nonlinear Odes ◽  
Precise Integration ◽  
Homotopy Perturbation ◽  
Analytical Scheme ◽  
Shannon Wavelet

Image segmentation variational method is good at processing the images with blurry and complicated contours, which is useful in quality identification of pathologic picture of onion. An adaptive Shannon wavelet precise integration method (WPIM) on digital image segmentation was proposed based on the image processing variational model to improve the processing speed and eliminate the artifacts of the images. First, taking full advantage of the interpolation property of the Shannon wavelet function, a multiscale Shannon wavelet interpolation scheme was constructed based on the homotopy perturbation method (HPM). The image pixels of the Burkholderia cepacia (ex-Burkholder) infected onions were taken as the collocation points of the WPIM. Then, with this scheme, the image segmentation model (C-V model) can be discretized into a system of nonlinear ODEs and solved by the half-analytical scheme combining the HPM and the precision integration method. At last, the numerical precision and efficiency of WPIM were discussed and compared with other common segmentation methods such as OSTU method and Sobel operator. The results show that the contour curve of the segmentation object obtained by the new method has many excellent properties such as closed and clear topological structure and the artifacts can be eliminated.

Globally convex variational model for multiphsae image segmentation

2015 ◽  
Author(s):  
Huaxiang Liu ◽  
Jiangxiong Fang ◽  
Liting Zhang ◽  
Huaxiang Liu ◽  
Jing Xiao ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Variational Model

scholarly journals PENERAPAN CITRA TERKOMPRESI PADA SEGMENTASI CITRA MENGGUNAKAN ALGORITMA K-MEANS

2018 ◽  
Vol 2 (1) ◽  
pp. 65-74
Author(s):  
Angga Wijaya Kusuma ◽  
Rossy Lydia Ellyana
Keyword(s):  
Image Processing ◽  
Image Segmentation ◽  
Medical Image ◽  
Performance Test ◽  
Input Image ◽  
Magnetic Resonance Imaging Image ◽  
Resonance Imaging ◽  
Compression Process ◽  
Mri Brain ◽  
Mri Image

In the development of an image not only as a documentation of events. One area that requires image processing is in the field of medicine is radiology. In radiology there is a medical image required by doctors and researchers to be processed for patient analysis. One of the important problems in image processing and pattern recognition is image segmentation into homogeneous areas. Segmentation in medical images will result in a medical image with area boundaries that are important information for analysis. This research applies k-means algorithm to MRI (Magnetic Resonance Imaging) image segmentation. The input image used is the image of MRI (brain and breast) has gone through the compression stage. This compression process is done with the aim of reducing memory usage but the critical information content of MRI image is still maintained. The image of the segmentation result is evaluated through performance test using GCE, VOI, MSE, and PSNR parameters.

scholarly journals Automated grading of mangoes based on surface defect detection using a combined approach of image segmentation

2020 ◽  
pp. 17-23
Author(s):  
Neeraj Kumari ◽  
Ashutosh Kumar Bhatt ◽  
Rakesh Kumar Dwivedi ◽  
Rajendra Belwal
Keyword(s):  
Feature Extraction ◽  
Feature Selection ◽  
Image Segmentation ◽  
Surface Defect ◽  
Input Image ◽  
Segmentation Technique ◽  
Segmentation Accuracy ◽  
Surface Defect Detection ◽  
Automated Grading ◽  
Processing Accuracy

Image segmentation is an essential and critical step in huge number of applications of image processing. Accuracy of image segmentation influence retrieved information for further processing in classification and other task. In image segmentation algorithms, a single segmentation technique is not sufficient in providing accurate segmentation results in many cases. In this paper we are proposing a combining approach of image segmentation techniques for improving segmentation accuracy. As a case study fruit mango is selected for classification based on surface defect. This classification method consists of three steps: (a) image pre-processing, (b) feature extraction and feature selection and (c) classification of mango. Feature extraction phase is performed on an enhanced input image. In feature selection PCA methodology is used. In classification three classifiers BPNN, Naïve bayes and LDA are used. Proposed image segmentation technique is tested on online dataset and our own collected images database. Proposed segmentation technique performance is compared with existing segmentation techniques. Classification results of BPNN in training and testing phase are acceptable for proposed segmentation technique.

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