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

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.

A Multiscale Algorithm for Image Segmentation by Variational Method

1994 ◽  
Vol 31 (1) ◽  
pp. 282-299 ◽  
Author(s):  
G. Koepfler ◽  
C. Lopez ◽  
J. M. Morel
Keyword(s):  
Image Segmentation ◽  
Variational Method ◽  
Multiscale Algorithm

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.

scholarly journals Semantic Image Segmentation with Deep Convolutional Neural Networks and Quick Shift

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 427 ◽  
Author(s):  
Sanxing Zhang ◽  
Zhenhuan Ma ◽  
Gang Zhang ◽  
Tao Lei ◽  
Rui Zhang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Image Segmentation ◽  
Convolutional Neural Networks ◽  
Semantic Segmentation ◽  
Autonomous Driving ◽  
Input Image ◽  
Feature Representation ◽  
Segmentation Algorithm ◽  
Deep Convolutional Neural Networks ◽  
Semantic Image Segmentation

Semantic image segmentation, as one of the most popular tasks in computer vision, has been widely used in autonomous driving, robotics and other fields. Currently, deep convolutional neural networks (DCNNs) are driving major advances in semantic segmentation due to their powerful feature representation. However, DCNNs extract high-level feature representations by strided convolution, which makes it impossible to segment foreground objects precisely, especially when locating object boundaries. This paper presents a novel semantic segmentation algorithm with DeepLab v3+ and super-pixel segmentation algorithm-quick shift. DeepLab v3+ is employed to generate a class-indexed score map for the input image. Quick shift is applied to segment the input image into superpixels. Outputs of them are then fed into a class voting module to refine the semantic segmentation results. Extensive experiments on proposed semantic image segmentation are performed over PASCAL VOC 2012 dataset, and results that the proposed method can provide a more efficient solution.

Study of Image Segmentation and Image Restoration Based on Variational Method

2014 ◽  
Vol 644-650 ◽  
pp. 4319-4321
Author(s):  
Xiu Bo Shi
Keyword(s):  
Image Segmentation ◽  
Variational Method ◽  
Image Restoration ◽  
Computer Technology ◽  
Image Understanding ◽  
Optical Instrument ◽  
Health Care Education ◽  
Industrial Health ◽  
Subsequent Target ◽  
Instrument Observation

People are very familiar to the image. Image can be obtained by optical instrument observation of the objective world or image in the eyes of people of objective scenery in the human visual system. With the development of computer technology, digital image technology has been widely used in scientific research, industrial, health care, education, entertainment and communication. Therefore, the research of image technology has vital significance. This article mainly research image segmentation and image restoration based on variational method. Image segmentation is to divide the image into some meaningful area, is the foundation of subsequent target recognition and image understanding.

scholarly journals LCC-Net: A Lightweight Cross-Consistency Network for Semisupervised Cardiac MR Image Segmentation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lai Song ◽  
Jiajin Yi ◽  
Jialin Peng
Keyword(s):  
Image Segmentation ◽  
Semantic Segmentation ◽  
Representation Learning ◽  
Input Image ◽  
Unlabeled Data ◽  
Clinical Practices ◽  
Mr Image ◽  
Vast Number ◽  
Computation Efficiency ◽  
Model Training

Semantic segmentation plays a crucial role in cardiac magnetic resonance (MR) image analysis. Although supervised deep learning methods have made significant performance improvements, they highly rely on a large amount of pixel-wise annotated data, which are often unavailable in clinical practices. Besides, top-performing methods usually have a vast number of parameters, which result in high computation complexity for model training and testing. This study addresses cardiac image segmentation in scenarios where few labeled data are available with a lightweight cross-consistency network named LCC-Net. Specifically, to reduce the risk of overfitting on small labeled datasets, we substitute computationally intensive standard convolutions with a lightweight module. To leverage plenty of unlabeled data, we introduce extreme consistency learning, which enforces equivariant constraints on the predictions of different perturbed versions of the input image. Cutting and mixing different training images, as an extreme perturbation on both the labeled and unlabeled data, are utilized to enhance the robust representation learning. Extensive comparisons demonstrate that the proposed model shows promising performance with high annotation- and computation-efficiency. With only two annotated subjects for model training, the LCC-Net obtains a performance gain of 14.4% in the mean Dice over the baseline U-Net trained from scratch.

scholarly journals Segmentation-less, automated vascular vectorization robustly extracts neurovascular network statistics from in vivo two-photon images

2020 ◽  
Author(s):  
Samuel A. Mihelic ◽  
William A. Sikora ◽  
Ahmed M. Hassan ◽  
Michael R. Williamson ◽  
Theresa A. Jones ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Statistical Power ◽  
Large Scale ◽  
Performance Metrics ◽  
Three Dimensional ◽  
Vascular Anatomy ◽  
Input Image ◽  
Network Graph ◽  
Two Photon

AbstractRecent advances in two-photon microscopy (2PM) have allowed large scale imaging and analysis of cortical blood vessel networks in living mice. However, extracting a network graph and vector representations for vessels remain bottlenecks in many applications. Vascular vectorization is algorithmically difficult because blood vessels have many shapes and sizes, the samples are often unevenly illuminated, and large image volumes are required to achieve good statistical power. State-of-the-art, three-dimensional, vascular vectorization approaches require a segmented/binary image, relying on manual or supervised-machine annotation. Therefore, voxel-by-voxel image segmentation is biased by the human annotator/trainer. Furthermore, segmented images oftentimes require remedial morphological filtering before skeletonization/vectorization. To address these limitations, we propose a vectorization method to extract vascular objects directly from unsegmented images. The Segmentation-Less, Automated, Vascular Vectorization (SLAVV) source code in MATLAB is openly available on GitHub. This novel method uses simple models of vascular anatomy, efficient linear filtering, and low-complexity vector extraction algorithms to remove the image segmentation requirement, replacing it with manual or automated vector classification. SLAVV is demonstrated on three in vivo 2PM image volumes of microvascular networks (capillaries, arterioles and venules) in the mouse cortex. Vectorization performance is proven robust to the choice of plasma- or endothelial-labeled contrast, and processing costs are shown to scale with input image volume. Fully-automated SLAVV performance is evaluated on various, simulated 2PM images based on the large, [1.4, 0.9, 0.6] mm input image, and performance metrics show greater robustness to image quality than an intensity-based thresholding approach.

scholarly journals Image segmentation and preserve the boundary of the image using b-spline basis

2021 ◽  
Vol 5 (2) ◽  
pp. 121-131
Author(s):  
Gajalakshmi N ◽  
Karunanith S
Keyword(s):  
Image Segmentation ◽  
Optimal Solution ◽  
Input Image ◽  
Mean Square ◽  
Knot Insertion ◽  
Spline Collocation ◽  
B Spline ◽  
B Splines ◽  
Number Of Zeros ◽  
Spline Basis

This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values

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