scholarly journals Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

2022 ◽  
Author(s):  
Huizhu Pan ◽  
Jintao Song ◽  
Wanquan Liu ◽  
Ling Li ◽  
Guanglu Zhou ◽  
...  
Keyword(s):  
Evolution Equations ◽  
Active Contour Model ◽  
Operator Splitting ◽  
The Self ◽  
Convergence Time ◽  
Variational Model ◽  
Split Bregman ◽  
Geodesic Active Contour ◽  
Non Local ◽  
Split Bregman Algorithm

AbstractPreserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

A Hybrid Active Contour Model based on New Edge-Stop Functions for Image Segmentation

2020 ◽  
Vol 11 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Xiaojun Yang ◽  
Xiaoliang Jiang
Keyword(s):  
Image Segmentation ◽  
Active Contour ◽  
Active Contour Model ◽  
Variational Model ◽  
Local Means ◽  
Area Of Interest ◽  
Complex Shapes ◽  
Sharp Edges ◽  
Non Local ◽  
Edge Based

Edge-based active contour methods are popular algorithms for image segmentation, with the purpose to extract the area of interest. However, they may face to boundary leakage and improper segmentation when handle images under weak edges or complex shapes. The extensive edge-stop functions adopt edge information, which cannot apply to guide the evolving curve approaching to target boundaries. To resolve this issue, a novel level set algorithm based on non-local means (NLM) filtering is constructed in this study. Firstly, the images are subjected to non-local means filtering to generate edge map. Secondly, a new edge-stop function constructed from this edge map as well as the fuzzy k-NN classification algorithm is incorporated into the variational model. Our experiments demonstrate that non-local means filtering is able to sharp edges both on medical and natural images. Thus, this analysis seems to be useful for clinical medical diagnosis.

scholarly journals A New Variational Model for Segmenting Objects of Interest from Color Images

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Yanli Zhai ◽  
Boying Wu ◽  
Dazhi Zhang ◽  
Jiebao Sun
Keyword(s):  
Active Contour ◽  
Active Contour Model ◽  
Energy Functional ◽  
Color Images ◽  
Variational Model ◽  
Geodesic Active Contour ◽  
Active Contour Models ◽  
New Model ◽  
New Energy ◽  
Contour Models

We propose a new variational model for segmenting objects of interest from color images. This model is inspired by the geodesic active contour model, the region-scalable fitting model, the weighted bounded variation model and the active contour models based on the Mumford-Shah model. In order to segment desired objects in color images, the energy functional in our model includes a discrimination function that determines whether an image pixel belongs to the desired objects or not. Compared with other active contour models, our new model cannot only avoid the usual drawback in the level set approach but also detect the objects of interest accurately. Moreover, we investigate the new model mathematically and establish the existence of the minimum to the new energy functional. Finally, numerical results show the effectiveness of our proposed model.

Multiple Aerosol Unmixing by the Split Bregman Algorithm

2011 ◽  
Author(s):  
Russell Warren ◽  
Stanley Osher ◽  
Richard Vanderbeek
Keyword(s):  
Split Bregman ◽  
Split Bregman Algorithm

scholarly journals Fast Split Bregman Based Deconvolution Algorithm for Airborne Radar Imaging

2020 ◽  
Vol 12 (11) ◽  
pp. 1747 ◽  
Author(s):  
Yin Zhang ◽  
Qiping Zhang ◽  
Yongchao Zhang ◽  
Jifang Pei ◽  
Yulin Huang ◽  
...  
Keyword(s):  
Real Time ◽  
Computing Time ◽  
Real Data ◽  
Radar Imaging ◽  
Matrix Inversion ◽  
Airborne Radar ◽  
Split Bregman ◽  
Regularization Problem ◽  
Azimuth Resolution ◽  
Split Bregman Algorithm

Deconvolution methods can be used to improve the azimuth resolution in airborne radar imaging. Due to the sparsity of targets in airborne radar imaging, an L 1 regularization problem usually needs to be solved. Recently, the Split Bregman algorithm (SBA) has been widely used to solve L 1 regularization problems. However, due to the high computational complexity of matrix inversion, the efficiency of the traditional SBA is low, which seriously restricts its real-time performance in airborne radar imaging. To overcome this disadvantage, a fast split Bregman algorithm (FSBA) is proposed in this paper to achieve real-time imaging with an airborne radar. Firstly, under the regularization framework, the problem of azimuth resolution improvement can be converted into an L 1 regularization problem. Then, the L 1 regularization problem can be solved with the proposed FSBA. By utilizing the low displacement rank features of Toeplitz matrix, the proposed FSBA is able to realize fast matrix inversion by using a Gohberg–Semencul (GS) representation. Through simulated and real data processing experiments, we prove that the proposed FSBA significantly improves the resolution, compared with the Wiener filtering (WF), truncated singular value decomposition (TSVD), Tikhonov regularization (REGU), Richardson–Lucy (RL), iterative adaptive approach (IAA) algorithms. The computational advantage of FSBA increases with the increase of echo dimension. Its computational efficiency is 51 times and 77 times of the traditional SBA, respectively, for echoes with dimensions of 218 × 400 and 400 × 400 , optimizing both the image quality and computing time. In addition, for a specific hardware platform, the proposed FSBA can process echo of greater dimensions than traditional SBA. Furthermore, the proposed FSBA causes little performance degradation, when compared with the traditional SBA.

THE NON-LOCAL TIME PROBLEM FOR ONE CLASS OF PSEUDODIFFERENTIAL EQUATIONS WITH SMOOTH SYMBOLS

2021 ◽  
Vol 9 (1) ◽  
pp. 107-127
Author(s):  
R. Kolisnyk ◽  
V. Gorodetskyi ◽  
O. Martynyuk
Keyword(s):  
Fundamental Solution ◽  
Initial Function ◽  
Adjoint Operator ◽  
Differentiation Operator ◽  
The Self ◽  
Multipoint Problem ◽  
Time Problem ◽  
Sigma 1 ◽  
Non Local ◽  
Differential Operator Equation

In this paper we investigate the differential-operator equation $$ \partial u (t, x) / \partial t + \varphi (i \partial / \partial x) u (t, x) = 0, \quad (t, x) \in (0, + \infty) \times \mathbb {R} \equiv \Omega, $$ where the function $ \varphi \in C ^ {\infty} (\mathbb {R}) $ and satisfies certain conditions. Using the explicit form of the spectral function of the self-adjoint operator $ i \partial / \partial x $, in $ L_2 (\mathbb {R}) $ it is established that the operator $ \varphi (i \partial / \partial x) $ can be understood as a pseudodifferential operator in a certain space of type $ S $. The evolution equation $ \partial u / \partial t + \sqrt {I- \Delta} u = 0 $, $ \Delta = D_x ^ 2 $, with the fractionation differentiation operator $ \sqrt { I- \Delta} = \varphi (i \partial / \partial x) $, where $ \varphi (\sigma) = (1+ \sigma ^ 2) ^ {1/2} $, $ \sigma \in \mathbb {R} $ is attributed to the considered equation. Considered equation is a nonlocal multipoint problem with the initial function $ f $, which is an element of a space of type $ S $ or type $ S '$ which is a topologically conjugate with a space of type $ S $ space. The properties of the fundamental solution of such a problem are established, the correct solvability of the problem in the half-space $ t> 0 $ is proved, the representation of the solution in the form of a convolution of the fundamental solution with the initial function is found, the behavior of the solution $ u (t, \cdot) $ for $ t \to + \infty $ (solution stabilization) in spaces of type $ S '$.

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