Image segmentation with depth information via simplified variational level set formulation

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Image segmentation with depth information via simplified variational level set formulation. / Tan, Lu; Pan, Zhenkuan; Liu, Wanquan; Duan, Jinming; Wei, Weibo; Wang, Guodong.

In: Journal of Mathematical Imaging and Vision, Vol. 60, No. 1, 01.2018, p. 1–17.

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Tan, Lu ; Pan, Zhenkuan ; Liu, Wanquan ; Duan, Jinming ; Wei, Weibo ; Wang, Guodong. / Image segmentation with depth information via simplified variational level set formulation. In: Journal of Mathematical Imaging and Vision. 2018 ; Vol. 60, No. 1. pp. 1–17.

Bibtex

@article{6cb39693f84840cbbaa15926b0999d87,
title = "Image segmentation with depth information via simplified variational level set formulation",
abstract = "Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss–Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency.",
keywords = "Alternating direction method of multipliers (ADMM), Fast Fourier Transform (FFT), Nitzberg–Mumford–Shiota (NMS)functional, Projection method, Segmentation with depth, Soft thresholding formulas, Variational level set formulation",
author = "Lu Tan and Zhenkuan Pan and Wanquan Liu and Jinming Duan and Weibo Wei and Guodong Wang",
year = "2018",
month = jan,
doi = "10.1007/s10851-017-0735-3",
language = "English",
volume = "60",
pages = "1–17",
journal = "Journal of Mathematical Imaging and Vision",
issn = "0924-9907",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Image segmentation with depth information via simplified variational level set formulation

AU - Tan, Lu

AU - Pan, Zhenkuan

AU - Liu, Wanquan

AU - Duan, Jinming

AU - Wei, Weibo

AU - Wang, Guodong

PY - 2018/1

Y1 - 2018/1

N2 - Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss–Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency.

AB - Image segmentation with depth information can be modeled as a minimization problem with Nitzberg–Mumford–Shiota functional, which can be transformed into a tractable variational level set formulation. However, such formulation leads to a series of complicated high-order nonlinear partial differential equations which are difficult to solve efficiently. In this paper, we first propose an equivalently reduced variational level set formulation without using curvatures by taking level set functions as signed distance functions. Then, an alternating direction method of multipliers (ADMM) based on this simplified variational level set formulation is designed by introducing some auxiliary variables, Lagrange multipliers via using alternating optimization strategy. With the proposed ADMM method, the minimization problem for this simplified variational level set formulation is transformed into a series of sub-problems, which can be solved easily via using the Gauss–Seidel iterations, fast Fourier transform and soft thresholding formulas. The level set functions are treated as signed distance functions during computation process via implementing a simple algebraic projection method, which avoids the traditional re-initialization process for conventional variational level set methods. Extensive experiments have been conducted on both synthetic and real images, which validate the proposed approach, and show advantages of the proposed ADMM projection over algorithms based on traditional gradient descent method in terms of computational efficiency.

KW - Alternating direction method of multipliers (ADMM)

KW - Fast Fourier Transform (FFT)

KW - Nitzberg–Mumford–Shiota (NMS)functional

KW - Projection method

KW - Segmentation with depth

KW - Soft thresholding formulas

KW - Variational level set formulation

UR - http://www.scopus.com/inward/record.url?scp=85019242421&partnerID=8YFLogxK

U2 - 10.1007/s10851-017-0735-3

DO - 10.1007/s10851-017-0735-3

M3 - Article

AN - SCOPUS:85019242421

VL - 60

SP - 1

EP - 17

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

IS - 1

ER -