Adaptive Image Segmentation Based on Region Information Coupling

Gengsheng Li; Guojun Liu; Wentao Ma

doi:10.3788/LOP202259.0210013

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 2 >Page 0210013 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 2, 0210013 (2022)

Adaptive Image Segmentation Based on Region Information Coupling

Gengsheng Li, Guojun Liu^*, and Wentao Ma

Author Affiliations

School of Mathematical Statistics, Ningxia University, Yinchuan , Ningxia 750021, China

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DOI: 10.3788/LOP202259.0210013 Cite this Article Set citation alerts

Gengsheng Li, Guojun Liu, Wentao Ma. Adaptive Image Segmentation Based on Region Information Coupling[J]. Laser & Optoelectronics Progress, 2022, 59(2): 0210013 Copy Citation Text

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Abstract

In order to solve the problem that the traditional variational level set segmentation algorithm is poor in segmenting uneven gray images and sensitive to the initial contours, we propose an adaptive active contour model based on local and global information coupling. By adjusting the proportion of local region fitting energy and global region fitting energy by weight function, a weight function which is adaptively updated with the evolution of the contour is given. Experiments results in synthetic images, real images and natural images show that the algorithm is robust to noise and insensitive to the initial position of the contours.

Keywords

active contour adaptive weight function image processing image segmentation variational level set

E^{C V} (c_{1}, c_{2}, C) = λ_{1} \int_{X_{i n s i d e} (C)} {|I (x) - c_{1}|}^{2} d x + λ_{2} \int_{X_{o u t s i d e} (C)} {|I (x) - c_{2}|}^{2} d x + μ \cdot X_{L e n g t h} (C)

，（1）

E^{C V} (c_{1}, c_{2}, ϕ) = λ_{1} \int_{Ω} {|I (x) - c_{1}|}^{2} H (ϕ) d x + λ_{2} \int_{Ω} {|I (x) - c_{2}|}^{2} [1 - H (ϕ)] d x

，（2）

H_{ε} (ϕ) = \frac{1}{2} {[1 + \frac{2}{π} a r c t a n (\frac{ϕ}{ε})]}^{2}

，（3）

\{\begin{array}{l} c_{1} = \frac{\int_{Ω} I (x) H_{ε} (ϕ) d x}{\int_{Ω} H_{ε} (ϕ) d x} \\ c_{2} = \frac{\int_{Ω} I (x) [1 - H_{ε} (ϕ)] d x}{\int_{Ω} [1 - H_{ε} (ϕ)] d x} \end{array}

。（4）

\frac{\partial ϕ}{\partial t} = δ_{ε} (ϕ) [- λ_{1} {(I - c_{1})}^{2} + λ_{2} {(I - c_{2})}^{2}]

，（5）

E^{L C V} = α \cdot E^{G 1} + β \cdot E^{L 1}

，（6）

E^{G 1} (c_{1}, c_{2}, C) = \int_{X_{i n s i d e} (C)} {|I (x) - c_{1}|}^{2} d x + \int_{X_{o u t s i d e} (C)} {|I (x) - c_{2}|}^{2} d x

，（7）

E^{L 1} (d_{1}, d_{2}, C) = \int_{X_{i n s i d e} (C)} {|g_{k} * I (x) - I (x) - d_{1}|}^{2} d x + \int_{X_{o u t s i d e} (C)} {|g_{k} * I (x) - I (x) - d_{2}|}^{2} d x

，（8）

\{\begin{array}{l} d_{1} = \frac{\int_{Ω} [g_{k} * I (x) - I (x)] H_{ε} (ϕ) d x}{\int_{Ω} H_{ε} (ϕ) d x} \\ d_{2} = \frac{\int_{Ω} [g_{k} * I (x) - I (x)] [1 - H_{ε} (ϕ)] d x}{\int_{Ω} [1 - H_{ε} (ϕ)] d x} \end{array}

。（9）

\begin{array}{l} \frac{\partial ϕ}{\partial t} = δ_{ε} (ϕ) \{- \{α {[I (x) - c_{1}]}^{2} + β {[g_{k} * I (x) - I (x) - d_{1}]}^{2}\}\} + \\ δ_{ε} (ϕ) \{- \{α {[I (x) - c_{2}]}^{2} + β {[g_{k} * I (x) - I (x) - d_{2}]}^{2}\}\} \end{array}

。（10）

\begin{matrix} E^{L B F} (f_{1}, f_{2}, C) = λ_{1} {\int_{Ω} \int_{X_{i n s i d e} (C)} K_{σ} (x - y) |I (y) - f_{1} (x)|}^{2} d y d x + \\ λ_{2} {\int_{Ω} \int_{X_{o u t s i d e} (C)} K_{σ} (x - y) |I (y) - f_{2} (x)|}^{2} d y d x \end{matrix}

，（11）

\begin{array}{l} \frac{\partial ϕ}{\partial t} = - λ_{1} \cdot δ_{ε} (ϕ) \cdot {\int_{Ω} K_{σ} (y - x) |I (x) - f_{1} (y)|}^{2} d y + \\ λ_{2} \cdot δ_{ε} (ϕ) \cdot {\int_{Ω} K_{σ} (y - x) |I (x) - f_{2} (y)|}^{2} d y \end{array}

。（12）

E^{G} (a_{1}, a_{2}, C) = λ_{1} \int_{X_{i n s i d e} (C)} {|g_{k} * I (x) - λ \cdot I (x) - a_{1}|}^{2} d x + λ_{2} \int_{X_{o u t s i d e} (C)} {|g_{k} * I (x) - λ \cdot I (x) - a_{2}|}^{2} d x

，（13）

E^{G} (a_{1}, a_{2}, ϕ) = λ_{1} \int_{Ω} {|g_{k} * I (x) - λ \cdot I (x) - a_{1}|}^{2} H (ϕ) d x + λ_{2} \int_{Ω} {|g_{k} * I (x) - λ \cdot I (x) - a_{2}|}^{2} [1 - H (ϕ)] d x

，（14）

\frac{\partial ϕ}{\partial t} = δ_{ε} (ϕ) \{- λ_{1} {[g_{k} * I (x) - I (x) - a_{1}]}^{2} + λ_{2} {[g_{k} * I (x) - I (x) - a_{2}]}^{2}\}

，（15）

\{\begin{array}{l} a_{1} = \frac{\int_{Ω} [g_{k} * I (x) - λ \cdot I (x)] H_{ε} (ϕ) d x}{\int_{Ω} H_{ε} (ϕ) d x} \\ a_{2} = \frac{\int_{Ω} [g_{k} * I (x) - λ \cdot I (x)] [1 - H_{ε} (ϕ)] d x}{\int_{Ω} 1 - H_{ε} (ϕ) d x} \end{array}

。（16）

\begin{array}{l} E^{L} (e_{1}, e_{2}, C) = λ_{1} {\int_{Ω} \int_{X_{i n s i d e} (C)} K_{σ} (x - y) |g_{k} * I (y) - λ \cdot I (y) - e_{1} (x)|}^{2} d y d x + \\ λ_{2} {\int_{Ω} \int_{X_{o u t s i d e} (C)} K_{σ} (x - y) |g_{k} * I (y) - λ \cdot I (y) - e_{2} (x)|}^{2} d y d x \end{array}

，（17）

\begin{array}{l} E^{L} (e_{1}, e_{2}, ϕ) = λ_{1} {\int_{Ω} \int_{X_{i n s i d e} (C)} K_{σ} (x - y) |g_{k} * I (y) - λ \cdot I (y) - e_{1} (x)|}^{2} H (ϕ) d y d x + \\ λ_{2} {\int_{Ω} \int_{X_{o u t s i d e} (C)} K_{σ} (x - y) |g_{k} * I (y) - λ \cdot I (y) - e_{2} (x)|}^{2} [1 - H (ϕ)] d y d x \end{array}

，（18）

\frac{\partial ϕ}{\partial t} = δ_{ε} (ϕ) (- λ_{1} A_{1} + λ_{2} A_{2})

，（19）

\{\begin{array}{l} e_{1} (x) = \frac{K_{σ} * \{H_{ε} (ϕ) [g_{k} * I (x) - λ \cdot I (x)]\}}{K_{σ} * H_{ε} (ϕ)} \\ e_{2} (x) = \frac{K_{σ} * \{[1 - H_{ε} (ϕ)] [g_{k} * I (x) - λ \cdot I (x)]\}}{K_{σ} * [1 - H_{ε} (ϕ)]} \end{array}

，（20）

\{\begin{matrix} A_{1} = \int_{Ω} K_{σ} (x - y) {|g_{k} * I (y) - λ \cdot I (y) - e_{1} (y)|}^{2} d y \\ A_{2} = \int_{Ω} K_{σ} (x - y) {|g_{k} * I (y) - λ \cdot I (y) - e_{2} (y)|}^{2} d y \end{matrix}

，（21）

P (ϕ) = \int_{Ω} \frac{1}{2} {(|\nabla ϕ (x)| - 1)}^{2} d x

。（22）

L (ϕ) = \int_{Ω} |\nabla H [ϕ (x)]| d x

。（23）

\begin{array}{l} E^{P r o p o s e d} = (1 - ω) \cdot E^{G} + ω \cdot E^{L} + \\ μ \cdot P (ϕ) + ν \cdot L (ϕ) \end{array}

，（24）

\begin{array}{l} \frac{\partial ϕ}{\partial t} = δ_{ε} (ϕ) (1 - ω) \{- λ_{1} {[g_{k} * I (x) - λ \cdot I (x) - a_{1}]}^{2} + λ_{2} {[g_{k} * I (x) - λ \cdot I (x) - a_{2}]}^{2}\} + \\ δ_{ε} (ϕ) ω (- λ_{1} A_{1} + λ_{2} A_{2}) + μ δ_{ε} (ϕ) d i v (\frac{\nabla ϕ}{|\nabla ϕ|}) + ν [\nabla^{2} ϕ - d i v (\frac{\nabla ϕ}{|\nabla ϕ|})] \end{array}

，（25）

J (m) = \frac{1}{1 + e x p (- k m + p)}

，（26）

ϕ^{0} = \{\begin{array}{l} - 2, x \in Ω_{0} - \partial Ω_{0} \\ 0, x \in \partial Ω_{0} \\ 2, x \in Ω - Ω_{0} \end{array}

，（27）

X_{J S} = \frac{|A ⋂ B|}{|A ⋃ B|}

，（28）

X_{D S C} = 2 \cdot \frac{|A ⋂ B|}{|A + B|}

，（29）

P = \frac{X_{T P}}{X_{T P} + X_{F P}}

，（30）

Gengsheng Li, Guojun Liu, Wentao Ma. Adaptive Image Segmentation Based on Region Information Coupling[J]. Laser & Optoelectronics Progress, 2022, 59(2): 0210013

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