GPU accelerated level set model solving by lattice boltzmann method with application to image segmentation

Wen-Jun SHI; Deng-Wei WANG; Wan-Suo LIU; Da-Gang JIANG

doi:10.11972/j.issn.1001-9014.2021.01.016

Journal of Infrared and Millimeter Waves, Volume. 40, Issue 1, 108(2021)

GPU accelerated level set model solving by lattice boltzmann method with application to image segmentation

Wen-Jun SHI¹, Deng-Wei WANG^2,3、*, Wan-Suo LIU¹, and Da-Gang JIANG^2,3

Author Affiliations

¹Aviation Maintenance School for NCO，Air Force Engineering University，Xinyang 464000，China

²School of Aeronautics and Astronautics，University of Electronic Science and Technology of China，Chengdu 611731，China

³Aircraft Swarm Intelligent Sensing and Cooperative Control Key Laboratory of Sichuan Province，Chengdu 611731，China

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Fig. 1. Explanation of how to adaptively determine the weight coefficient of global fitting term

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Fig. 2. Spatial structure of the D2Q9 LBM lattic

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Fig. 3. The flowchart the proposed GPU accelerated segmentation model

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Fig. 4. Segmentation comparisons of C-V model, K-means model, PCNN model and our method on five laser radar range images.The first row: Input images along with initial contours,the second row: C-V model, the third row: K-means model,the fourth row: PCNN model;the fifth row: our model.

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Fig. 5. The segmentation results on several sampleimagesof the PASCAL VOC 2012 dataset.The first column shows the input images along with initial contours, and the second to fifth columns is the segmentation results by using C-V, K-means, PCNNand our models respectively

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Fig. 6. Quantitative evaluation results of four different comparison algorithms on VOC 2012 dataset.The sub-graphs (a) and (b) are the statistical distributions of the two metrics JS and DSC, respectively. Any single boxplot corresponds to the comprehensive response results of an algorithm participating in the comparison on the VOC 2012 dataset.

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Fig. 7. Segmentation comparisons of our model with LBF model on an infrared human body image under three different initializations.The first row: Input images along with initial contours; the second row: Final segmentation results of LBF model; the third row:Final segmentation results of our model

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Fig. 8. Segmentation comparisons of our model with LBF model on an infrared pig image under three different initializations.The first row: Input images along with initial contours; the second row: Final segmentation results of LBF model; the third to fifth rows: Three intermediate results of our model; the sixth row:Final segmentation results of our model

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Fig. 9. The statistical results corresponding to the evolution process shown in Fig. 8.The first row is the global mean image at convergence state, the second to third rows are the numerical distribution images of $e_{1}$ and $e_{2}$ at convergence state, the fourth row is the energy variation curve with respect to the evolution time, and the fifth row is the evolution process of three-dimensional stacking form.

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Fig. 10. A set of experiments to test the rapidity of evolution process.The first row is the input images along with initial curves, the second to fourth rows are three intermediate results of the evolution process, and the fifth row is the final segmentation results.

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Fig. 11. The statistical results corresponding to the experimental process shown in Fig. 10.The first row is the global mean image at convergence state, the second to third rows are the numerical distribution images of $e_{1}$ and $e_{2}$ at convergence state, the fourth row is the energy variation curve with respect to the evolution time, and the fifth row is the evolution process of three-dimensional stacking form.

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Fig. 12. The test image used to verify the effect of adaptive weighting coefficient on segmentation results and the different expressions of adaptive weighting coefficients. (a) Example image with two sampling points A and B; (b) The image representation form of the adaptive weighting matrix and the coefficient values corresponding to the two sampling points in (a); (c) The 3D surface representation of adaptive weighting coefficient matrix.

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Fig. 13. A verification experiment used to test the effect of adaptive weighting coefficients on segmentation results (a) Input image along with initial contour; (b) Segmentation result when regional term plays a dominant role; (c) Segmentation result when edge term plays a dominant role; (d) Segmentation result returned by the proposed model.

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Fig. 14. The relationship between function $δ_{ε}^{n e w} (x)$ and its independent variable $x$ under different parameter $ε$

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Table 1. Corresponding forms of $τ$ and $F$ in D2Q9 LBM equation for level set methods

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Table 1. Corresponding forms of $τ$ and $F$ in D2Q9 LBM equation for level set methods

Method

Level set equation

τ

and

F

C-V model

\begin{array}{l} \frac{\partial ϕ}{\partial t} = δ_{ε} (ϕ) [μ d i v (\frac{\nabla ϕ}{|\nabla ϕ|}) - ν - \\ λ_{1}^{C V} {(I - M_{i n})}^{2} + λ_{2}^{C V} {(I - M_{o u t})}^{2}] \end{array}

$τ = \frac{9}{4} \cdot μ \cdot δ_{ε} (ϕ) + 0.5$ ,

$\begin{array}{l} F = δ_{ε} (ϕ) [- ν - λ_{1}^{C V} {(I - M_{i n})}^{2} + \\ λ_{2}^{C V} {(I - M_{o u t})}^{2}] \end{array}$

LBF model

\frac{\partial ϕ}{\partial t} = - δ_{ε} (ϕ) (λ_{1}^{L B F} e_{1} - λ_{2}^{L B F} e_{2})

Our model

\begin{array}{l} \frac{\partial ϕ}{\partial t} = \\ w \cdot δ_{ε} (ϕ) (- λ_{1}^{C V} {(I - M_{i n})}^{2} + λ_{2}^{C V} {(I - M_{o u t})}^{2}) - \\ δ_{ε} (ϕ) (λ_{1}^{L B F} e_{1} - λ_{2}^{L B F} e_{2}) + \\ μ \cdot (Δ ϕ - d i v (\frac{\nabla ϕ}{|\nabla ϕ|})) + \\ ν \cdot δ_{ε} (ϕ) d i v (\frac{\nabla ϕ}{|\nabla ϕ|}) \end{array}

$τ = \frac{9}{4} \cdot (ν \cdot δ_{ε} (ϕ) - μ) + 0.5$ ,

$\begin{array}{l} F = w \cdot δ_{ε} (ϕ) (- λ_{1}^{C V} {(I - M_{i n})}^{2} + \\ λ_{2}^{C V} {(I - M_{o u t})}^{2}) - \\ δ_{ε} (ϕ) (λ_{1}^{L B F} e_{1} - λ_{2}^{L B F} e_{2}) + \\ μ \cdot Δ ϕ \end{array}$

Table 2. Segmentation metrics for the five images in Fig. 4numberedin order from left to right

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Table 2. Segmentation metrics for the five images in Fig. 4numberedin order from left to right

Image No.	Algorithm	Metrics (JS-DSC)
image #1	CV	0.6533 0.7903
	K-means	0.5172 0.6818
	PCNN	0.5625 0.7200
	Our method	0.9757 0.9877
image #2	CV	0.7285 0.8429
	K-means	0.7340 0.8466
	PCNN	0.7290 0.8432
	Our method	0.9598 0.9795
image #3	CV	0.5026 0.6690
	K-means	0.6124 0.7596
	PCNN	0.6676 0.8007
	Our method	0.9897 0.9948
image #4	CV	0.6713 0.8033
	K-means	0.7292 0.8434
	PCNN	0.7043 0.8265
	Our method	0.9807 0.9903
image #5	CV	0.4389 0.6100
	K-means	0.2642 0.4180
	PCNN	0.5068 0.6726
	Our method	0.9726 0.9861

Table 3. Comparisons of speed metrics of evolution process for the three images in Fig. 10 numbered in order from left to right

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Table 3. Comparisons of speed metrics of evolution process for the three images in Fig. 10 numbered in order from left to right

Input No.	Algorithm	Iterations	Time cost (s)	Accelerated rate
image #1 (320×240 pixels)	HFE	272	23.167	1.0
	HFE +LBM+CPU	113	9.653	2.4
	HFE +LBM+GPU	113	0.209	110.7
image #2 (320×240 pixels)	HFE	182	13.195	1.0
	HFE +LBM+CPU	58	4.256	3.1
	HFE +LBM+GPU	58	0.110	120.5
image #3 (320×240 pixels)	HFE	399	34.517	1.0
	HFE +LBM+CPU	137	11.902	2.9
	HFE +LBM+GPU	137	0.293	117.9

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Wen-Jun SHI, Deng-Wei WANG, Wan-Suo LIU, Da-Gang JIANG. GPU accelerated level set model solving by lattice boltzmann method with application to image segmentation[J]. Journal of Infrared and Millimeter Waves, 2021, 40(1): 108

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Paper Information

Category: Research Articles

Received: Nov. 6, 2019

Accepted: --

Published Online: Aug. 30, 2021

The Author Email: Deng-Wei WANG (wdengwei@126.com)

DOI:10.11972/j.issn.1001-9014.2021.01.016

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Corresponding forms of τ and F in D2Q9 LBM equation for level set methods

Table 1. Corresponding forms of τ and F in D2Q9 LBM equation for level set methods

Table 2. Segmentation metrics for the five images in Fig. 4numberedin order from left to right

Table 2. Segmentation metrics for the five images in Fig. 4numberedin order from left to right

Table 3. Comparisons of speed metrics of evolution process for the three images in Fig. 10 numbered in order from left to right

Table 3. Comparisons of speed metrics of evolution process for the three images in Fig. 10 numbered in order from left to right

Table 1. Corresponding forms of $τ$ and $F$ in D2Q9 LBM equation for level set methods

Table 1. Corresponding forms of $τ$ and $F$ in D2Q9 LBM equation for level set methods