• Optics and Precision Engineering
  • Vol. 32, Issue 16, 2550 (2024)
Gengsheng LI1,2 and Guojun LIU1,*
Author Affiliations
  • 1School of Mathematics and Statistics, Ningxia University, Yinchuan75002, China
  • 2School of Mathematics and Information Technology, Longnan Normal University, Longnan74500, China
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    DOI: 10.37188/OPE.20243216.2550 Cite this Article
    Gengsheng LI, Guojun LIU. Local region image segmentation by fusion of statistical norm metrics[J]. Optics and Precision Engineering, 2024, 32(16): 2550 Copy Citation Text show less

    Abstract

    Active Contour Model (ACM) has become one of the most commonly used image segmentation tools. However, the existing algorithms are time-consuming and lead to a sharp decrease in segmentation accuracy when dealing with images with intensity inhomogeneity. Therefore, in this paper, a statistical paradigm was proposed for image segmentation by combining local image information. First, the image was modeled using a new bias field model that decomposed the gray scale inhomogeneity of the image into a component of the observed image. Compared with the traditional multiplicative bias field, the additive bias field module enabled the energy generalization to extract the texture information of the image from a new dimension. Next, a local information fusion strategy was used to compute the feature fitting maps inside and outside the contours. Finally, the statistical paradigm was utilized to portray the similarity between the feature fitting map and the original feature map. Thus, the newly designed energy generalization deals with images with complex backgrounds by utilizing hierarchical local features, global spatial consistency, and multiscale abstract representation. The experimental results show that for segmenting non-homogeneous medical images, the model in this paper requires only 50 iterations, while the other models are all over 100; the algorithm takes only 8 seconds to run, but the rest of the models are much higher than 8 seconds. At the same time, the proposed algorithm was evaluated using objective evaluation indicators: the average value of the DC indicator is 0.985 1, the average value of the FP indicator is 0.005 2, the average value of the JCS indicator is 0.970 6, the average value of the P indicator is 0.994 7, and the average value of the TP indicator is 0.975 7. The model in this paper is able to extract more information about the texture structure and is robust to gray scale inhomogeneity and initial contours.
    EεLGDFϕ=μRpϕ+Eεϕ(1)

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    Hεx=121+2πarctanxε(2)

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    δεx=1πεε2+x2(3)

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    Ix=bx+rx+nx(4)

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    EABCϕ,r,b=i=12Gσy-xA2dyMiϕxdx,(5)

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    Iy=by+ry+ny(6)

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    Gσy-x=λe-y-x22σ2,    y-xρ0, otherwise(7)

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    Ex=-i=12OxΩilogpidy(8)

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    pi=12πσixexp-Iy-IiLIx22σi2x(9)

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    Ex=-i=12ΩiGσy-xlogpidy(9)

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    E=Exdx(10)

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    ESABϕ,r,u,σ,b=-i=12Gσy-xlogpiMiϕydydx.(11)

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    ESABu1=Gσy-xIy-rx-b1xM1ϕydy-Gσy-xu1x                            M1ϕydy=0,                        (12)(13)

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    u1x=Gσy-xIy-rx-b1xM1ϕydyGσy-xM1ϕydy,(13)

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    b1x=Gσy-xIy-rx-u1xM1ϕydyGσy-xM1ϕydy,(14)

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    u2x=Gσy-xIy-rx-b2xM2ϕydyGσy-xM2ϕydy,(15)

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    b2x=Gσy-xIy-rx-u2xM2ϕydyGσy-xM2ϕydy,(16)

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    σ12x=Gσy-xIy-I1LIx2M1ϕydyGσy-xM1ϕydy,(17)

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    σ22x=Gσy-xIy-I2LIx2M2ϕydyGσy-xM2ϕydy(18)

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    ESABr=-2Gσy-xIy-I1LIx2σ12xM1ϕydy+-2Gσy-xIy-I2LIx2σ22xM2ϕydy.(19)

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    rx=Nr1x+Nr2xDr1x+Dr2x(20)

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    Nr1x=Gσy-xIyM1ϕydyσ12x-b1x+u1xGσy-xM1ϕydyσ12x,(21)

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    Nr2x=Gσy-xIyM2ϕydyσ22x-b2x+u2xGσy-xM2ϕydyσ22x,(22)

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    Dr1x=Gσy-xM1ϕydyσ12x(23)

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    Dr2x=Gσy-xM2ϕydyσ22x(24)

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    ϕt=-ESABϕ=-δεϕe1-e2(25)

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    ei=Gσy-xlogσix+Iy-rx-bix-uix22σi2xdy.(26)

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    ϕR=tanhηϕn(27)

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    ϕ0=-2,xΩ0-Ω00,xΩ02,xΩ-Ω0(28)

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    DC=2IOIgIO+Ig(30)

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    JCS=IoIgIoIg(31)

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    Gengsheng LI, Guojun LIU. Local region image segmentation by fusion of statistical norm metrics[J]. Optics and Precision Engineering, 2024, 32(16): 2550
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