# American Institute of Mathematical Sciences

doi: 10.3934/ipi.2022014
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## Robust region-based active contour models via local statistical similarity and local similarity factor for intensity inhomogeneity and high noise image segmentation

 1 Department of Mathematics, University of Peshawar, Peshawar 2 School of Information Science and Engineering, University of Jinan, China 3 Bahcesehir University, Istanbul, Turkey

Received  April 2021 Revised  February 2022 Early access April 2022

In this paper, we design a novel variational segmentation method for two types of segmentation problems, namely, global segmentation (all objects /features in a given image are aimed to be segmented) and selective/ interactive segmentation (an objects /feature of interest in a given image is aimed to be segmented) for inhomogeneous and severe additive noisy images. The proposed segmentation models implement a local denoising constraint, capable to tackle efficiently noise/outliers and coping with intensity inhomogeneity issues, combined with local similarity factor based on spatial distances and intensity differences in the local region that guides accurately the level set function to distinguish between outliers and minute important details. Furthermore, to exhibit the accuracy of the proposed models, an experimental comparison is inducted and shown comparisons with state-of-art models on synthetic images, outdoor images, and medical images.

Citation: Ibrar Hussain, Haider Ali, Muhammad Shahkar Khan, Sijie Niu, Lavdie Rada. Robust region-based active contour models via local statistical similarity and local similarity factor for intensity inhomogeneity and high noise image segmentation. Inverse Problems and Imaging, doi: 10.3934/ipi.2022014
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##### References:
Segmentation comparison, on various synthetic images, as shown in the first column, between Ali et al. model (second column after 200 iterations and the third column the final segmentation with this method) and the proposed model (fourth column showing intermediate results after 200 iterations and the last column the final results)
Segmentation of different images using the proposed model. In the first row the given images has been shown whereas in the second row segmentation results are indicated with blue outlines
Segmentation of an airplane image using various models. (a) The given image, (b) the initial contour on object, (c) segmentation results of LIF model, (d) segmentation results of LBF model, (e) segmentation results of RLSF model, (f) segmentation results of SPGA model, (g) segmentation results of BFE field correction model, and (h) the proposed model
Performance of LBF model, SPGA model, RLSF model and the proposed model in second, third, fourth and fifth column, respectively
Performance of proposed model for blood vessel image segmentation corrupted by Gaussian noise from left to right respectively. In the second row, segmentation results of proposed model corresponding to images given in first row
Windows size choice and the number of iterations for corrupted images segmentation with noise level 0.002 in the first row and 0.02 in the second row
Segmentation results of given images with Gaussian noise level 0.002 (first column) with RLSF method in the second column and the proposed method in the last column
Quantitative comparisons of segmentation accuracy on histogram (using Jaccard similarity coefficient) of the proposed, the RLSF, the SPGA, the LIF and the LBF model respectively
Consecutive denoising and segmentation results for images with speckle noise $0.2$. The segmentation results of pre-processed denoised images by AA model [3] are followed by (a) the LIF segmentation model, (b) the LBF segmentation model, (c) the SPGA segmentation model (d) the RLSF segmentation model, (e) segmentation results of the proposed model
Consecutive denoising and segmentation results for images with $10 \%$ Gaussian noise. Segmentation results of pre-processed denoised images followed by (a) the LIF segmentation model, (b) the LBF segmentation model, (c) the SPGA segmentation model (d) the RLSF segmentation model, (e) segmentation results of the proposed model without any denoising pre-processing
The non-convexity of the model shown through different initial contours produce different results
Segmentation performance of Liu et al. [30], Mabood et al. [32], Rada et al. [35] models in comparison with the proposed method with noise level $\sigma = 0.1$
Segmentation performance comparison between Liu et al [30], Mabood et al. [32] and Rada e al. [35] incapable to complete the selective segmentation task given the initial points as shown in first column. Our proposed successfully can segment the aimed object. The noise level is $\sigma = 0.2$
Speed comparison of AOS cheme with the explicit Time Marching for different image size and number of iterations
 Size Explicit AOS Image Size Iteration CPU Iteration CPU $110\times110$ 250 52.21 80 45.65 $150\times150$ 400 136.47 100 110.29 $200\times200$ 750 410.33 110 167.44 $300\times300$ 1500 2100.92 130 460.58 $500\times500$ 2000 stuck 250 580.39
 Size Explicit AOS Image Size Iteration CPU Iteration CPU $110\times110$ 250 52.21 80 45.65 $150\times150$ 400 136.47 100 110.29 $200\times200$ 750 410.33 110 167.44 $300\times300$ 1500 2100.92 130 460.58 $500\times500$ 2000 stuck 250 580.39
Speed comparison of the Liu et al. [30], Mabood et al. [32], Rada et al. [35] and proposed model of Fig. 12 and 13a, 13b, and 13c
 IMG. Liu Mabood Rada Our model Iter CPU Iter CPU Iter CPU Iter CPU Fig. 12 200 68.1153 200 21.6026 150 17.8908 20 5.2901 Fig. 13a 200 32.4277 200 25.9021 150 12.0173 20 7.0322 Fig. 13b 200 51.9043 200 33.7350 150 24.5707 50 8.3102 Fig. 13c 200 44.1836 200 27.6316 150 13.0754 30 10.4117
 IMG. Liu Mabood Rada Our model Iter CPU Iter CPU Iter CPU Iter CPU Fig. 12 200 68.1153 200 21.6026 150 17.8908 20 5.2901 Fig. 13a 200 32.4277 200 25.9021 150 12.0173 20 7.0322 Fig. 13b 200 51.9043 200 33.7350 150 24.5707 50 8.3102 Fig. 13c 200 44.1836 200 27.6316 150 13.0754 30 10.4117
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