In this paper, we present a novel approach to improve the robustness of region-based active contour models for image segmentation, particularly in the presence of noise. Traditional active contour methods often struggle with noise sensitivity and intensity variations within the image. To overcome these limitations, we propose an enhanced segmentation model that integrates the average convolution with entropy-based mean gray level values. Our method leverages the local statistical information by introducing a local similarity factor and local region relative entropy to build a robust energy functional. This energy functional balances the intensity differences between neighboring pixels and regions within the local window, while reducing the impact of noise. By incorporating convolution and entropy into the energy formulation, our model distinguishes between the interior and exterior regions of an image more effectively, thus leading to more accurate segmentation results. We demonstrate the numerical implementation of the proposed model, along with its convexity properties, to ensure stability and reliability. The experimental results show that our method significantly improves the segmentation performance, even in challenging scenarios with varying noise levels. This advancement has the potential to improve image analyses in fields such as medical imaging, object detection, and texture classification.
Citation: Ming Shi, Ibrar Hussain. Improved region-based active contour segmentation through divergence and convolution techniques[J]. AIMS Mathematics, 2025, 10(1): 654-671. doi: 10.3934/math.2025029
In this paper, we present a novel approach to improve the robustness of region-based active contour models for image segmentation, particularly in the presence of noise. Traditional active contour methods often struggle with noise sensitivity and intensity variations within the image. To overcome these limitations, we propose an enhanced segmentation model that integrates the average convolution with entropy-based mean gray level values. Our method leverages the local statistical information by introducing a local similarity factor and local region relative entropy to build a robust energy functional. This energy functional balances the intensity differences between neighboring pixels and regions within the local window, while reducing the impact of noise. By incorporating convolution and entropy into the energy formulation, our model distinguishes between the interior and exterior regions of an image more effectively, thus leading to more accurate segmentation results. We demonstrate the numerical implementation of the proposed model, along with its convexity properties, to ensure stability and reliability. The experimental results show that our method significantly improves the segmentation performance, even in challenging scenarios with varying noise levels. This advancement has the potential to improve image analyses in fields such as medical imaging, object detection, and texture classification.
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Ming Shi, Ibrar Hussain. Improved region-based active contour segmentation through divergence and convolution techniques[J]. AIMS Mathematics, 2025, 10(1): 654-671. doi: 10.3934/math.2025029
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