Sensing High-Density IC Substrates: Adaptive Fractional Differentiation for Accurate Image Segmentation

As the fabrication of high-density integrated circuit (IC) substrates advances in precision, the task of sensing and visually inspecting defects becomes increasingly challenging. These challenges arise from the need for precise segmentation of metallographic substrate images, complicated by variations in gray levels, noise interference, and rich textures. To address these issues, an adaptive fractional differentiation (AFD)-based active contour model (ACM) is proposed, which integrates global and local terms for a more accurate depiction of sensed image information. Using local image statistics, we construct an adaptive fractional-order model to find the optimal order for the fractional gradient. This gradient is then integrated into the Chan-Vese model as the global fitting term. The fusion of the original image with the fractional gradient image forms the local fitting object, refined by a Gaussian kernel function. Adaptive weight parameters are designed to enhance segmentation performance and accelerate evolution, adjusting the balance between global and local terms. Additionally, a distance penalty term is introduced to prevent reinitialization and improve segmentation efficiency. Experimental results show that the AFD model achieves accurate segmentation of high-density IC substrate images, with average improvements in DSC and JS scores of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${16}.{95}\%$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${28}.{52}\%$ </tex-math></inline-formula>, respectively. Moreover, it reduces average processing times by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${59}.{47}\%$ </tex-math></inline-formula>, demonstrating better efficiency and robustness than other models.