Detection of Tail Parts in Double-Layer Rebar Hyperbola Using Sobel Filters and Radon Transform

Ground Penetrating Radar (GPR) is widely used for non-destructive testing of concrete structures, yet its interpretation remains highly dependent on manual analysis. Identifying the hyperbolic responses of reinforcing bars (rebar) is crucial, particularly in the case of double-layered reinforcement, where electromagnetic wave reflections obscure deeper layers. This study presents a novel approach to detecting the tail parts of hyperbolas in double-layer rebar using a combination of rotational Sobel filters and the Radon transform. In this method, after detecting the concrete bottom surface and trimming the received image, a diagonal Sobel filter is applied to extract the convex shape of the hyperbola, thereby enhancing the tail part. Subsequently, a logistic function is used to suppress noise while emphasizing relevant pixels. The Radon transform is then applied to detect quasi-linear structures representing hyperbola tails, which are clustered to distinguish structural components. Experimental results demonstrate that this approach successfully detects the second-layer rebar's hyperbolic tail, even when the vertex is indistinct, thereby improving rebar location and depth estimation. The proposed method provides a robust alternative to deep learning-based techniques, offering a practical and cost-effective solution for infrastructure inspection.