Mumford–Shah Regularized DBSCAN for Unsupervised Image Segmentation

Abstract Image segmentation is a fundamental pre-processing task in computer vision, enabling region-based analysis for a wide range of applications. Density-based clustering methods such as DBSCAN naturally preserve spatial connectivity and can identify arbitrarily shaped regions; however, when applied directly to image data, they often suffer from parameter sensitivity and noisy segmentation results due to the lack of explicit boundary modeling. Conversely, variational approaches such as the Mumford–Shah model produce coherent regions with smooth boundaries but are computationally expensive for large images. This paper proposes a hybrid image segmentation framework that integrates Mumford–Shah-inspired boundary regularization into a density-based DBSCAN clustering process. Boundary information derived from image gradients is incorporated into the neighborhood expansion mechanism to discourage cluster growth across strong edges. In addition, an automatic region merging strategy is applied to reduce over-segmentation and improve region consistency. The proposed method avoids the computational overhead of full variational optimization while retaining essential boundary-preserving properties. Experimental results on natural and textured images demonstrate that the proposed approach produces more coherent and boundary-aligned segmentations than standard and adaptive DBSCAN variants, while maintaining practical computational efficiency.