<p>Edge detection is one of the most fundamental problems in computer vision and image processing, providing structural information essential for various higher-level tasks such as image segmentation, object recognition, and object detection. The purpose of this paper is to introduce an unsupervised approach to edge detection by embedding a variational energy minimization framework into a deep learning architecture. Inspired by the Ambrosio–Tortorelli functional, we reformulate edge detection as the minimization of a differentiable loss function that enforces edge consistency, spatial regularization, and structural fidelity. We train our dual-output encoder–decoder network by minimizing a variational energy function, which ensures edge consistency, spatial regularization, and structural fidelity without relying on ground truth annotations.. We present numerical results of the proposed method and compare them with those obtained by existing approaches. Experimental results demonstrate that our approach outperforms both classical and deep learning-based methods in terms of precision, recall, and F1-score.</p>