The detection of vascular structures from noisy images is a fundamental process for extracting meaningful information in many applications. Most well-known vascular enhancing techniques often rely on Hessian-based filters. This paper investigates the feasibility and deficiencies of detecting curve-like structures using a Hessian matrix. The main contribution is a novel enhancement function, which overcomes the deficiencies of established methods. Our approach has been evaluated quantitatively and qualitatively using synthetic examples and a wide range of real 2D and 3D biomedical images. Compared with other existing approaches, the experimental results prove that our proposed approach achieves high-quality curvilinear structure enhancement.