Shape-from-shading (SfS) is a fundamental problem in computer vision. At its basis lies the image irradiance equation. Recently, the authors proposed to base the image irradiance equation on the assumption of perspective projection rather than the common orthographic one. The current paper presents a greatly-improved reconstruction method based on the perspective formulation. The proposed model is solved efficiently via a modification of the fast marching method of Kimmel and Sethian. We compare the two versions of the fast marching method (orthographic vs. perspective) on medical images. The perspective algorithm outperformed the orthographic one. This shows that the more realistic hypothesis of perspective projection improves reconstruction significantly. The comparison also demonstrates the usability of perspective SfS for real-life applications such as medical endoscopy.