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Visualizations of vascular structures are frequently used in radiological investigations to detect and analyze vascular diseases. Obstructions of the blood flow through a vessel are one of the main interests of physicians, and several methods have been proposed to aid the visual assessment of calcifications on vessel walls. Curved Planar Reformation (CPR) is a wide-spread method that is designed for peripheral arteries which exhibit one dominant direction. To analyze the lumen of arbitrarily oriented vessels, Centerline Reformation (CR) has been proposed. Both methods project the vascular structures into 2D image space in order to reconstruct the vessel lumen. In this paper, we propose Curved Surface Reformation (CSR), a technique that computes the vessel lumen fully in 3D. This offers high-quality interactive visualizations of vessel lumina and does not suffer from problems of earlier methods such as ambiguous visibility cues or premature discretization of centerline data. Our method maintains exact visibility information until the final query of the 3D lumina data. We also present feedback from several domain experts.