Abstract: The shapes of many natural or man-made objects have curve features. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we introduce a photogrammetric method for recovering free-form objects with curvilinear structures. Our method chooses to obtain the topology and geometry of a sparse 3D wireframe of the object first instead of directly recovering a surface or volume model. Surface patches covering the object are then constructed to interpolate the curves in this wireframe while satisfying certain heuristics such as minimal bending energy. The result is an object surface model with curvilinear structures from a sparse set of images. We can produce realistic texture-mapped renderings of the object model from arbitrary viewpoints. Reconstruction results on multiple real objects are presented to demonstrate the effectiveness of our approach.