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We present a system for constructing 3D models of real-world objects with optically challenging surfaces. The system utilizes a new range imaging concept called multipeak range imaging, which stores multiple candidates of range measurements for each point on the object surface. The multiple measurements include the erroneous range data caused by various surface properties that are not ideal for structured-light range sensing. False measurements generated by spurious reflections are eliminated by applying a series of constraint tests. The constraint tests based on local surface and local sensor visibility are applied first to individual range images. The constraint tests based on global consistency of coordinates and visibility are then applied to all range images acquired from different viewpoints. We show the effectiveness of our method by constructing 3D models of five different optically challenging objects. To evaluate the performance of the constraint tests and to examine the effects of the parameters used in the constraint tests, we acquired the ground-truth data by painting those objects to suppress the surface-related properties that cause difficulties in range sensing. Experimental results indicate that our method significantly improves upon the traditional methods for constructing reliable 3D models of optically challenging objects.