Fast, accurate and low-cost 3D scans are the key in designing personalized products. In this paper, using close-range photogrammetry technique, we aim at finding the “just enough” number of cameras and their spatial configurations for a full 3D reconstruction of the human hand. Given an object, we establish a mathematical model to describe the 3D constructible ratio based on the field of the view and the depth of field of each camera, as well as the visibility of each part of the object in the view of each camera. Furthermore, we introduce spatial constrains to arrange cameras along two rings for: 1) solving the problem of the large number of parameters in the unconstrained optimization, and 2) the feasibility and flexibility in the construction. Based on the found number of cameras and the spatial configuration of each camera, a prototype scanner was built to verify the effectiveness of the proposed method. The mean absolute error between the 3D scan of a 3D printed hand and its original CAD model was found to be 0.38mm, which is smaller than that (0.52mm) of using the conventional setup. Besides, the distribution of errors is smaller as well, which implicates a better full 3D reconstruction of the scanned hand.

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