Using Multiple Scanning Devices for 3-D Modeling
Medical applications for 3D printing are expanding rapidly and are expected to revolutionize health care (Hammoudi et al. in Extracting wire-frame models of street facades from 3D point clouds and the corresponding cadastral map, Saint-Mandé, France, pp. 91–96, 2010) . Medical uses for 3D printing, both actual and potential, can be organized into several broad categories, including: tissue and organ fabrication; creation of customized prosthetics, implants, and anatomical models; and pharmaceutical research regarding drug dosage forms, delivery, and discovery (Sitek in IEEE Trans Med Imag 25:1172, 2006) . The application of 3D printing in medicine can provide many benefits, including: the customization and personalization of medical products, drugs, and equipment; cost-effectiveness; increased productivity; the democratization of design and manufacturing; and enhanced collaboration (Bernardini in Comput Graph Forum 21(2):149–172, 2002) . Reconstruction of the object from 3D scans can be achieved either by use of sophisticated algorithms (Ozbolat and Yu in IEEE Trans Biomed Eng 60(3):691–699, 2013)  or directly from the point clouds (Hoy in Med Ref Serv Q 32(1):94–99, 2013) , (3D Print Exchange in National Institutes of Health, 2014) . The second approach has an advantage of much higher speed since no image recognition is necessary. However it may also result in the loss of accuracy. To speed-up the scanning procedure we propose use of multiple scanners to obtain a point cloud of a given object. A few mathematical problems will arise with this approach. The most important among them is the calibration of multiple scanners. It is considered in the paper. We propose mathematical formulation of the calibration problem and give a linear time complexity algorithm to approximately solve this problem. The other problems including the study of how the measurement errors propagate to the errors of the image and how to recalculate point clouds from different scanner, is the subject of our current research and are not considered in the paper.
KeywordsCalibration 3-D printing 3-D scanners Applied mathematics Barycentric coordinates Linear algebra
The authors would like to thank Simon Kudernatsch, Dr. Takafumi Asaki (TAMUT innovation lab) for many interesting discussions.
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