Linear octrees by volume intersection |
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| Affiliation: | 1. ERC Inc., USA;2. In-Space Propulsion Branch, Air Force Research Laboratory, Edwards AFB, CA 93524, USA;1. Kocaeli University Faculty of Medicine, Division of Pediatric Rheumatology, Department of Pediatrics, Kocaeli, Turkey;2. Atlas University Faculty of Health Sciences, Department of Speech and Language Therapy, Istanbul, Turkey;3. Kocaeli University Faculty of Medicine, Department of Child and Adolescent Psychiatry, Kocaeli, Turkey;4. Kocaeli University Faculty of Medicine, Division of Child Neurology, Department of Pediatrics, Kocaeli, Turkey;5. Kocaeli University Faculty of Medicine, Division of Child Neuroradiology, Department of Radiology, Kocaeli, Turkey;1. Federal University of Santa Catarina, Brazil;2. Nursing Department, Federal University of Santa Catarina, Brazil;3. Restauração Hospital Governor Paulo Guerra, Brazil;4. July 9 de Hospital, Brazil;5. Santo Antônio de Jesus Regional Hospital Regional, Brazil;6. João XXIII Hospital, Brazil;7. North Wing Regional Hospital, Brazil;8. Vila Penteado General Hospital, Brazil;9. Urgency State Hospital Governor Otávio Lage de Siqueira, Brazil;10. São Paulo Hospital, Federal University of São Paulo, Brazil;11. Pediatric Department, Federal University of Santa Catarina, Brazil;1. Center for Computational Science and Engineering, Massachusetts Institute of Technology, MA, USA;2. California Institute for Quantitative Biosciences, University of California Berkeley, CA, USA;3. Department of Biomedical Engineering and Applied Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA;4. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA |
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| Abstract: | The paper describes a new algorithm for constructing a 3D approximation of an object from three orthogonal 2D silhouettes. The 2D views are represented as binary arrays and 3D approximation is obtained as a linear octree. The algorithm makes use of volume intersection of three cylinders obtained by sweeping three views in respective directions. The algorithm takes less time than an existing algorithm which makes use of three quadtrees and an octree for 2D and 3D image representation, respectively. Unlike the previous algorithm, the present algorithm does not require any preprocessing stage or condensation. It is Shown that the proposed algorithm is of o(T), where T is the total number of nodes in the resulting octree. |
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