This research aims at investigating algorithms for 3D surface reconstruction from cross sections. We look at topologically motivated algorithms for robust surface reconstruction.
Object reconstruction is a challenging problem at the forefront of computer graphics and vision. A rather less-explored problem is of reconstruction from linear cross sections. Two types of problems addressed in this research are reconstruction from an organised set of cross sections and reconstruction from arbitrarily placed cross sections. We focus on topologically motivated methods for smooth reconstruction using concepts from the theory of homotopy continuation. The first problem is looked upon in the context of acoustic signals wherein the object cross sections show a definite geometric arrangement. A reconstruction in this case can take advantage of the inherent arrangement. The problem of reconstruction from arbitrary cross sections is a generic problem and is consequently more challenging.
3D Reconstruction using SDT (2017): https://github.com/ojaswa/3DReconstructionSDT
O. Sharma and N. Agarwal, “Signed Distance based 3D Surface Reconstruction from Unorganized Planar Cross-sections,” Computers & Graphics, vol. 62, pp. 67-76, 2017.
O. Sharma and N. Agarwal, “3D Surface Reconstruction from Unorganized Sparse Cross Sections,” in Graphics Interface, 2016.
O. Sharma and F. Anton, “Homotopic object reconstruction using natural neighbor barycentric coordinates,” in Transactions on Computational Science XIV, Springer Berlin Heidelberg, 2011, pp. 188-210.
O. Sharma and F. Anton, “Homotopy-based surface reconstruction with application to acoustic signals,” The Visual Computer, vol. 27, iss. 5, pp. 373-386, 2011.
O. Sharma and F. Anton, “Homotopic object reconstruction using natural neighbor barycentric coordinates,” in International Symposium Voronoi Diagrams in Science and Engineering (ISVD), 2010, pp. 181-188.