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Accurate estimation of curvatures using the conformal structure

Project Description:
Recent development of 3D scanners allows us to obtain data of surfaces effectively. The collected data can be used to construct 3D digital surface models useful for a wide variety of applications, such as face recognition, medical research, computer graphic, etc. For most situations, a single scan is not enough to produce a complete model of the 3D object. In order to obtain information of the entire object, several measurements have to be taken from different viewpoints around the object. These multiple scans from different directions are then integrated into one surface model. The integration process mainly consists of two procedures:(1) surface alignment or registration that matches overlapping areas of the multiple scans; (2) surface merging that merges all scans to create a complete surface model. These processes are commonly done by a qualified person whose tasks include manual processing/segmentation of the input range images, picking up feature points manually on every surface scans, surface registration and merging of scans semi-automatically, visual verification of the resulting surface model. These processes have to be repeated over and over until the resulting merged surface does not have folds, holes and misalignment. It is indeed a very time-consuming process. Therefore, it is of interest to look for an automatic algorithm to
register and merge surface scans together. In this project, we propose an automatic method to merge 3D attribute meshes using conformal parameterization. Geodesic patch extraction is firstly carried out
to determine the overlapping region and remove the redundant region. The surfaces are then parameterized conformally onto 2D rectangular domains. Surface registration is performed on the conformal parameter domain to match curvatures and the conformal factor. Finally, we propose the Partition of Unity Merging algorithm to merge the surfaces and obtain a smooth surface model.


Publication:

  • L.M. Lui, Y. Wang, J. Kwan, and S. T. Yau, Computation of Curvatures using Conformal Parameterization, Communications in Information and Systems, Volume 8, Number 1 (2008), 1-16


Result: