1. CENG 789 – Digital Geometry Processing 9- Least-Squares Solutions Asst. Prof. Yusuf Sahillioğlu Computer Eng. Dept,, Turkey

2. Outline 2 / 12 In this class we will First warm up with some geometric problems (distances, intersections, etc.) Then formulate and solve some least-squares problems (fitting, transformations, etc.) The following cool book is used in the preparation of some of the following slides A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing, Cohen-Or et al., 2015

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7. 7 / 12 This new scale-adaptive version of ICP has been introduced in this paper: Skuller: A Volumetric Shape Registration Algorithm for Modeling Skull Deformities, Sahillioglu and Kavan, Medical Image Analysis, 2015.

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12. What’s Next? 12 / 12 A cool term project topic might be Fitting a surface to a 3D point cloud in the Least-Squares sense (slide 11), or Implementing the Least-Squares paper (http://igl.ethz.ch/publications/) or any other paper citing/cited-by by this paper (use google scholar to see cited-by papers)http://igl.ethz.ch/publications/