• basic differential geometry of curves
• Revised and corrected, basic differential geometry of surfaces, with more notes on Christoffel symbols
• scan from "Geometry from a Differentiable Viewpoint" on isometries
• geodesics
• contour generators, outlines, and koenderink's theorem (updated to include some SOR and SHGC stuff)
• some singularity theory
• rough notes on representing geometry, 1 - volume representations and shape from contour
• rough notes on representing geometry and applications, 2-b reps, scattered data interpolation and shape from shading
• my slides on shape from shading (the first Mrs Rochester!) and the keynote version (these are pre- Barron+Malik slides!)
• some notes on curve representations, FOR BACKGROUND
• some notes on tensor product surfaces, FOR BACKGROUND
• some notes on b spline subdivision, FOR BACKGROUND
• some notes on the Catmull-Clark algorithm, FOR BACKGROUND
• some quick notes on transformations, vectors and tensors
• some notes on Riemannian geometry (now significantly revised and expanded since last appeared on the website; you should re download)
• some notes on Riemannian mean shift

This isn't a comprehensive list of books on the topic; it's just ones I consult reasonably regularly

• An introduction to differentiable manifolds and Riemannian geometry, W.M. Boothby (Really nice at getting details into place; not much on curvature and topology).
• Riemannian geometry, Gallot, Hulin, Lafontaine (This is a springer title, and you may be able to consult an electronic version online via the library; does much more than we do, but beware the odd typo; nice exercise solutions)
• Riemannian geometry, Do Carmo (Very tight and informative; much more than I did in class; note that his coordinates go the opposite direction, which isn't important, but can confuse)
• A Panoramic View of Riemannian Geometry, Berger (lots and lots and lots of stuff; lots and lots and lots of pointers; can't say I understand most of it, but quite good at giving a sense of how the geometric enterprise hangs together, and rather stimulating)

• "What does the occluding contour tell us about solid shape?" JJ Koenderink, Perception, 1984. We've discussed most of this stuff, but here's a chance to get used to Koenderink's rather unique point of view and mode of expression; also, you get the juicy details of Marr's error.
• "Photometric invariants related to solid shape" JJ Koenderink and AJ van Doorn, Optica Acta, 1980. Hardest of the three, but provides much insight into how gauss maps work, and gives a chance to reason with them and singularity theory. I'll go through several examples. If you're having trouble downloading the paper, do it from within the University VPN
• "The shape of smooth objects and the way contours end" JJ Koenderink and AJ van Doorn, Perception, 1982. Quite a lot of this we haven't discussed, and it isn't easy; I'll do some singularity theory in class and that will help. If you're having trouble downloading the paper, do it from within the University VPN
• "Single view reconstruction of curved surfaces," M Prasad, A Fitzgibbon Computer Vision and Pattern Recognition, 2006 IEEE Computer Society
• Playing with Puffball: simple scale-invariant inflation for use in vision and graphics, Nathaniel R. Twarog, Marshall F. Tappen and Edward H. Adelson Proceedings of the ACM Symposium on Applied Perception, 2012
• "An Approximate Shading Model for Object Relighting" Zicheng Liao, Kevin Karsch, David Forsyth, Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) 2015
• "Shape, illumination, and reflectance from shading, " J Barron, J Malik - 2013 IEEE TPAMI
• Jean-Denis Durou, Maurizio Falcone, and Manuela Sagona. 2008. Numerical methods for shape-from-shading: A new survey with benchmarks. Comput. Vis. Image Underst. 109, 1 (January 2008), 22-43. DOI=http://dx.doi.org/10.1016/j.cviu.2007.09.003
• A new point matching algorithm for non-rigid registration , Haili Chuia and Anand Rangarajanb, CVIU, 2003
• Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes Andrew E. Johnson, Member, IEEE, and Martial Hebert, Member, IEEE, PAMI 1999
• A Spectral Technique for Correspondence Problems Using Pairwise Constraints, Marius Leordeanu, Martial Hebert, ICCV 2005
• Catmull, E.; Clark, J. (1978). "Recursively generated B-spline surfaces on arbitrary topological meshes" (PDF). Computer-Aided Design 10 (6): 350. doi:10.1016/0010-4485(78)90110-0.
• A. Edelman, T.A. Arias, S.T. Smith, "The Geometry of Algorithms with Orthogonality Constraints", In Press, SIAM J. Matrix Anal. Appl.
• R. Subbarao and P. Meer, "Nonlinear Mean Shift over Riemannian Manifolds", IJCV, 2009, 84:1-20

• Exercise 1

• Using contour information for detection
• Building aspect classes
• Improving shape from contour by using (say) CSG representations
• Building useful surface priors
• Getting geometric reasoning into deep nets: how and why?
• Improving matching across instances
• Discriminative methods to recover surfaces from contour, etc. cues