A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct Analytical Methods for Solving Poisson Equations in Computer Vision Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Height and gradient from shading
International Journal of Computer Vision
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIAM Review
Geometric surface processing via normal maps
ACM Transactions on Graphics (TOG)
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
International Journal of Computer Vision
Weighted Minimal Hypersurface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves
ACM Transactions on Mathematical Software (TOMS)
Gradient domain mesh deformation: a survey
Journal of Computer Science and Technology
Integrating the Normal Field of a Surface in the Presence of Discontinuities
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Generalized Newton-Type Methods for Energy Formulations in Image Processing
SIAM Journal on Imaging Sciences
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
A gradient descent procedure for variational dynamic surface problems with constraints
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Multiview specular stereo reconstruction of large mirror surfaces
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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We address the task of adjusting a surface to a vector field of desired surface normals in space. The described method is entirely geometric in the sense, that it does not depend on a particular parametrization of the surface in question. It amounts to solving a nonlinear least-squares problem in shape space. Previously, the corresponding minimization has been performed by gradient descent, which suffers from slow convergence and susceptibility to local minima. Newton-type methods, although significantly more robust and efficient, have not been attempted as they require second-order Hadamard differentials. These are difficult to compute for the problem of interest and in general fail to be positive-definite symmetric. We propose a novel approximation of the shape Hessian, which is not only rigorously justified but also leads to excellent numerical performance of the actual optimization. Moreover, a remarkable connection to Sobolev flows is exposed. Three other established algorithms from image and geometry processing turn out to be special cases of ours. Our numerical implementation founds on a fast finite-elements formulation on the minimizing sequence of triangulated shapes. A series of examples from a wide range of different applications is discussed to underline flexibility and efficiency of the approach.