The variational approach to shape from shading
Computer Vision, Graphics, and Image Processing
A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from shading as a partially well-constrained problem
CVGIP: Image Understanding
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Shape from shading: level set propagation and viscosity solutions
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from Shading: A Well-Posed Problem?
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
What is the range of surface reconstructions from a gradient field?
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Properties of Higher Order Nonlinear Diffusion Filtering
Journal of Mathematical Imaging and Vision
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Although variational methods are popular techniques in the context of shape-from-shading, they are in general restricted to indirect approaches that only estimate the gradient of the surface depth. Such methods suffer from two drawbacks: (i) They need additional constraints to enforce the integrability of the solution. (ii) They require the application of depth-from-gradient algorithms to obtain the actual surface. In this paper we present three novel approaches that avoid the aforementioned drawbacks by construction: (i) First, we present a method that is based on homogeneous higher order regularisation. Thus it becomes possible to estimate the surface depth directly by solving a single partial differential equation. (ii) Secondly, we develop a refined technique that adapts this higher order regularisation to semantically important structures in the original image. This addresses another drawback of existing variational methods: the blurring of the results due to the regularisation. (iii) Thirdly, we present an even further improved approach, in which the smoothness process is steered directly by the evolving depth map. This in turn allows to tackle the well-known problem of spontaneous concave-convex switches in the solution. In our experimental section both qualitative and quantitative experiments on standard shape-from-shading data sets are performed. A comparison to the popular variational method of Frankot and Chellappa shows the superiority of all three approaches.