Computation of Surface Orientation and Structure of Objects Using Grid Coding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Solid shape
Non-rigid motion analysis: isometric motion
CVGIP: Image Understanding
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Bending and Creasing Virtual Paper
IEEE Computer Graphics and Applications
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Metric Rectification for Perspective Images of Planes
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
A Video Based Interface to Textual Information for the Visually Impaired
ICMI '02 Proceedings of the 4th IEEE International Conference on Multimodal Interfaces
Composition of a dewarped and enhanced document image from two view images
IEEE Transactions on Image Processing
Digitization of deformed documents using a high-speed multi-camera array
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part II
Reconstruction of 3d surface and restoration of flat document image from monocular image sequence
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
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The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.