The variational approach to shape from shading
Computer Vision, Graphics, and Image Processing
A line-integration based method for depth recovery from surface normals
Computer Vision, Graphics, and Image Processing
A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Pattern Recognition
Height and gradient from shading
International Journal of Computer Vision
Tracking level sets by level sets: a method for solving the shape from shading problem
Computer Vision and Image Understanding
Shape from shading: level set propagation and viscosity solutions
International Journal of Computer Vision
Iterative curve organisation with the EM algorithm
Pattern Recognition Letters
Quantitative measures of change based on feature organization: eigenvalues and eigenvectors
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Authoritative sources in a hyperlinked environment
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
New Constraints on Data-Closeness and Needle Map Consistency for Shape-from-Shading
IEEE Transactions on Pattern Analysis and Machine Intelligence
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Robot Vision
Computer Vision: Three-Dimensional Data from Images
Computer Vision: Three-Dimensional Data from Images
A Factorization Approach to Grouping
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
String Edit Distance, Random Walks and Graph Matching
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
A Graph-Spectral Approach to Surface Segmentation
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 3 - Volume 3
Terrain Analysis Using Radar Shape-from-Shading
IEEE Transactions on Pattern Analysis and Machine Intelligence
Edit Distance From Graph Spectra
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Reconstructing discontinuous surfaces from a given gradient field using partial integrability
Computer Vision and Image Understanding
Noise Reduction in Surface Reconstruction from a Given Gradient Field
International Journal of Computer Vision
A graph-spectral approach to shape-from-shading
IEEE Transactions on Image Processing
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This paper describes a graph-spectral method for 3D surface integration. The algorithm takes as its input a 2D field of surface normal estimates, delivered, for instance, by a shape-from-shading or shape-from-texture procedure. We commence by using the surface normals to obtain an affinity weight matrix whose elements are related to the surface curvature. The weight matrix is used to compute a row-normalized transition probability matrix, and we pose the recovery of the integration path as that of finding the steady-state random walk for the Markov chain defined by this matrix. The steady-state random walk is given by the leading eigenvector of the original affinity weight matrix. By threading the surface normals together along the path specified by the magnitude order of the components of the leading eigenvector we perform surface integration. The height increments along the path are simply related to the traversed path length and the slope of the local tangent plane. The method is evaluated on needle-maps delivered by a shape-from-shading algorithm applied to real-world data and also on synthetic data. The method is compared with the local geometric height reconstruction method of Bors, Hancock and Wilson, and the global methods of Horn and Brooks and Frankot and Chellappa.