Geometric invariance in computer vision
Geometric invariance in computer vision
Generalization of the Lambertian model and implications for machine vision
International Journal of Computer Vision
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topographic Maps and Local Contrast Changes in Natural Images
International Journal of Computer Vision
Hierarchical face clustering on polygonal surfaces
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Geometry and Color in Natural Images
Journal of Mathematical Imaging and Vision
Shape segmentation using local slippage analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
Features for Recognition: Viewpoint Invariance for Non-Planar Scenes
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Finite Volume Methods on Spheres and Spherical Centroidal Voronoi Meshes
SIAM Journal on Numerical Analysis
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Geometric Description of Images as Topographic Maps
Geometric Description of Images as Topographic Maps
SIAM Journal on Imaging Sciences
Robust and efficient delaunay triangulations of points on or close to a sphere
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Least squares quantization in PCM
IEEE Transactions on Information Theory
Fast computation of a contrast-invariant image representation
IEEE Transactions on Image Processing
Invariance for Single Curved Manifold
SIBGRAPI '12 Proceedings of the 2012 25th SIBGRAPI Conference on Graphics, Patterns and Images
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Recently, it has been shown that for the Lambert illumination model, only scenes composed of developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework. We show that, in general, the requirement for such invariances is quite strong and is related to the differential geometry of the objects. More precisely, we prove that single-curved manifolds, i.e., manifolds such that at each point, there is at most one principal curvature direction, produce invariant isosurfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed of single-curved objects. A direct consequence is that the Weiss et al. image change detection algorithm (On the illumination invariance of the level lines under directed light: Application to change detection. SIAM J Imag Sci 2011;4(1):448-71) can be extended to detect whether a manifold is single curved or not, in any finite dimension. We design a mesh segmentation procedure based on such a result, and we implement the procedure in 3D.