Technometrics
Trace Inference, Curvature Consistency, and Curve Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision, Graphics, and Image Processing
Perceptual grouping of curved lines
Proceedings of a workshop on Image understanding workshop
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A computational model of color perception and color naming
A computational model of color perception and color naming
Inference of multiple curves and surfaces from sparse data
Inference of multiple curves and surfaces from sparse data
Computer Vision and Image Understanding
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
IEEE Transactions on Pattern Analysis and Machine Intelligence
Segmenting Unstructured 3D Points into Surfaces
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Co-dimension 2 Geodesic Active Contours for MRA Segmentation
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
Normalized Cuts and Image Segmentation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Analytic solution of stochastic completion fields
ISCV '95 Proceedings of the International Symposium on Computer Vision
A Theory of Networks for Approximation and Learning
A Theory of Networks for Approximation and Learning
Face detection using quantized skin color regions merging andwavelet packet analysis
IEEE Transactions on Multimedia
International Journal of Computer Vision - Special Issue on Content-Based Image Retrieval
Texture design using a simplicial complex of morphable textures
ACM SIGGRAPH 2005 Papers
Qualitative characterization and use of prior information
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Color lines: image specific color representation
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Monocular reconstruction of human motion by qualitative selection
FGR' 04 Proceedings of the Sixth IEEE international conference on Automatic face and gesture recognition
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We present a novel algorithm for recovering a smooth manifold of unknown dimension and topology from a set of points known to belong to it. Numerous applications in computer vision can be naturally interpreted as instanciations of this fundamental problem. Recently, a non-iterative discrete approach, tensor voting, has been introduced to solve this problem and has been applied successfully to various applications. As an alternative, we propose a variational formulation of this problem in the continuous setting and derive an iterative algorithm which approximates its solutions. This method and tensor voting are somewhat the differential and integral form of one another. Although iterative methods are slower in general, the strength of the suggested method is that it can easily be applied when the ambient space is not Euclidean, which is important in many applications. The algorithm consists in solving a partial differential equation that performs a special anisotropic diffusion on an implicit representation of the known set of points. This results in connecting isolated neighbouring points. This approach is very simple, mathematically sound, robust and powerful since it handles in a homogeneous way manifolds of arbitrary dimension and topology, embedded in Euclidean or non-Euclidean spaces, with or without border. We shall present this approach and demonstrate both its benefits and shortcomings in two different contexts: (i) data visual analysis, (ii) skin detection in color images.