Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
The approximation power of moving least-squares
Mathematics of Computation
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Curvature computation on free-form 3-D meshes at multiple scales
Computer Vision and Image Understanding
Saliency sequential surface organization for free-form object recognition
Computer Vision and Image Understanding
Multi-Scale Classification of 3-D Objects
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Point-based multiscale surface representation
ACM Transactions on Graphics (TOG)
Reassembling fractured objects by geometric matching
ACM SIGGRAPH 2006 Papers
ACM SIGGRAPH 2007 papers
Multi-scale features for approximate alignment of point-based surfaces
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Robust principal curvatures on multiple scales
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Integral invariants for robust geometry processing
Computer Aided Geometric Design
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Bandwidth Selection and Reconstruction Quality in Point-Based Surfaces
IEEE Transactions on Visualization and Computer Graphics
Front-End Vision and Multi-Scale Image Analysis: Multi-scale Computer Vision Theory and Applications, written in Mathematica
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Multi-Scale Surface Descriptors
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH ASIA 2009 Courses
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Semantic 3D Media and Content: Surface partial matching and application to archaeology
Computers and Graphics
Object detection with feature stability over scale space
Journal of Visual Communication and Image Representation
Adaptive discrete Laplace operator
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part II
Scalar Field Analysis over Point Cloud Data
Discrete & Computational Geometry
Screen-space curvature for production-quality rendering and compositing
ACM SIGGRAPH 2013 Talks
Proceedings of the 25ième conférence francophone on l'Interaction Homme-Machine
Noise-adaptive shape reconstruction from raw point sets
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a novel approach to the multi-scale analysis of point-sampled manifolds of co-dimension 1. It is based on a variant of Moving Least Squares, whereby the evolution of a geometric descriptor at increasing scales is used to locate pertinent locations in scale-space, hence the name “Growing Least Squares”. Compared to existing scale-space analysis methods, our approach is the first to provide a continuous solution in space and scale dimensions, without requiring any parametrization, connectivity or uniform sampling. An important implication is that we identify multiple pertinent scales for any point on a manifold, a property that had not yet been demonstrated in the literature. In practice, our approach exhibits an improved robustness to change of input, and is easily implemented in a parallel fashion on the GPU. We compare our method to state-of-the-art scale-space analysis techniques and illustrate its practical relevance in a few application scenarios. © 2012 Wiley Periodicals, Inc.