Shape Priors for Level Set Representations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Nonlinear Shape Statistics in Mumford-Shah Based Segmentation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Geodesic Curves for Analysis of Continuous Implicit Shapes
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
The pre-image problem in kernel methods
IEEE Transactions on Neural Networks
Partial differences as tools for filtering data on graphs
Pattern Recognition Letters
Diffusion maps as a framework for shape modeling
Computer Vision and Image Understanding
| Hi-index | 0.00 |
In the context of shape and image modeling by manifold learning, we focus on the problem of denoising. A set of shapes or images being known through given samples, we capture its structure thanks to the Diffusion Maps method. Denoising a new element classically boils down to the key-problem of pre-image determination , i.e. recovering a point, given its embedding. We propose to model the underlying manifold as the set of Karcher means of close sample points. This non-linear interpolation is particularly well-adapted to the case of shapes and images. We define the pre-image as such an interpolation having the targeted embedding. Results on synthetic 2D shapes and on real 2D images and 3D shapes are presented and demonstrate the superiority of our pre-image method compared to several state-of-the-art techniques in shape and image denoising based on statistical learning techniques.