A note on the gradient of a multi-image
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Krylov subspace methods on supercomputers
SIAM Journal on Scientific and Statistical Computing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive Smoothing: A General Tool for Early Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Combinatorial Theory Series A
Random walk approach to image enhancement
Signal Processing - Special section on digital signal processing for multimedia communications and services
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering
International Journal of Computer Vision
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Quantitative Measures of Change based on Feature Organization: Eigenvalues and Eigenvectors
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Smart Nonlinear Diffusion: A Probabilistic Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multilabel Random Walker Image Segmentation Using Prior Models
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
Image scale-space from the heat kernel
CIARP'05 Proceedings of the 10th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis and Applications
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Behavioral analysis of anisotropic diffusion in image processing
IEEE Transactions on Image Processing
Anisotropic diffusion of multivalued images with applications to color filtering
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
A general framework for low level vision
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
Graph-Based Representations in Pattern Recognition and Computational Intelligence
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
Graph characterization using gaussian wave packet signature
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
| Hi-index | 0.01 |
A new method for smoothing both gray-scale and color images is presented that relies on the heat diffusion equation on a graph. We represent the image pixel lattice using a weighted undirected graph. The edge weights of the graph are determined by the Gaussian weighted distances between local neighboring windows. We then compute the associated Laplacian matrix (the degree matrix minus the adjacency matrix). Anisotropic diffusion across this weighted graph-structure with time is captured by the heat equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigensystem with time. Image smoothing is accomplished by convolving the heat kernel with the image, and its numerical implementation is realized by using the Krylov subspace technique. The method has the effect of smoothing within regions, but does not blur region boundaries. We also demonstrate the relationship between our method, standard diffusion-based PDEs, Fourier domain signal processing and spectral clustering. Experiments and comparisons on standard images illustrate the effectiveness of the method.