Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Elements of information theory
Elements of information theory
Handbook of mathematics (3rd ed.)
Handbook of mathematics (3rd ed.)
Probability Models for Clutter in Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Contour and Texture Analysis for Image Segmentation
International Journal of Computer Vision
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Object Localization by Bayesian Correlation
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
GRADE: Gibbs Reaction and Diffusion Equitions
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Image compression via joint statistical characterization in the wavelet domain
IEEE Transactions on Image Processing
On Advances in Statistical Modeling of Natural Images
Journal of Mathematical Imaging and Vision
Guest Editorial: Computational Vision at Brown
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Physics-motivated features for distinguishing photographic images and computer graphics
Proceedings of the 13th annual ACM international conference on Multimedia
Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Homeostatic image perception: an artificial system
Computer Vision and Image Understanding
Hypotheses for Image Features, Icons and Textons
International Journal of Computer Vision
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
The Second Order Local-Image-Structure Solid
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multivariate Statistical Models for Image Denoising in the Wavelet Domain
International Journal of Computer Vision
A stochastic grammar of images
Foundations and Trends® in Computer Graphics and Vision
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Increasing depth lateral resolution based on sensor fusion
International Journal of Intelligent Systems Technologies and Applications
Manifold models for signals and images
Computer Vision and Image Understanding
Continuous dimensionality characterization of image structures
Image and Vision Computing
Homeostatic image perception: An artificial system
Computer Vision and Image Understanding
An adaptable k-nearest neighbors algorithm for MMSE image interpolation
IEEE Transactions on Image Processing
High-dimensional statistical measure for region-of-interest tracking
IEEE Transactions on Image Processing
Learning explicit and implicit visual manifolds by information projection
Pattern Recognition Letters
Texture synthesis and modification with a patch-valued wavelet transform
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Image reconstruction using particle filters and multiple hypotheses testing
IEEE Transactions on Image Processing
MRI tissue classification with neighborhood statistics: a nonparametric, entropy-minimizing approach
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Inpainting with image patches for compression
Journal of Visual Communication and Image Representation
Image representation in visual cortex and high nonlinear approximation
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Random walks, constrained multiple hypothesis testing and image enhancement
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Direct energy minimization for super-resolution on nonlinear manifolds
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Sparse and silent coding in neural circuits
Neurocomputing
Unsupervised texture segmentation with nonparametric neighborhood statistics
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
IWDW'11 Proceedings of the 10th international conference on Digital-Forensics and Watermarking
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Patch complexity, finite pixel correlations and optimal denoising
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
Texture Description Through Histograms of Equivalent Patterns
Journal of Mathematical Imaging and Vision
PCA based video denoising in a non-local means framework
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Journal of Visual Communication and Image Representation
A Klein-Bottle-Based Dictionary for Texture Representation
International Journal of Computer Vision
| Hi-index | 0.00 |
Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely “sparse” with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases.