A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
Local Scale Control for Edge Detection and Blur Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Probabilistic interpretation of population codes
Neural Computation
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
Channel Smoothing: Efficient Robust Smoothing of Low-Level Signal Features
IEEE Transactions on Pattern Analysis and Machine Intelligence
P-Channels: Robust Multivariate M-Estimation of Large Datasets
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Efficient computation of channel-coded feature maps through piecewise polynomials
Image and Vision Computing
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Robust multi-scale extraction of blob features
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Learning Higher-Order Markov Models for Object Tracking in Image Sequences
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
Incremental computation of feature hierarchies
Proceedings of the 32nd DAGM conference on Pattern recognition
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Linear scale-space theory is the fundamental building block for many approaches to image processing like pyramids or scale-selection. However, linear smoothing does not preserve image structures very well and thus non-linear techniques are mostly applied for image enhancement. A different perspective is given in the framework of channel-smoothing, where the feature domain is not considered as a linear space, but it is decomposed into local basis functions. One major drawback is the larger memory requirement for this type of representation, which is avoided if the channel representation is subsampled in the spatial domain. This general type of feature representation is called channel-coded feature map (CCFM) in the literature and a special case using linear channels is the SIFT descriptor. For computing CCFMs the spatial resolution and the feature resolution need to be selected. In this paper, we focus on the spatio-featural scale-space from a scale-selection perspective. We propose a coupled scheme for selecting the spatial and the featural scales. The scheme is based on an analysis of lower bounds for the product of uncertainties, which is summarized in a theorem about a spatio-featural uncertainty relation. As a practical application of the derived theory, we reconstruct images from CCFMs with resolutions according to our theory. The results are very similar to the results of non-linear evolution schemes, but our algorithm has the fundamental advantage of being non-iterative. Any level of smoothing can be achieved with about the same computational effort.