Representation of local geometry in the visual system
Biological Cybernetics
Extensions of Scale-Space Filtering to Machine-Sensing Systems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models and Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Local Scale Control for Edge Detection and Blur Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
Scale-Space Derived From B-Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-based fuzzy connected image segmentation: theory, algorithms, and validation
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
Adaptive-Scale Filtering and Feature Detection Using Range Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Object Recognition from Local Scale-Invariant Features
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Multiscale image segmentation by integrated edge and region detection
IEEE Transactions on Image Processing
Scale space classification using area morphology
IEEE Transactions on Image Processing
Nonlinear scale-space filtering and multiresolution system
IEEE Transactions on Image Processing
Strongly normal sets of contractible tiles in N dimensions
Pattern Recognition
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Scale is a fundamental concept useful in almost all image processing and analysis tasks including segmentation, filtering, interpolation, registration, visualization, and quantitative analysis. Broadly speaking, scale related work can be divided into three categories: (1) multi-scale or scale-space representation, (2) local scale, and (3) locally adaptive scale. The original formulation of scale in the form of scale-space theory came from the consideration of the presence of multiple scales in nature and the desire to represent measured signals at multiple scales. However, since this representation did not suggest how to select appropriate scales, the notion of local scale was proposed to pick the right scale for a particular application from the multi-scale representation of the image. Recently, there has been considerable interest in developing locally adaptive scales, the idea being to consider the local size of object in carrying out whatever local operations that are to be done on the image. However, existing locally adaptive models are limited by shape, size, and anisotropic constraints. In this work, we propose a generalized scale model which is spatially adaptive like other local morphometric models, and yet possesses the global spirit of multi-scale representations. We postulate that this semi-locally adaptive nature of generalized scale confers it certain distinct advantages over other global and local scale formulations. We also present a variant of the generalized scale notion that we refer to as the generalized ball scale, which, in addition to having the advantages of the generalized scale model, also has superior noise resistance properties. Both scale models are dependent only on two parameters for their estimation, and we demonstrate means by which optimal values for these parameters can be estimated. Both the generalized scales can be readily applied to solving a range of image processing problems. One such problem that we address in this paper is correcting for slowly varying background spatial intensity in Magnetic Resonance images. We demonstrate the superiority of the generalized scale based inhomogeneity correction methods over an existing scale-based correction technique.