Artificial Intelligence
Texture description and segmentation through fractal geometry
Computer Vision, Graphics, and Image Processing
Automatic thresholding of gray-level pictures using two-dimensional entropy
Computer Vision, Graphics, and Image Processing
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detection, Localization, and Estimation of Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast algorithm for computing fractal dimensions of image segments
Recent Issues in Pattern Analysis and Recognition
On the Quantitative Evaluation of Edge Detection Schemes and their Comparison with Human Performance
IEEE Transactions on Computers
Fractal-Based Description of Natural Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological Operators with Discrete Line Segments
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
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Considering gray tone images as sets in the Euclidean space enables measurements of fundamental parameters of an image such as its surface, volume, and connectivity number. However, resulting measurements may have a questionable meaning as the gray tone axis is generally not homogeneous with the image. We therefore introduce the notion of dimensionality to assess the appropriateness of an image measurement. Dimensionality holds for the inhomogeneity of image dimensions since it separates the scaling of the image into a scaling along thex-y plane and a scaling along the gray tone axis. This allows us to review the fundamental measurements on sets to determine those satisfying the dimensionality criterion. Then, we show that dimensionality is of equal importance when processing images. A segmentation experiment illustrates this assertion. Finally, we briefly discuss specific conditions under which dimensionality can be circumvented.