A general approach to parameter evaluation in fuzzy digital pictures
Pattern Recognition Letters
Fuzzy Sets and Systems - Special issue on fuzzy methods for computer vision and pattern recognition
A New Way to Represent the Relative Position between Areal Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Content-Based Image Retrieval at the End of the Early Years
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Handbook of Brain Theory and Neural Networks
The Handbook of Brain Theory and Neural Networks
Fast and robust recognition of orbit and sinus drawings using histograms of forces
Pattern Recognition Letters
Understanding the spatial organization of image regions by means of force histograms: a guided tour
Applying soft computing in defining spatial relations
Empirical Evaluation of Dissimilarity Measures for Color and Texture
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Directional Relations Composition by Orientation Histogram Fusion
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
The Use of Force Histograms for Affine-Invariant Relative Position Description
IEEE Transactions on Pattern Analysis and Machine Intelligence
Object Localization Based on Directional Information: Case of 2D Raster Data
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Algorithm for computer control of a digital plotter
IBM Systems Journal
Linguistic description of relative positions in images
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Quantitative analysis of properties and spatial relations of fuzzy image regions
IEEE Transactions on Fuzzy Systems
A gravitational approach to edge detection based on triangular norms
Pattern Recognition
A stochastic gravitational approach to feature based color image segmentation
Engineering Applications of Artificial Intelligence
Hi-index | 0.01 |
The relative position between two 2-D spatial regions is often represented quantitatively by a force histogram. In the case of raster data, force histograms are usually computed in O(KN@/N) time, where N is the number of pixels in the image and K is the number of directions in which forces are considered. When the regions are defined as fuzzy sets instead of crisp sets, the complexity also depends on the number M of possible membership degrees. In this paper, we show that the force histogram can be defined in a completely different but equivalent way, one which leads to an O(NlogN) algorithm, with complexity independent of K and M. Moreover, the equivalent definition is better adapted to the solving of theoretical issues. We use it here to determine the behavior of the force histogram towards any invertible affine transformation.