An image can be regarded as a fuzzy subset of a plane. A fuzzy entropy measuring the blur in an image is a functional which increases when the sharpness of its argument image decreases. We generalize and extend the relation "sharper than" between fuzzy sets in view of implementing the properties of a relation "sharper than" between images. We show that there are infinitely many implementations of this relation into an ordering between fuzzy sets (equivalently, images). Relying upon these orderings, we construct classes of fuzzy entropies which are useful for image thresholding by cost minimization. Assuming the image to be a degraded version of an ideal two level image (object/background), a fuzzy entropy can be introduced in a cost functional to force the fitting function to be as close as possible to a two-valued function. The minimization problem is numerically solved, and the results obtained on a synthetic image are reported.

In this paper we suggest a variant of a binary image representation based on run length encoding. This variant allows one to build a "graph representation" for a number of computing tasks like component labeling, computations of Euler number, diameter and convex hull, and the detection of local extrema and multiple points. Finally, a running application in the raster-to-vector conversion of digital maps is provide.

The use of a constructive algorithm for pattern classification is examined. The algorithm, a ‘Perceptron Cascade’, has been shown to converge to zero errors whilst learning any consistent classification of real-valued pattern vectors (Burgess, 1992). Limiting network size and producing bounded decision regions are noted to be important for the generalization ability of a network. A scheme is suggested by which a result on generalization (Vapnik, 1992) may enable calculation of the optimal network size. A fast algorithm for principal component analysis (Sirat, 1991) is used to construct ‘hyper-boxes’ around each class of patterns to ensure bounded decision regions. Performance is compared with the Gaussian Maximum Likelihood procedure in three artificial problems simulating real pattern classification applications.