Quantale Modules and their Operators, with Applications

The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators - that turn out to be precisely the homomorphisms between free objects in those categories - find concrete applications in two different branches of image processing, namely fuzzy image compression and mathematical morphology

A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology

In this paper we show how certain techniques of image processing, having different scopes, can be joined together under a common "algebraic roof"

A Fast Multilevel Fuzzy Transform Image Compression Method

We present a fast algorithm that improves on the performance of the multilevel fuzzy transform image compression method. The multilevel F-transform (for short, MF-tr) algorithm is an image compression method based on fuzzy transforms that, compared to the classic fuzzy transform (F-transform) image compression method, has the advantage of being able to reconstruct an image with the required quality. However, this method can be computationally expensive in terms of execution time since, based on the compression ratio used, different iterations may be necessary in order to reconstruct the image with the required quality. To solve this problem, we propose a fast variation of the multilevel F-transform algorithm in which the optimal compression ratio is found in order to reconstruct the image in as few iterations as possible. Comparison tests show that our method reconstructs the image in at most half of the CPU time used by the MF-tr algorithm

Fuzzy transform for high-resolution satellite images compression

Many compression methods have been developed until now, especially for very high-resolution satellites images, which, due to the massive information contained in them, need compression for a more efficient storage and transmission. This paper modifies Perfilieva's Fuzzy transform using pseudo-exponential function to compress very high-resolution satellite images. We found that very high-resolution satellite images can be compressed by F-transform with pseudo-exponential function as the membership function. The compressed images have good quality as shown by the PSNR values ranging around 59-66 dB. However, the process is quite time-consuming with average 187.1954 seconds needed to compress one image. These compressed images qualities are better than the standard compression methods such as CCSDS and Wavelet method, but still inferior regarding time consumption

The semiring-theoretic approach to MV-algebras: a survey

In this paper we review some of the main achievements of the semiring-theoretic approach to MV-algebras initiated and pursued mainly by the present authors and their collaborators. The survey focuses mainly on the connections between MV-algebras and other theories that such a semiringbased approach enabled, and on an application of such a framework to Digital Image Processing. We also give some suggestions for further developments by stating several open problems and possible research lines.Comment: Published versio

Removal Of Blocking Artifacts From JPEG-Compressed Images Using An Adaptive Filtering Algorithm

The aim of this research was to develop an algorithm that will produce a considerable improvement in the quality of JPEG images, by removing blocking and ringing artifacts, irrespective of the level of compression present in the image. We review multiple published related works, and finally present a computationally efficient algorithm for reducing the blocky and Gibbs oscillation artifacts commonly present in JPEG compressed images. The algorithm alpha-blends a smoothed version of the image with the original image; however, the blending is controlled by a limit factor that considers the amount of compression present and any local edge information derived from the application of a Prewitt filter. In addition, the actual value of the blending coefficient (α) is derived from the local Mean Structural Similarity Index Measure (MSSIM) which is also adjusted by a factor that also considers the amount of compression present. We also present our results as well as the results for a variety of other papers whose authors used other post compression filtering methods

Learning, Categorization, Rule Formation, and Prediction by Fuzzy Neural Networks

National Science Foundation (IRI 94-01659); Office of Naval Research (N00014-91-J-4100, N00014-92-J-4015) Air Force Office of Scientific Research (90-0083, N00014-92-J-4015

MINKOWSKI-ADDITIVE MULTIMEASURES, MONOTONICITY AND SELF-SIMILARITY

We discuss the main properties of positive multimeasures and we show how to define a notion of self-similarity based on a generalized Markov operator