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 fuzzified BRAIN algorithm for learning DNF from incomplete data

Aim of this paper is to address the problem of learning Boolean functions from training data with missing values. We present an extension of the BRAIN algorithm, called U-BRAIN (Uncertainty-managing Batch Relevance-based Artificial INtelligence), conceived for learning DNF Boolean formulas from partial truth tables, possibly with uncertain values or missing bits. Such an algorithm is obtained from BRAIN by introducing fuzzy sets in order to manage uncertainty. In the case where no missing bits are present, the algorithm reduces to the original BRAIN

Representation of Perfect and Local MV-algebras

We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as quasi-constant functions on an ultraproduct of the reals. All the above theorems are proved to have a uniform version, depending only on the cardinality of the algebra to be embedded, as well as a definable construction in ZFC. The paper contains both known and new results and provides a complete overview of representation theorems for such classes

Quantale Modules, with Applications to Logic and Image Processing

We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.Comment: 150 pages, 17 figures, 3 tables, Doctoral dissertation, Univ Salern

Gravity Network for end-to-end small lesion detection

This paper introduces a novel one-stage end-to-end detector specifically designed to detect small lesions in medical images. Precise localization of small lesions presents challenges due to their appearance and the diverse contextual backgrounds in which they are found. To address this, our approach introduces a new type of pixel-based anchor that dynamically moves towards the targeted lesion for detection. We refer to this new architecture as GravityNet, and the novel anchors as gravity points since they appear to be "attracted" by the lesions. We conducted experiments on two well-established medical problems involving small lesions to evaluate the performance of the proposed approach: microcalcifications detection in digital mammograms and microaneurysms detection in digital fundus images. Our method demonstrates promising results in effectively detecting small lesions in these medical imaging tasks