Rafael Marcos Luque‐Baena

Nivar Anwer, Ezequiel López-Rubio, David Elizondo et al.

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled quantitative abstraction. This work develops a unified theory of such abstraction by integrating category theory, coalgebra, quantitative logic, and optimal transport, centred on a canonical $\varepsilon$-quotient of the behavioral pseudo-metric with a universal property: among all abstractions that collapse behavioral differences below $\varepsilon$, it is the most detailed, and every other abstraction achieving the same discounted value-loss guarantee factors uniquely through it. Categorically, a quotient functor $Q_\varepsilon$ from a category of probabilistic systems to a category of metric specifications admits, via the Special Adjoint Functor Theorem, a right adjoint $R_\varepsilon$, yielding an adjunction $Q_\varepsilon \dashv R_\varepsilon$ that formalizes a duality between abstraction and realization; logically, a quantitative modal $μ$-calculus with separate reward and transition modalities is shown, for a broad class of systems, to be expressively complete for the behavioral pseudo-metric, with a countable fully abstract fragment suitable for computation. The theory is developed coalgebraically over Polish spaces and the Giry monad and validated on finite-state models using optimal-transport solvers, with experiments corroborating the predicted contraction properties and structural stability and aligning with the theoretical value-loss bounds, thereby providing a rigorous foundation for quantitative state abstraction and representation learning in probabilistic domains.

Iván García, Rafael Marcos Luque, Ezequiel López

The vast number of existing IP cameras in current road networks is an opportunity to take advantage of the captured data and analyze the video and detect any significant events. For this purpose, it is necessary to detect moving vehicles, a task that was carried out using classical artificial vision techniques until a few years ago. Nowadays, significant improvements have been obtained by deep learning networks. Still, object detection is considered one of the leading open issues within computer vision. The current scenario is constantly evolving, and new models and techniques are appearing trying to improve this field. In particular, new problems and drawbacks appear regarding detecting small objects, which correspond mainly to the vehicles that appear in the road scenes. All this means that new solutions that try to improve the low detection rate of small elements are essential. Among the different emerging research lines, this work focuses on the detection of small objects. In particular, our proposal aims to vehicle detection from images captured by video surveillance cameras. In this work, we propose a new procedure for detecting small-scale objects by applying super-resolution processes based on detections performed by convolutional neural networks \emph{(CNN)}. The neural network is integrated with processes that are in charge of increasing the resolution of the images to improve the object detection performance. This solution has been tested for a set of traffic images containing elements of different scales to test the efficiency according to the detections obtained by the model, thus demonstrating that our proposal achieves good results in a wide range of situations.