The problem of finding the best path trajectory in a graph is highly complex due to its combinatorial nature, making it difficult to solve. Standard search algorithms focus on selecting the best path trajectory by introducing constraints to estimate a suitable solution, but this approach may overlook potentially better alternatives. Despite the number of restrictions and variables in path planning, no solution minimizes the computational resources used to reach the goal. To address this issue, a framework is proposed to compute the best trajectory in a graph by introducing the mathematical morphology concept. The framework builds a lattice over the graph space using mathematical morphology operators. The searching algorithm creates a metric space by applying the morphological covering operator to the graph and weighing the cost of traveling across the lattice. Ultimately, the cumulative traveling criterion creates the optimal path trajectory by selecting the minima/maxima cost. A test is introduced to validate the framework’s functionality, and a sample application is presented to validate its usefulness. The application uses the structure of the avenues as a graph. It proposes a computable approach to find the most suitable paths from a given start and destination reference. The results confirm that this is a generalized graph search framework based on morphological operators that can be compared to the Dijkstra approach.

Navigatingdensely connected networks can be complex due to the different connection structures present within a network. No explicit algorithms are designed specifically for this navigation, so heuristic approaches and existing network systems are often employed. However, this task can become computationally asymmetrical, as the complexity of creating a representation of the city is lower than the complexity involved in identifying a set of feasible paths in a combinatorial order. This paper extends the applicability of morphological approaches to compute the shortest path in smart cities, driven by the complexity and size of the vital communication infrastructure. As is well known, this communication infrastructure changes dynamically, particularly with the evolving connection paths due to continuous population growth. Consequently, efficient communication trajectories can quickly become obsolete. The challenge of computing the best trajectories to respond more quickly to the growing population comes with high computational complexity. This paper presents an application that uses a discrete algorithm designed to compute the shortest path through a morphological approach. Specifically, it seeks to identify the best trajectory within a densely populated city based on a complex density graph. By incorporating morphological approaches into path-search algorithms, we can define a new family of methods that operate in discrete spaces with a morphological representation, resulting in approaches that have lower computational requirements. Other well-known applications in this context include the delivery of resources, such as managing electrical power consumption or minimizing time delays in resource delivery. This task is essential but classified as an NP problem, making it an appropriate scenario for applying the proposed algorithm to navigate a dense graph. The paper highlights the well-known problem of finding the shortest path as one of the potential applications of the introduced algorithm. The algorithm aims to identify the optimal path trajectory within a graph representing a dense city’s real scenario. This discussion compares and contrasts the proposal with other established approaches, highlighting the advantages and characteristics of the proposed method.

Wind dynamics in urban environments exhibit non-stationarity and marked spatial variability, complicating stochastic modeling when a single global distribution is assumed. This article discusses the estimation of wind density under quasi-stationary regimes at the local level using SICABI, a two-phase framework: (i) Stationary Region Identification (ISR) estimates, through spectral power analysis, a specific dominant period for each location and validates the induced subsampling using the Augmented Dickey–Fuller (ADF) test, and (ii) RAPID adjusts an adaptive parametric density by recursively updating the mixture parameters and creating new components when a normalized membership distance exceeds a threshold. The analysis uses wind speed records collected from eight stations in the Metropolitan Area of Queretaro, Mexico, during the period from 1 January 2023 to 31 December 2023, aggregated at a 10 min resolution, from which $X_{\delta ,s}$ is constructed for each site. RAPID is compared against Gaussian Kernel Density Estimation (KDE) with Silverman bandwidth and EM-fitted Gaussian mixtures with BIC-based selection ($K_{max}=12$). The resulting densities were compared with an empirical density estimated from a histogram over a fixed grid ($m=50$) using the MISE and RMSE metrics. The results reveal marked site-dependent differences in dominant periodicity and residual behavior, including asymmetry and heavy tails. ISR identified dominant periods ranging from 37 to 166 days, and RAPID adapted its complexity with $K_s\in [5,10]$ without fixing the number of mixture components in advance. Quantitatively, RAPID achieved the lowest RMSE at 6/8 sites and the lowest MISE at 5/8 sites, while also exhibiting shorter execution times than KDE and MoG under the same input $X_{\delta ,s}$. The results support RAPID as a competitive adaptive method for site-specific density estimation in non-stationary urban climate signals. In this context, local regimes can be viewed as approximate invariants under time translation in the weak stochastic sense, while deviations from this assumption are reflected in increased distributional complexity across sites.

SEL, a State-based Language for Video Surveillance Modeling, is a formal language designed to represent and identify activities in surveillance systems through scenario semantics and the creation of motion primitives structured in programs. Motion primitives represent the temporal evolution of motion evidence. They are the most basic motion structures detected as motion evidence, including operators such as sequence, parallel, and concurrency, which indicate trajectory evolution, simultaneity, and synchronization. SEL is a very expressive language that characterizes interactions by describing the relationships between motion primitives. These interactions determine the scenario’s activity and meaning. An experimental model is constructed to demonstrate the value of SEL, incorporating challenging activities in surveillance systems. This approach assesses the language’s suitability for describing complicated tasks.

Artificial vision system applications have generated significant interest as they allow information to be obtained through one or several of the cameras that can be found in daily life in many places, such as parks, avenues, squares, houses, etc. When the aim is to obtain information from large areas, it can become complicated if it is necessary to track an object of interest, such as people or vehicles, due to the vision space that a single camera can cover; this opens the way to distributed zone monitoring systems made up of a set of cameras that aim to cover a larger area. Distributed zone monitoring systems add great versatility, becoming more complex in terms of the complexity of information analysis, communication, interoperability, and heterogeneity in the interpretation of information. In the literature, the development of distributed schemes has focused on representing data communication and sharing challenges. Currently, there are no specific criteria for information exchange and analysis in a distributed system; hence, different models and architectures have been proposed. In this work, the authors present a framework to provide homogeneity in a distributed monitoring system. The information is obtained from different cameras, where a global reference system is defined for generated trajectories, which are mapped independently of the model used to obtain the dynamics of the movement of people within the vision area of a distributed system, thus allowing for its use in works where there is a large amount of information from heterogeneous sources. Furthermore, we propose a novel similarity metric that allows for information queries from heterogeneous sources. Finally, to evaluate the proposed performance, the authors developed several distributed query applications in an augmented reality system based on realistic environments and historical data retrieval using a client–server model.

UAV-based detection systems operating under real-world conditions exhibit failures under severe domain shifts and scale degradation, where average metrics may conceal critical vulnerabilities. This work hypothesizes that data-centric optimization, through structural deduplication (pHash/DCT) and teacher–student semantic auditing, improves worst-case robustness and cross-domain generalization in lightweight detectors without increasing model complexity under Edge AI constraints. A Data-Centric AI (DCAI) framework tailored for Edge AI is proposed, integrating: (i) perceptual deduplication via pHash to reduce structural redundancy; (ii) a teacher–student auditing scheme using YOLO11x to control semantic noise and geometric consistency; and (iii) a search space formulated as a hierarchical Design of Experiments (DoE) ablation framework (R0–R4), with minimum-recall gating and multicriteria decision-making (MCDM) selection under the Wald maximin criterion. Experimental results show limited improvements in average metrics (~1%), but consistent gains under failure scenarios, reaching up to +5.95% in precision and +1.36% in recall in the worst-case setting. GLM/ANOVA analysis demonstrates that dataset and scenario dominate performance variance (η²â‚š ≈ 0.96–0.99), while seed effects are not statistically significant (p > 0.05), confirming stability and reproducibility. Validation on Raspberry Pi 5 using NCNN demonstrates edge deployment feasibility, maintaining precision > 0.94 and recall > 0.90 at distances between 5–25 m under controlled degradation. The contribution lies in the systemic integration of a DCAI model within a hierarchical DoE framework evaluated under a maximin criterion (MCDM), enabling causal attribution of performance improvements to data design rather than to architecture under real-world Edge AI constraints for UAV applications.