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Open AccessProceeding Paper

A Comparative Evaluation of Classical and Deep Learning-Based Visual Odometry Methods for Autonomous Vehicle Navigation

by Armand Nagy and János Hollósi

Eng. Proc. 2025, 113(1), 16; https://doi.org/10.3390/engproc2025113016 - 29 Oct 2025

Viewed by 936

This study introduces a comprehensive benchmarking framework for evaluating visual odometry (VO) methods, combining classical, learning-based, and hybrid approaches. We assess 52 configurations—spanning 19 keypoint detectors, 21 descriptors, and 4 matchers—across two widely used benchmark datasets: KITTI and EuRoC. Six key trajectory metrics, including Absolute Trajectory Error (ATE) and Final Displacement Error (FDE), provide a detailed performance comparison under various environmental conditions, such as motion blur, occlusions, and dynamic lighting. Our results highlight the critical role of feature matchers, with the LightGlue–SIFT combination consistently outperforming others across both datasets. Additionally, learning-based matchers can be integrated with classical pipelines, improving robustness without requiring end-to-end training. Hybrid configurations combining classical detectors with learned components offer a balanced trade-off between accuracy, robustness, and computational efficiency, making them suitable for real-world applications in autonomous systems and robotics. Full article

(This article belongs to the Proceedings of The Sustainable Mobility and Transportation Symposium 2025)

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17 pages, 590 KB

Open AccessArticle

New Generalized Jacobi Polynomial Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Boundary Value Problems

by Hany Mostafa Ahmed

Fractal Fract. 2024, 8(4), 199; https://doi.org/10.3390/fractalfract8040199 - 29 Mar 2024

Cited by 7 | Viewed by 1708

Abstract

In this study, we present a novel approach for the numerical solution of high-order ODEs and MTVOFDEs with BCs. Our method leverages a class of GSJPs that possess the crucial property of satisfying the given BCs. By establishing OMs for both the ODs and VOFDs of the GSJPs, we integrate them into the SCM, enabling efficient and accurate numerical computations. An error analysis and convergence study are conducted to validate the efficacy of the proposed algorithm. We demonstrate the applicability and accuracy of our method through eight numerical examples. Comparative analyses with prior research highlight the improved accuracy and efficiency achieved by our approach. The recommended approach exhibits excellent agreement between approximate and precise results in tables and graphs, demonstrating its high accuracy. This research contributes to the advancement of numerical methods for ODEs and MTVOFDEs with BCs, providing a reliable and efficient tool for solving complex BVPs with exceptional accuracy. Full article

(This article belongs to the Special Issue Feature Papers for Numerical and Computational Methods Section)

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26 pages, 22673 KB

Open AccessArticle

New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations

by Hany Mostafa Ahmed

Fractal Fract. 2024, 8(1), 68; https://doi.org/10.3390/fractalfract8010068 - 18 Jan 2024

Cited by 25 | Viewed by 2193

Abstract

The current study discusses a novel approach for numerically solving MTVO-TFDWEs under various conditions, such as IBCs and DBCs. It uses a class of GSJPs that satisfy the given conditions (IBCs or DBCs). One of the important parts of our method is establishing OMs for Ods and VOFDs of GSJPs. The second part is using the SCM by utilizing these OMs. This algorithm enables the extraction of precision and efficacy in numerical solutions. We provide theoretical assurances of the treatment’s efficacy by validating its convergent and error investigations. Four examples are offered to clarify the approach’s practicability and precision; in each one, the IBCs and DBCs are considered. The findings are compared to those of preceding studies, verifying that our treatment is more effective and precise than that of its competitors. Full article

(This article belongs to the Special Issue Feature Papers for Numerical and Computational Methods Section)

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12 pages, 2163 KB

Open AccessArticle

Distance Estimation Approach for Maritime Traffic Surveillance Using Instance Segmentation

by Miro Petković and Igor Vujović

J. Mar. Sci. Eng. 2024, 12(1), 78; https://doi.org/10.3390/jmse12010078 - 28 Dec 2023

Cited by 6 | Viewed by 3252

Abstract

Maritime traffic monitoring systems are particularly important in Mediterranean ports, as they provide more comprehensive data collection compared to traditional systems such as the Automatic Identification System (AIS), which is not mandatory for all vessels. This paper improves the existing real-time maritime traffic monitoring systems by introducing a distance estimation algorithm for monocular cameras, which aims to provide high quality maritime traffic metadata collection for traffic density analysis. Two distance estimation methods based on a pinhole camera model are presented: the Vessel-Focused Distance Estimation (VFDE) and the novel Vessel Object-Focused Distance Estimation (VOFDE). While VFDE uses the predefined height of a vessel for distance estimation, VOFDE uses standardized dimensions of objects on the vessel, detected with a Convolutional Neural Network (CNN) for instance segmentation to enhance estimation accuracy. Our evaluation covers distances up to 414 m, which is significantly beyond the scope of previous studies. When compared to the distances measured with a precise instrument, VOFDE achieves a Percentage Deviation Index (PDI) of 1.34% to 9.45%. This advance holds significant potential for improving maritime surveillance with monocular cameras and is also applicable in other areas, such as low-cost maritime vehicles equipped with single cameras. Full article

(This article belongs to the Special Issue Safety and Efficiency of Maritime Transportation and Ship Operations)

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11 pages, 329 KB

Open AccessArticle

An ε-Approximate Approach for Solving Variable-Order Fractional Differential Equations

by Yahong Wang, Wenmin Wang, Liangcai Mei, Yingzhen Lin and Hongbo Sun

Fractal Fract. 2023, 7(1), 90; https://doi.org/10.3390/fractalfract7010090 - 13 Jan 2023

Cited by 1 | Viewed by 2111

Abstract

As a mathematical tool, variable-order (VO) fractional calculus (FC) was developed rapidly in the engineering field due to it better describing the anomalous diffusion problems in engineering; thus, the research of the solutions of VO fractional differential equations (FDEs) has become a hot [...] Read more.

ε

-approximate approach, based on the least squares theory and the idea of residuals, for the solutions of VO-FDEs and VO fractional integro-differential equations (VO-FIDEs). First, the VO-FDEs and VO-FIDEs are considered to be analyzed in appropriate Sobolev spaces

H_{2}^{n} [0, 1]

and the corresponding orthonormal bases are constructed based on scale functions. Then, the space

H_{2, 0}^{2} [0, 1]

is chosen which is just suitable for one of the models the authors want to solve to demonstrate the algorithm. Next, the numerical scheme is given, and the stability and convergence are discussed. Finally, four examples with different characteristics are shown, which reflect the accuracy, effectiveness, and wide application of the algorithm. Full article

(This article belongs to the Special Issue Fractional Diffusion Equations: Numerical Analysis, Modeling and Application)

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17 pages, 813 KB

Open AccessArticle

Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings

by Mohammed K. A. Kaabar, Ahmed Refice, Mohammed Said Souid, Francisco Martínez, Sina Etemad, Zailan Siri and Shahram Rezapour

Mathematics 2021, 9(14), 1693; https://doi.org/10.3390/math9141693 - 19 Jul 2021

Cited by 20 | Viewed by 2598

Abstract

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings. Full article

(This article belongs to the Special Issue Nonlinear Differential Equations and Functional Analysis: Theory and Applications)

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