Real Algebraic Geometry and Applications in Robotics and Computer Vision

Dear Colleagues,

This Special Issue explores the theoretical field of real algebraic geometry and its interactions with robotics and computer vision applications. Real algebraic geometry provides theoretical frameworks and computational tools that transform the applied fields above through its fundamental structures—semi-algebraic sets, real varieties, toric geometry, and related algorithms. These mathematical approaches offer elegant solutions to complex problems, such modeling configuration spaces in robotics and camera calibration in computer vision, providing global guarantees that purely numerical methods cannot. Recent advances have enabled breakthroughs in motion planning, geometric vision problems, and robotic manipulation. The field continues to evolve through emerging connections with machine learning, topological data analysis, and verification methods, creating new research opportunities at this interdisciplinary frontier.

This Special Issue welcomes original research contributions that showcase real algebraic geometry developments and innovative applications in robotics and computer vision, as well as theoretical developments inspired by challenges in these domains. We particularly encourage submissions that bridge the gap between mathematical theory and practical implementation, demonstrating how algebraic methods can enhance robustness, efficiency, and capabilities in real-world systems.

Contributions on the following topics are particularly welcome, though the list is not exhaustive:

Theoretical Foundations:

• Semi-algebraic geometry for configuration spaces;
• Real algebraic varieties and stratifications;
• Computational aspects of real algebraic geometry;
• Toric varieties and their applications;
• Effective algorithms for polynomial systems over the reals.

Robotics Applications:

• Kinematic and dynamic modeling using algebraic methods;
• Robot motion planning with algebraic guarantees;
• Singularity analysis of mechanisms;
• Algebraic approaches to robotic grasping and manipulation;
• Workspace analysis and synthesis;
• Sensor placement and calibration optimization.

Computer Vision Applications:

• Multi-view geometry and camera models;
• Structure from motion and SLAM using algebraic methods;
• Three-dimensional reconstruction algorithms with optimality guarantees;
• Object recognition and pose estimation;
• Visual servoing and tracking;
• Feature extraction and matching using algebraic invariants.

Emerging Connections:

• Integration of algebraic methods with deep learning;
• Topological data analysis for robotics and vision;
• Verification and certification using real algebraic geometry;
• Privacy-preserving vision algorithms with algebraic foundations;
• Algebraic techniques for sensor fusion;
• Computational complexity and approximation algorithms.

Dr. Alvaro Anton-Sancho
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• real algebraic geometry
• semi-algebraic sets
• computational algebraic geometry
• robot kinematics
• motion planning
• configuration spaces
• multi-view geometry
• three-dimensional reconstruction
• visual servoing
• grasping and manipulation
• singularity analysis
• computer vision algorithms
• structure from motion
• SLAM (simultaneous localization and mapping)
• pose estimation
• polynomial optimization
• algebraic vision
• geometric deep learning
• geometric verification
• topological data analysis
• robot workspace analysis
• camera calibration