Structure from Motion: Theoretical Foundations of a Novel Approach Using Custom Built Invariants

2002/01/22 by Pierre‐Louis Bazin, Pierre-Louis Bazin, Mireille Boutin +2 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Mathematics #I.2.10 #I.4.8 #Nonlinear Waves and Solitons #cs.CV #math.DG

paper · pdf · doi:10.48550/arxiv.cs/0201019

15 pages

arxiv created 2002/01/22 · openalex publication_date 2002/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We rephrase the problem of 3D reconstruction from images in terms of intersections of projections of orbits of custom built Lie groups actions. We then use an algorithmic method based on moving frames "a la Fels-Olver" to obtain a fundamental set of invariants of these groups actions. The invariants are used to define a set of equations to be solved by the points of the 3D object, providing a new technique for recovering 3D structure from motion.

Cited by

• Invariants of objects and their images under surjective maps

Related

• A Taxonomy of Structure from Motion Methods
• An Unsupervised Algorithm For Learning Lie Group Transformations
• Introducing the Classical Method of Moving Frames
• Structural rigidity and flexibility using graphs of groups
• A structure from motion inequality