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Title / Key Mathematical modeling of advanced multi-device vision systems (23B8391)
Curriculum Doctorate of Sciences in Digital Systems
Institution Center for Research and Development of Digital Technology
Instituto Politécnico Nacional
Duration 18 weeks / 72 hours, 5 Credits
Professor Rigoberto Juarez-Salazar
Description The thematic content covers theoretical concepts organized in order of increasing complexity to design and calibrate modern digital vision systems. Students develop didactic activities per thematic unit to reinforce the understanding of abstract concepts as well as to improve their computational implementation skills.

Content

  1. Introduction
    1. Homogeneous coordinates
    2. Parallel coordinates
    3. Plucker coordinates and dual quaternions
    4. Least-squares and singular value decomposition
    5. Classical pinhole model and linear estimation

  2. Advanced imaging devices
    1. Telecentric imaging
    2. Lens distortion of lenses
    3. Distorted pinhole model
    4. Nonlinear calibration
    5. Camera-projector pairs

  3. Multi-device imaging systems
    1. Monocular vision and relative measurements
    2. Stereo vision and epipolar geometry
    3. Rectification and disparity maps
    4. Multi-device systems and triangulation
    5. Bundle adjustment
    6. Multi-focus image fusion

  4. Applications
    1. Planes in space and perspective correction
    2. Lines in space and relative length measurements
    3. Points and metric measurement of objects
    4. 3D scanning of visual navigation

Bibliography

  1. Peter Corke, Robotic vision. Fundamental algorithms in Matlab, Springer, 2022.

  2. Xiang Gao and Tao Zhang, Introduction to Visual SLAM: From Theory to Practice, Springer, 2021.

  3. J. Chen, B. Jia, and K. Zhang, Multi-view geometry based visual perception and control of robotic systems, CRC Press, 2018.

  4. Richard Leach, Advances in optical form and coordinate metrology, IOP Publishing Ltd, 2020.

  5. G. Farin and D. Hansford, Practical Linear Algebra: A Geometry Toolbox, 4th Ed., CRC Press, 2022

  6. David A. Forsyth and Jean Ponce, Computer Vision: A Modern Approach, 2nd Ed., Pearson Education, 2012.

  7. Zhang, S., High-Speed 3D Imaging with Digital Fringe Projection Techniques, CRC Press, 2016.

  8. B. Cyganek and J. Siebert, An Introduction to 3D Computer Vision Techniques and Algorithms, John Wiley & Sons, 2009.

  9. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd Ed., Cambridge University Press, 2003.