Optimal camera placement for accurate reconstruction

Three-dimensional (3D) measurements can be recovered from several views by triangulation. This paper deals with the problem of where to place the cameras in order to obtain a minimal error in the 3D measurements, also called camera network design in photogrammetry. We pose the problem in terms of an optimization design, dividing it into two main components: (1) an analytical part dedicated to the analysis of error propagation from which a criterion is derived, and (2) a global optimization process to minimize this criterion. In this way, the approach consists of an uncertainty analysis applied to the reconstruction process from which a covariance matrix is computed. This matrix represents the uncertainty of the detection from which the criterion is derived. Moreover, the optimization has discontinuities due to the presence of occluding surfaces between the viewpoint and the object point group, which leads to a combinatorial optimization process. These aspects are solved using a multi-cellular genetic algorithm. Experimental results are provided to illustrate the effectiveness and efficiency of the solution.

[1]  G. Olague.  DESIGN AND SIMULATION OF PHOTOGRAMMETRIC NETWORKS USING GENETIC ALGORITHMS , 2000 .

[2]  Luce Morin,et al.  Quelques contributions des invariants projectifs à la vision par ordinateur , 1993 .

[3]  Konstantinos A. Tarabanis,et al.  Dynamic sensor planning , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[4]  C. Fraser.  Photogrammetric measurement to one part in a million , 1992 .

[5]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[6]  Konstantinos A. Tarabanis,et al.  Computing viewpoints that satisfy optical constraints , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[7]  Roger Y. Tsai,et al.  Automated sensor planning for robotic vision tasks , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  El-Ghazali Talbi,et al.  The "Ariadne's clew" algorithm: global planning with local methods , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

[9]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[10]  Gustavo Olague.  Planification du placement de caméras pour des mesures 3D de précision. (Planning Camera Placement for Accurate 3D Measurements) , 1998 .

[11]  Roger Mohr,et al.  Optimal camera placement to obtain accurate 3D point positions , 1997, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170).

[12]  O. Faugeras.  Three-dimensional computer vision: a geometric viewpoint , 1993 .

[13]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[14]  Armin Grün,et al.  Automatic Sensor Placement for Accurate Dimensional Inspection , 1995, Comput. Vis. Image Underst..

[15]  Scott Mason.  Expert system based design of photogrammetric networks , 1994 .

[16]  S. Mason.  Heuristic reasoning strategy for automated sensor placement , 1997 .

[17]  Peter Kovesi,et al.  Automatic Sensor Placement from Vision Task Requirements , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  H. Beyer.  Geometric and radiometric analysis of a CCD-camera based photogrammetric close-range system , 1992 .

[19]  Yoshiaki Shirai,et al.  Illumination setup planning for a hand-eye system based on an environmental model , 1991, Adv. Robotics.

[20]  Dieter Fritsch,et al.  First order design strategies for industrial photogrammetry , 1990, ISPRS International Conference on Computer Vision and Remote Sensing.

[21]  Robert M. Haralick,et al.  Optimal Sensor and Light Source Positioning for Machine Vision , 1995, Comput. Vis. Image Underst..

[22]  Vidroha Debroy,et al.  Genetic Programming , 1998, Lecture Notes in Computer Science.

[23]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[24]  William H. Press,et al.  Numerical recipes in C , 2002 .

[25]  Glenn H. Tarbox,et al.  Planning for Complete Sensor Coverage in Inspection , 1995, Comput. Vis. Image Underst..

[26]  Richard Pito,et al.  A Solution to the Next Best View Problem for Automated Surface Acquisition , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Lothar Thiele,et al.  A Mathematical Analysis of Tournament Selection , 1995, ICGA.

[28]  J. K. Kinnear,et al.  Advances in Genetic Programming , 1994 .

[29]  Tomomasa Sato,et al.  Automatic planning of light source and camera placement for an active photometric stereo system , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[30]  Roger Mohr,et al.  Projective Geometry and Computer Vision , 1993, Handbook of Pattern Recognition and Computer Vision.

[31]  K. Atkinson.  Close Range Photogrammetry and Machine Vision , 1996 .

[32]  S. Mason.  Conceptual model of the convergent multistation network configuration task , 1995 .

[33]  Bharath Modayur,et al.  Automatic light-source placement for detecting object features , 1992, Other Conferences.

[34]  John Holland,et al.  Adaptation in Natural and Artificial Sys-tems: An Introductory Analysis with Applications to Biology , 1975 .

[35]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[36]  Gustavo Olague,et al.  Autonomous Photogrammetric Network Design Using Genetic Algorithms , 2001, EvoWorkshops.

[37]  A. Gruen.  ADAPTIVE LEAST SQUARES CORRELATION: A POWERFUL IMAGE MATCHING TECHNIQUE , 1985 .

[38]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[39]  Olivier Faugeras,et al.  Three-Dimensional Computer Vision , 1993 .