Implementing a Multi-Model Estimation Method

We revisit the problem of parameter estimation in computer vision, reconsidering and implementing what may be called the Kanatani's estimation method, presented here as a simple optimisation problem, so (a) without any direct reference to a probabilistic framework but (b) considering (i) non-linear implicit measurement equations and parameter constraints, plus (ii) robust estimation in the presence of outliers and (iii) multi-model comparisons.Here, (A) a projection algorithm based on generalisations of square-root decompositions allows an efficient and numerically stable local resolution of a set of non-linear equations. On the other hand, (B) a robust estimation module of a hierarchy of non-linear models has been designed and validated.A step ahead, (C) the software architecture of the estimation module is discussed with the goal of being integrated in reactive software environments or within applications with time constraints, while an experimentation considering the parameterisation of retinal displacements between two views is proposed as an illustration of the estimation module.

[1]  Philip H. S. Torr,et al.  The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix , 1997, International Journal of Computer Vision.

[2]  Olivier D. Faugeras,et al.  The First Order Expansion of Motion Equations in the Uncalibrated Case , 1996, Comput. Vis. Image Underst..

[3]  Peter Meer,et al.  A general method for Errors-in-Variables problems in computer vision , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[4]  W. Rey.  Introduction to Robust and Quasi-Robust Statistical Methods , 1983 .

[5]  Azriel Rosenfeld,et al.  Robust regression methods for computer vision: A review , 1991, International Journal of Computer Vision.

[6]  Richard I. Hartley,et al.  In Defense of the Eight-Point Algorithm , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Reyes Enciso,et al.  Experimental Self-Calibration from Four Views , 1995, ICIAP.

[8]  Kenichi Kanatani,et al.  Geometric computation for machine vision , 1993 .

[9]  Soraya Arias,et al.  Formalisation et intégration en vision par ordinateur temps réel. (Formalisation and Integration for Real Time Computer Vision) , 1999 .

[10]  J. Miller.  Numerical Analysis , 1966, Nature.

[11]  Thierry Viéville,et al.  Implementing a Variant of the Kanatani's Estimation Method , 2000 .

[12]  Yonathan Bard,et al.  Nonlinear parameter estimation , 1974 .

[13]  Thierry Viéville,et al.  Using collineations to compute motion and structure in an uncalibrated image sequence , 1996, International Journal of Computer Vision.

[14]  金谷 健一.  Statistical optimization for geometric computation : theory and practice , 2005 .

[15]  Diane Lingrand,et al.  Analyse adaptative du mouvement dans des séquences monoculaires non calibrées , 1999 .

[16]  P. Torr.  Geometric motion segmentation and model selection , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[17]  Rachid Deriche,et al.  A Robust Technique for Matching two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry , 1995, Artif. Intell..

[18]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[19]  Richard I. Hartley,et al.  Estimation of Relative Camera Positions for Uncalibrated Cameras , 1992, ECCV.

[20]  Olivier D. Faugeras,et al.  A theory of self-calibration of a moving camera , 1992, International Journal of Computer Vision.

[21]  Thierry Viéville,et al.  Hierarchical Visual Perception without Calibration , 1996 .

[22]  N. Draper,et al.  Applied Regression Analysis. , 1967 .

[23]  Philip E. Gill,et al.  Practical optimization , 1981 .

[24]  Patrick Rives,et al.  Réalisation et calibration d'un système expérimental de vision composé d'une caméra mobile embarquée sur un robot-manipulateur , 1989 .

[25]  Walerian Kipiniak,et al.  Optimal Estimation, Identification, and Control , 1964 .

[26]  Kenichi Kanatani,et al.  Informat ion Criter ion , 2005 .

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

[28]  Q. WeiG.,et al.  Implicit and Explicit Camera Calibration , 1994 .

[29]  K. Kanatani,et al.  Statistical optimization and geometric inference in computer vision , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[30]  Charles V. Stewart,et al.  Bias in robust estimation caused by discontinuities and multiple structures , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Richard I. Hartley,et al.  In defence of the 8-point algorithm , 1995, Proceedings of IEEE International Conference on Computer Vision.

[32]  Bill Triggs.  Optimal Estimation of Matching Constraints , 1998, SMILE.

[33]  M. J. D. Powell,et al.  THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS , 1978 .

[34]  Zhengyou Zhang,et al.  Parameter estimation techniques: a tutorial with application to conic fitting , 1997, Image Vis. Comput..

[35]  J. Grimm,et al.  Optimal Time and Minimum Space-Time Product for Reversing a Certain Class of Programs , 1996 .

[36]  Robert C. Bolles,et al.  A RANSAC-Based Approach to Model Fitting and Its Application to Finding Cylinders in Range Data , 1981, IJCAI.

[37]  O. Faugeras,et al.  On determining the fundamental matrix : analysis of different methods and experimental results , 1993 .

[38]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[39]  Hirotugu Akaike,et al.  On entropy maximization principle , 1977 .

[40]  Yoram Leedan.  Statistical analysis of quadratic problems in computer vision , 1997 .

[41]  G. Celeux,et al.  Assessing a Mixture Model for Clustering with the Integrated Classification Likelihood , 1998 .

[42]  Thierry Viéville,et al.  Using Specific Displacements to Analyze Motion without Calibration , 1999, International Journal of Computer Vision.

[43]  T. Viéville,et al.  Using pseudo Kalman-filters in the presence of constraints application to sensing behaviors , 1992 .

[44]  Songde Ma,et al.  Implicit and Explicit Camera Calibration: Theory and Experiments , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[45]  Olivier D. Faugeras,et al.  Motion of points and lines in the uncalibrated case , 2004, International Journal of Computer Vision.

[46]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

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

[48]  Peter Meer,et al.  Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint , 2000, International Journal of Computer Vision.

[49]  William L. Brogan.  Applied Optimal Estimation (Arthur Gels, ed.) , 1977 .

[50]  PlaneFrançois GaspardandThierry ViévilleRobotvis.  Non Linear Minimization and Visual Localization of a , 2000 .

[51]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.