Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 119-123) and index.

1. Introduction -- 1.1 Ellipse fitting -- 1.2 Representation of ellipses -- 1.3 Least squares approach -- 1.4 Noise and covariance matrices -- 1.5 Ellipse fitting approaches -- 1.6 Supplemental note --

2. Algebraic fitting -- 2.1 Iterative reweight and least squares -- 2.2 Renormalization and the Taubin method -- 2.3 Hyper-renormalization and hyperls -- 2.4 Summary -- 2.5 Supplemental note --

3. Geometric fitting -- 3.1 Geometric distance and Sampson error -- 3.2 FNS -- 3.3 Geometric distance minimization -- 3.4 Hyperaccurate correction -- 3.5 Derivations -- 3.6 Supplemental note --

4. Robust fitting -- 4.1 Outlier removal -- 4.2 Ellipse-specific fitting -- 4.3 Supplemental note --

5. Ellipse-based 3-D computation -- 5.1 Intersections of ellipses -- 5.2 Ellipse centers, tangents, and perpendiculars -- 5.3 Perspective projection and camera rotation -- 5.4 3-D reconstruction of the supporting plane -- 5.5 Projected center of circle -- 5.6 Front image of the circle -- 5.7 Derivations -- 5.8 Supplemental note --

6. Experiments and examples -- 6.1 Ellipse fitting examples -- 6.2 Statistical accuracy comparison -- 6.3 Real image examples 1 -- 6.4 Robust fitting -- 6.5 Ellipse-specific methods -- 6.6 Real image examples 2 -- 6.7 Ellipse-based 3-D computation examples -- 6.8 Supplemental note --

7. Extension and generalization -- 7.1 Fundamental matrix computation -- 7.1.1 Formulation -- 7.1.2 Rank constraint -- 7.1.3 Outlier removal -- 7.2 Homography computation -- 7.2.1 Formulation -- 7.2.2 Outlier removal -- 7.3 Supplemental note --

8. Accuracy of algebraic fitting -- 8.1 Error analysis -- 8.2 Covariance and bias -- 8.3 Bias elimination and hyper-renormalization -- 8.4 Derivations -- 8.5 Supplemental note --

9. Maximum likelihood and geometric fitting -- 9.1 Maximum likelihood and Sampson error -- 9.2 Error analysis -- 9.3 Bias analysis and hyperaccurate correction -- 9.4 Derivations -- 9.5 Supplemental note --

10. Theoretical accuracy limit -- 10.1 KCR lower bound -- 10.2 Derivation of the KCR lower bound -- 10.3 Expression of the KCR lower bound -- 10.4 Supplemental note -- Answers -- Bibliography -- Authors' biographies -- Index.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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Because circular objects are projected to ellipses in images, ellipse fitting is a first step for 3-D analysis of circular objects in computer vision applications. For this reason, the study of ellipse fitting began as soon as computers came into use for image analysis in the 1970s, but it is only recently that optimal computation techniques based on the statistical properties of noise were established. These include renormalization (1993), which was then improved as FNS (2000) and HEIV (2000). Later, further improvements, called hyperaccurate correction (2006), HyperLS (2009), and hyper-renormalization (2012), were presented. Today, these are regarded as the most accurate fitting methods among all known techniques. This book describes these algorithms as well implementation details and applications to 3-D scene analysis. We also present general mathematical theories of statistical optimization underlying all ellipse fitting algorithms, including rigorous covariance and bias analyses and the theoretical accuracy limit. The results can be directly applied to other computer vision tasks including computing fundamental matrices and homographies between images. This book can serve not simply as a reference of ellipse fitting algorithms for researchers, but also as learning material for beginners who want to start computer vision research. The sample program codes are downloadable from the website: https://sites.google.com/a/morganclaypool.com/ellipse-fitting-forcomputer- vision-implementation-and-applications/.

Also available in print.

Title from PDF title page (viewed on May 13, 2016).