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Titlebook: Ellipse Fitting for Computer Vision; Implementation and A Kenichi Kanatani,Yasuyuki Sugaya,Yasushi Kanazawa Book 2016 Springer Nature Switz

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书目名称Ellipse Fitting for Computer Vision
副标题Implementation and A
编辑Kenichi Kanatani,Yasuyuki Sugaya,Yasushi Kanazawa
视频video
丛书名称Synthesis Lectures on Computer Vision
图书封面Titlebook: Ellipse Fitting for Computer Vision; Implementation and A Kenichi Kanatani,Yasuyuki Sugaya,Yasushi Kanazawa Book 2016 Springer Nature Switz
描述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
出版日期Book 2016
版次1
doihttps://doi.org/10.1007/978-3-031-01815-2
isbn_softcover978-3-031-00687-6
isbn_ebook978-3-031-01815-2Series ISSN 2153-1056 Series E-ISSN 2153-1064
issn_series 2153-1056
copyrightSpringer Nature Switzerland AG 2016
The information of publication is updating

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Robust Fitting, case, we discuss how to remove unwanted segments, or “outliners,” that do not belong to the ellipse under consideration. In the latter case, which occurs when the segment is too short or too noisy, a hyperbola can be fit. We describe methods that force the fit to be an ellipse, although accuracy is
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Ellipse-based 3-D Computation,their images. We start with techniques for computing attributes of ellipses such as intersections, centers, tangents, and perpendiculars. then, we describe how to compute the position and orientation of a circle and its center in the scene from its image. This allows us to generate an image of the c
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Extension and Generalization,lems for computer vision applications. To illustrate this, we show two typical problems that have the same mathematical structure as ellipse fitting: computing the fundamental matrix from two images and computing the homography between two planar surface images. They are both themselves indispensabl
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Accuracy of Algebraic Fitting,essions for the covariance and bias of the solution. The hyper-renormalization procedure is derived in this framework. In order that the result directly applies to the fundamental matrix computation described in Section 7.1, we treat {itθ} and {itξ}{in{itga}} as {itn}-D vectors ({itn} = 6 for ellips
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Theoretical Accuracy Limit, “KCR lower bound,” on the covariance matrix of the solution {itθ}. The resulting form indicates that all iterative algebraic and geometric methods achieve this bound up to higher order terms in {itσ}, meaning that these are all optimal with respect to covariance. As in Chapters 8 and 9, we treat {i
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2153-1056 esults can be directly applied to other computer vision tasks including computing fundamental matrices and homographies between images. This book can serve not 978-3-031-00687-6978-3-031-01815-2Series ISSN 2153-1056 Series E-ISSN 2153-1064
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