Geometric Computation for Machine Vision
Machine vision is the study of how to build intelligent machines which can understand the environment by vision. Among many existing books on this subject, this book is unique in that the entire volume is devoted to computational problems, which most books do not deal with. One of the main subjects of this book is the mathematics underlying all vision problems - projective geometry, in particular. Since projective geometry has been developed by mathematicians without any regard to machine vision applications, our first attempt is to `tune' it into the form applicable to machine vision problems. The resulting formulation is termed computational projective geometry and applied to 3-D shape analysis, camera calibration, road scene analysis, 3-D motion analysis, optical flow analysis, and conic image analysis. A salient characteristic of machine vision problems is that data are not necessarily accurate. Hence, computational procedures defined by using exact relationships may break down if blindly applied to inaccurate data. In this book, special emphasis is put on robustness, which means that the computed result is not only exact when the data are accurate but also is expected to give a good approximation in the prescence of noise. The analysis of how the computation is affected by the inaccuracy of the data is also crucial. Statistical analysis of computations based on image data is also one of the main subjects of this book.
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Computational Projective Geometry 1
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3-D interpretation 3-D motion angle antisymmetric matrix approximation arbitrary axis camera rotation centre collinear conjugate coordinate system Corollary corresponding covariance matrix critical surface cross ratio decomposable defined determined edge segments eigenvalue epipolar equation error essential matrix estimated Exercise feature points finite motion focal length focus of expansion form of eq given by eq Hence IEEE Transactions image coordinates image line image origin image plane image points intersection least-squares linear machine vision matrix G motion parameters n-dimensional obtain eq optical flow orthogonal matrix orthogonal projection orthonormal system perturbation pixels planar surface point of N-vector polar presence of noise problem procedure projective geometry Proof Proposition quaternion respectively rotation matrix scene Section Show singular value decomposition smallest eigenvalue solution space line space point statistical stereo supporting plane surface normal symmetric matrix tensor Theorem Transactions on Pattern transformation unit eigenvector unit surface normal unit vector vanishing line vanishing points viewpoint