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Chapter 3: A Feature Saliency Descriptor for Registration and Pose Recovery 29After the recovery of the motion parameters, 3D points are reconstructed throughrobust triangulation from matches in two or more images. In addition to the two viewscase, extensive work was done recently on computing the relationship betweenmultiple views within the framework of projective geometry [Hartley00][Faugeras01].In these cases relations between the views are described by multi-linear algebraicstructures such as the 4trilinear tensor used for three images.3.2.2 SFM without CorrespondencesWe outlined earlier (literature review section) Dellaert’s approach to the recovery ofcamera motion without prior knowledge of point correspondences [Deallert00]. Wewill describe here a different approach that we developed to address this problem[Boughorbel03]. The idea behind our method is based on the following facts: (1) Ifthe 3D pose parameters, relating two perspective views of a scene are at hand, it isknown that we can use the epipolar geometry (Fig. 3.3) to constrain the search forcorrespondences to a line search. At the correct camera pose the structurereconstructed from these matches (using for example window based matching) will beclose to the actual scene geometry, although it can be noisy. (2) If we are far from thecorrect pose parameters, relying on the epipolar geometry will lead to false matchessince the search for correspondences will be done in the wrong area (Fig. 3.4). In thiscase, the reconstruction will be close to a random cloud of points.Fig. 3.5 shows the reconstructed structure, resulting from edge-based matching, as therelative rotation parameter ϕ xis moved away from its correct value. The set oftriangulated 3D points is exhibiting the expected increasing disorder. The key toexploiting this fact for pose estimation is to quantify how structured the set of points is.Or to use another term how salient a set of points is.
Chapter 3: A Feature Saliency Descriptor for Registration and Pose Recovery 30(a)Fig. 3.4. The search for a match for the point in the left (a) image is limited by the epipolarconstraints to a line search. For the correct pose parameters we are more likely to find thecorrect match (lower point in (b)). But in the case of wrong pose parameters the matchingprocess leads to wrong correspondences (upper point in (b)). (Images from CVPR01 calibratedtest dataset, http://vision.cse.psu.edu/cvpr2001/main1.html).(b)(a) (b) (c) (d)Fig. 3.5. The degradation of the structure reconstructed from the images of Fig. 3.4 (from. (a)to (d)) as we move away from the correct pose parameters.
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Bibliography 144BIBLIOGRAPHY[Anders
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Bibliography 146[Chiba98] N. Chiba
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Bibliography 148[Fruh01] C. Früh,
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Bibliography 150[Jebara99] T. Jebar
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Bibliography 152IEEE International
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Bibliography 154[Schmid00] C. Schmi
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Bibliography 156[Wollny02] G. Wolln
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