By Yi Ma, Stefano Soatto, Jana Kosecká, S. Shankar Sastry
This publication introduces the geometry of 3D imaginative and prescient, that's, the reconstruction of 3D versions of gadgets from a suite of 2-D photos. It information the vintage concept of 2 view geometry and exhibits extra right instrument for learning the geometry of a number of perspectives is the so-called rank attention of the a number of view matrix. It additionally develops useful reconstruction algorithms and discusses attainable extensions of the idea.
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Additional info for An Invitation to 3-D Vision: From Images to Geometric Models
This result was later unified in the two papers of [Spetsakis and Aloimonos, 1990a, Spetsakis and Aloimonos, 1990b] for both the point and line cases, together with unified algorithms. An alternative derivation of the trilinear constraint for three uncalibrated images of points was suggested in [Shashua, 1994] and its equivalence to the line case was soon pointed out by [Hartley, 1995]. While early studies in multiple-view geometry often concentrated on finding out what the minimum amount of data needed for a reconstruction is, the advance of modem computer technologies has certainly changed the focus of the investigation.
0 2. 28 Chapter 2. Representation of a Three-Dimensional Moving Scene The two sets of parentheses contain the Taylor series for sin(t) and (1 - cos(t)), respectively. Thus, we have e iA = 1+ wsin(t) + w2 (1 - cos(t)). 0 Using Rodrigues' formula, it is immediate to see that if IIwll have = 1, t = 2k7r, we for all k E Z. Hence, for a given rotation matrix R E SO(3), there are infinitely many exponential coordinates w E JR3 such that eW = R. The exponential map exp : 80(3) - t SO(3) is therefore not one-to-one.
Their findings led to the current treatment of this subject, which has since been widely adopted. In this chapter, we will start with an introduction to three-dimensional Euclidean space as well as to rigid-body motions. The next chapter will then focus on the perspective projection model of the camera. Both chapters require familiarity with some basic notions from linear algebra, many of which are reviewed in Appendix A at the end of this book. Y. , An Invitation to 3-D Vision © Springer Science+Business Media New York 2004 16 Chapter 2.
An Invitation to 3-D Vision: From Images to Geometric Models by Yi Ma, Stefano Soatto, Jana Kosecká, S. Shankar Sastry