Multiple View Geometry in Computer Vision by Richard Hartley

By Richard Hartley

A uncomplicated challenge in desktop imaginative and prescient is to appreciate the constitution of a true international scene. This publication covers proper geometric ideas and the way to symbolize items algebraically to allow them to be computed and utilized. fresh significant advancements within the thought and perform of scene reconstruction are defined intimately in a unified framework. Richard Hartley and Andrew Zisserman supply accomplished history fabric and clarify easy methods to follow the equipment and enforce the algorithms. First variation HB (2000): 0-521-62304-9

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Just as the fundamental matrix is determined by the two camera matrices, and determines them up to projective transformation, so in three views, the trifocal tensor is determined by the three camera matrices, and in turn determines them, again up to projective transformation. Thus, the trifocal tensor encapsulates the relative projective geometry of the three cameras. For reasons that will be explained in chapter 15 it is usual to write some of the indices of a tensor as lower and some as upper indices.

The algorithm given here is an outline only, and each part of it is examined in detail in this book. The algorithm should not be implemented directly from this brief description. 4 Three-view geometry In the last section it was discussed how reconstruction of a set of points, and the relative placement of the cameras, is possible from two views of a set of points. The reconstruction is possible only up to a projective transformation of space, and the corresponding adjustment to the camera matrices.

9, a projectivity is defined in terms of a coordinate-free geometric concept of point line incidence. An equivalent algebraic definition of a projectivity is possible, based on the following result. 10. A mapping h : IP2 —• IP2 w a projectivity if and only if there exists a non-singular 3 x 3 matrix H such that for any point in IP2 represented by a vector x it is true that h(x) = Hx. To interpret this theorem, any point in IP2 is represented as a homogeneous 3-vector, x, and Hx is a linear mapping of homogeneous coordinates.

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