Download An Invitation to 3-D Vision: From Images to Geometric Models by Yi Ma, Stefano Soatto, Jana Kosecká, S. Shankar Sastry PDF

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By Yi Ma, Stefano Soatto, Jana Kosecká, S. Shankar Sastry

Endowing machines with a feeling of imaginative and prescient has been a dream of scientists and engineers alike for over part a century. simply some time past decade, even though, has the geometry of imaginative and prescient been understood to the purpose the place this dream turns into possible, thank you additionally to the notable growth in imaging and computing undefined.

This publication addresses a vital challenge in machine imaginative and prescient -- the best way to get well three-D constitution and movement from a suite of 2-D pictures -- utilizing recommendations drawn often from linear algebra and matrix conception. the strain is on constructing a unified framework for learning the geometry of a number of photos of a 3-D scene and reconstructing geometric versions from these pictures. The ebook additionally covers suitable elements of snapshot formation, easy snapshot processing, and have extraction. The authors bridge the distance among conception and perform via supplying step by step directions for the implementation of operating imaginative and prescient algorithms and structures.

Written basically as a textbook, the purpose of this booklet is to offer senior undergraduate and starting graduate scholars in computing device imaginative and prescient, robotics, and special effects an excellent theoretical and algorithmic origin for destiny study during this burgeoning box. it really is solely self-contained with important historical past fabric coated firstly chapters and appendices, and many routines, examples, and illustrations given during the text.

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Additional resources for An Invitation to 3-D Vision: From Images to Geometric Models

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Since the triple product corresponds to the volume of the parallelepiped spanned by the three vectors, rigid-body motion also preserves volumes. • How do these properties help us describe a rigid-body motion concisely? The fact that distances and orientations are preserved by a rigid-body motion means that individual points cannot move relative to each other. As a consequence, a rigid-body motion can be described by the motion of a chosen point on the body and the rotation of a coordinate frame attached to that point.

Given a trajectory R(t) : R -+ 80(3) that describes a continuous rotational motion, the rotation must satisfy the following constraint Computing the derivative of the above equation with respect to time t and noticing that the right-hand side is a constant matrix, we obtain R(t)RT(t) + R(t)RT(t) =0 R(t)RT(t) =} = -(R(t)RT(t)f . The resulting equation reflects the fact that the matrix R(t)RT(t) E R 3x 3 is a skew-symmetric matrix. 4, there must exist a vector, say w(t) E R 3 , such that R(t)RT(t) = w(t).

V)11 = Ilvll for all free vectors v E ]R3. A map that preserves the distance is called a Euclidean transformation. In the 3-D space, the set all Euclidean transformations is denoted by E(3) . Note that preserving distances between points is not sufficient to characterize a rigid object moving in space. In fact, there are transformations that preserve distances, and yet they are not physically realizable. For instance, the map f: [Xl, X 2 , X3]T f-+ [Xl, X 2 , -X3]T preserves distances but not orientations.

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