Download Image-Based Modeling by Long Quan PDF

By Long Quan

“This booklet courses you within the trip of 3D modeling from the speculation with dependent arithmetic to purposes with attractive 3D version images. Written in an easy, hassle-free, and concise demeanour, readers will examine the cutting-edge of 3D reconstruction and modeling.” —Professor Takeo Kanade, Carnegie Mellon college

About this ebook:

  • The desktop imaginative and prescient and pictures groups use varied terminologies for a similar ideas
  • This books offers a translation, allowing pictures researchers to use imaginative and prescient options, and vice-versa
  • Independence of chapters permits readers to without delay leap right into a particular bankruptcy of curiosity
  • Compared to different texts, offers extra succinct therapy total, and focuses totally on imaginative and prescient geometry

Image-Based Modeling is for graduate scholars, researchers, and engineers operating within the components of desktop imaginative and prescient, special effects, photo processing, robotics, digital fact, and photogrammetry.

About the writer: lengthy Quan is a Professor of the dept of machine technology and Engineering on the Hong Kong college of technological know-how and know-how. He obtained a Ph.D. measure in desktop technology from INRIA, and has been a CNRS researcher at INRIA. Professor Quan is a Fellow of the IEEE computing device Society.

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Extra resources for Image-Based Modeling

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Fs ∈ k[x1 , . . , xn ], then I = f1 , . . , fs is an ideal of k[x1 , . . , xn ], generated by f1 , . . fs . The ideal I generated by fi = 0 consists of all polynomial consequences of the equations fi = 0. Intuitively, the solutions of the ideal is the same as those of the generating polynomials. Definition. The variety V (f1 , . . , fs ) ∈ kn is the set of all solutions of the system of equations f1 = f2 = . . = fs = 0, V = {(a1 , . . , an ) ∈ kn : fi (a1 , . . , an ) = 0 for all 1 ≤ i ≤ s}.

2 Projective geometry 13 The 2D projective plane The projective plane is the most convenient space to introduce concepts and describe properties. Points. • The homogeneous coordinates of a point on a projective plane are x = (x1 , x2 , x3 )T . • The points at infinity are those characterized by (x1 , x2 , 0)T , or x3 = 0, which is the line at infinity. There is one point at infinity per direction. • Three points (non-collinear) define a projective basis. The coordinates of the basis points can be chosen arbitrarily as long as they are independent, the simplest possible ones are called the canonical or standard coordinates of the basis points, which are: (1, 0, 0), (0, 1, 0), (0, 0, 1) and (1, 1, 1).

Cf. 6). Equivalently, this is to say that the corresponding points in two views and the point in space are on the same plane! This is the coplanarity constraint, from which all the geometries of two views are derived. A point in one view generates a line in the other view, which we call the epipolar line. The geometry is called the epipolar geometry. The line connecting the two camera centers intersect with each image plane at a point, which we call the epipole. In other words, the epipole in one view is the image of the other camera center.

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