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Spatial Geometry for Augmented Reality Applications

Does anyone know any good book or web resource for the geometric and mathematical foundations of augmented reality?

Thanks!

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4 answers

Here's a good library for augmented reality:

ARToolKit

Ports to various platforms:

Nyartoolkit

A simple but still impressive sample application using this library:

Marble Project

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Excellent reading Chapter 10 on the black art of programming 3D games. All the AR / 3D math you'll ever need is there.

Once you master this material, you will be ready for 3D spatial projections, etc. to track AR / Target.

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I can’t specify any particular book right now, but depending on your mathematical background, I would suggest going in that order

  • Vector and linear algebra, intermediate level, up to matrix operations, LU decomposition, cross product.
  • Projective geometry, to homogeneous coordinates, plane homography
  • 3D graphics, viewing and projecting matrix, frustum
  • Basics of image processing, thresholds, edge detection, line detection.

After these four two you can understand the tracking of rectangular markers

  1. Calculus of many variables, Fourier transform, DFT
  2. Least square method
  3. Intermediate linear algebra, eigenvalues, eigenvectors, SVD
  4. Extended numerical methods, nonlinear least squares, Gauss-Newton, Levenberg-Marquardt
  5. Advanced image processing, blob detection SIFT / SURF / FAST
  6. Intermediate projective geometry: basic and fundamental matrices, epipolar geometry
  7. Kit adjustment

After that you can understand mirrorless tracking

And even more advanced math, which is used in the cutting edge AR:

  1. Understanding the basics of Lie groups and algebras
  2. Statistics, reliable estimates
  3. Quaternions
  4. Kalman Filters
  5. Clifford Algebras (Geometric Algebra) - A Generalization of Quaternions
  6. Bursts
  7. Extended projective geometry (e.g. trifocal tensor, 5-point algorithm)
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I would recommend the following two books. Both of them are expensive, but they contain a lot of useful materials in Projective Geometry that you need to know.

This is tough, although if you really don't want to understand the math behind it, you might want to use a third-party library, as suggested above.

Multidimensional geometry in computer vision by Hartkey and Zisserman

and

3D Computer Vision: A Geometric View from Faugeras

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