Spatial geometry for augmented reality applications

Question

Hi,

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

Thanks!

Answer 1

Here's a good library for Augmented Reality:

ARToolKit

Ports to various platforms:

NyARToolKit

A simple but still impressive sample application using this library:

Project Marble

Answer 2

A great read is Chapter 10 of the Black Art of 3d Game Programming. All the AR/3D maths you'll ever need is there.

Once you've mastered this stuff, you'll be ready for 3d spatial projections etc, for AR/Target tracking.

Answer 3

I can't point any specific book right now, but depending on your math background I'd suggest go in this order

1. Vector and Linear algebra, intermediate level, up to matrix operation, LU decomposition, cross product.
2. Projective geometry, up to homogenious coordinates, planar homography
3. 3d graphics, viewing and projection matrix, frustum
4. Basics of image processing, thresholds, edge detection, line detection

After those 4 two you can understand rectangular marker tracking

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

After that you can understand markerless tracking

And some more advanced math which is used in cutting edge AR:

1. Understanding of basics of Lie groups and algebras
2. Statistics, robust estimators
3. Quaternions
4. Kalman filters
5. Clifford algebras (Geometric algebra) - generalization of quaternions
6. Wavelets
7. Advanced projective geometry (like trifocal tensor, 5-point algorithm)