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Outline

Outline. H. Murase, and S. K. Nayar, “Visual learning and recognition of 3-D objects from appearance,” International Journal of Computer Vision, vol. 14, pp. 5-24, 1995. Basic Ideas.

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Outline

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  1. Outline • H. Murase, and S. K. Nayar, “Visual learning and recognition of 3-D objects from appearance,” International Journal of Computer Vision, vol. 14, pp. 5-24, 1995.

  2. Basic Ideas • Each 3-D object of interest is represented by views under different poses and illuminations (possibly other conditions) • The view, or the appearance of a 3-D object depends on the object’s shape, reflectance properties, pose (viewing angle), and the illumination conditions (lighting conditions) Computer Vision

  3. One Example Computer Vision

  4. Parametric Manifolds • All the possible images of a 3-D object under different view angles form a curve in a high dimensional image space Computer Vision

  5. Parametric Manifolds Computer Vision

  6. Parametric Manifolds • If we change the view angle and the lighting conditions, all the images of a 3-D object form a 2-D manifold in the high dimensional image space Computer Vision

  7. Parametric Manifolds Computer Vision

  8. Parametric Manifolds Computer Vision

  9. Parametric Manifolds Computer Vision

  10. Parametric Manifolds Computer Vision

  11. Recognition and Pose Estimation • The recognition is achieved by finding the manifold that has the minimum distance to the input image, which is done by Computer Vision

  12. Recognition and Pose Estimation Computer Vision

  13. Computational Issues • Since the images are of high dimensional, it is computationally expensive to perform the minimization • The solution is to perform dimension reduction using principal component analysis Computer Vision

  14. Image Sets • Each object has an image set • The universal image set Computer Vision

  15. Computing Eigenspace • For the universal set, we first compute the average of all of the images • Then we form a new set by subtracting the average from all the images • Then we compute the covariance matrix • We obtain eigenvectors and corresponding eigenvalues Computer Vision

  16. How Many Eigenvectors to Use? • One way to select the first k eigenvectors with largest eigenvalues to capture appearance variations in the image set Computer Vision

  17. More Efficient to Compute Eigenspace • When the number of images is much smaller than the dimension of an image, we can compute the eigenvectors and eigenvalues more efficiently Computer Vision

  18. Parametric Eigenspace Representation • After we compute the eigenvectors, we project all the images by • The representations of an object should form a manifold • Which is approximated using a standard cubic-spline interpolation algorithm Computer Vision

  19. Object’s Eigenspace • Similarly, we can compute eigenvectors and representations of images of an object using its image set only Computer Vision

  20. More Efficient Recognition and Pose Estimation • The recognition is done in the universal eigenspace • The pose estimation is done in the object specific eigenspace Computer Vision

  21. Recognition and Pose Estimation Results for Object Set 1 Computer Vision

  22. Real-Time Recognition System Computer Vision

  23. Real-Time Recognition System Computer Vision

  24. Real-Time Recognition System Computer Vision

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