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)
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Computer Vision

3. One Example
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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
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Computer Vision

5. Parametric Manifolds
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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
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Computer Vision

7. Parametric Manifolds
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Computer Vision

8. Parametric Manifolds
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Computer Vision

9. Parametric Manifolds
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Computer Vision

10. Parametric Manifolds
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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
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Computer Vision

12. Recognition and Pose Estimation
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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
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Computer Vision

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

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

21. Recognition and Pose Estimation Results for Object Set 1
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22. Real-Time Recognition System
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23. Real-Time Recognition System
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24. Real-Time Recognition System
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Computer Vision