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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
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
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


One example
One Example

Computer Vision


Parametric manifolds
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


Parametric manifolds1
Parametric Manifolds

Computer Vision


Parametric manifolds2
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


Parametric manifolds3
Parametric Manifolds

Computer Vision


Parametric manifolds4
Parametric Manifolds

Computer Vision


Parametric manifolds5
Parametric Manifolds

Computer Vision


Parametric manifolds6
Parametric Manifolds

Computer Vision


Recognition and pose estimation
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



Computational issues
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


Image sets
Image Sets

  • Each object has an image set

  • The universal image set

Computer Vision


Computing eigenspace
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


How many eigenvectors to use
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


More efficient to compute eigenspace
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


Parametric eigenspace representation
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


Object s eigenspace
Object’s Eigenspace

  • Similarly, we can compute eigenvectors and representations of images of an object using its image set only

Computer Vision


More efficient recognition and pose estimation
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






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