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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

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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

• 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

Computer Vision

### 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

Computer Vision

### 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

Computer Vision

Computer Vision

Computer Vision

Computer Vision

### 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

Computer Vision

### 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

• Each object has an image set

• The universal image set

Computer Vision

### 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?

• 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

• 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

• 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

• 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

• The recognition is done in the universal eigenspace

• The pose estimation is done in the object specific eigenspace

Computer Vision

Computer Vision

Computer Vision

Computer Vision

Computer Vision