Texture and Image Pyramids
Prof. Dr. Elli AngelopoulouChair of Pattern Recognition (Computer Science 5)
Friedrich-Alexander-University Erlangen-Nuremberg
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Elli Angelopoulou Texture and Image Pyramids
Texture
Texture : a repeatable pattern of small elements Stripes Brick wall
Appearance related Single leaf vs. foliage Single stripe vs. the stripes on a zebra
Texture can be formed by: The presence of a large number of small objects
Pebbles Coffee beans
Orderly patterns that look like large numbers of small elements Spots on cats Grains on wooden surfaces
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Elli Angelopoulou Texture and Image Pyramids
Examples of Texture
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Elli Angelopoulou Texture and Image Pyramids
Examples of Texture
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Elli Angelopoulou Texture and Image Pyramids
Texture Filters
Sample texture filters 2 dot filters 6 bar filters
Original image
Squared response of each texture filter.
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Elli Angelopoulou Texture and Image Pyramids
Texture Filters
Same sample texture filters 2 dot filters 6 bar filters
Original image at half size
Squared response of each texture filter.
Filtering was performed at coarser scale, since the filter size remained fixed but the image was half the size of the original.
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Elli Angelopoulou Texture and Image Pyramids
Texture Filtering at Different Scales
Finer Scale
Enlarged coarser scale
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Elli Angelopoulou Texture and Image Pyramids
The Gaussian Pyramid
Low-pass Pyramid First smooth an image
Downsample smoothed image, typically by a factor of two.
Repeat
Each successive layer is a low-pass filtered image of the higher resolution image.
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Elli Angelopoulou Texture and Image Pyramids
Gaussian Pyramid Example
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Elli Angelopoulou Texture and Image Pyramids
The Laplacian Pyramid
Band-pass Pyramid Given a Gaussian (or other lowpass) pyramid
Store the difference between adjacent levels. Lowest resolution image must be first upsampled via some form of interpolation to allow for pixel-wise difference computation.
Each successive layer stores the information lost (the error) between an expanded coarser level and its preceding finer level.
Caution: The Laplacian pyramid, does not compute the Laplacian of Gaussian (LoG) of an image.
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Elli Angelopoulou Texture and Image Pyramids
Laplacian Pyramid Example
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Elli Angelopoulou Texture and Image Pyramids
Shape from Texture
When the texture pattern is known, we can use its distortion to infer shape.
We can only compute the surface normals.
The sphere on the left is projected on the image plane using perspective projection. The one on the right using orthographic projection.
Texture images courtesy of J.T. Todd, L. Thaler, T.M.H. Dijkstra, J.J. Koenderink, and A.M.L. Kappers.
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Elli Angelopoulou Texture and Image Pyramids
Sample Results of Shape from Texture
Images courtesy of A.M. Loh
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Elli Angelopoulou Texture and Image Pyramids
Most of the material in this presentation is based on the slides by D. A. Forsyth for his book “Computer Vision - A Modern Approach”
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