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Exploring Texture and Image Pyramids in Computer Vision

This presentation by Prof. Dr. Elli Angelopoulou delves into the concepts of texture and image pyramids in computer vision. Texture, defined as a repeatable pattern of small elements, can be observed in various natural forms—such as stripes, brick walls, and foliage. The talk introduces texture filters, the Gaussian pyramid, and the Laplacian pyramid, explaining their roles in multi-scale image processing. By analyzing texture, we can infer shape using surface normals. The material is based on slides from D. A. Forsyth's "Computer Vision: A Modern Approach."

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Exploring Texture and Image Pyramids in Computer Vision

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  1. Texture and Image Pyramids Prof. Dr. Elli Angelopoulou Chair of Pattern Recognition (Computer Science 5) Friedrich-Alexander-University Erlangen-Nuremberg

  2. 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

  3. Examples of Texture

  4. Examples of Texture

  5. Texture Filters • Sample texture filters • 2 dot filters • 6 bar filters • Original image • Squared response of each texture filter.

  6. 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.

  7. Texture Filtering at Different Scales • Finer Scale • Enlarged coarser scale

  8. 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.

  9. Gaussian Pyramid Example

  10. 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.

  11. Laplacian Pyramid Example

  12. 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.

  13. Sample Results of Shape from Texture Images courtesy of A.M. Loh

  14. 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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