Texture and Image Pyramids Prof Dr Elli Angelopoulou

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

Page 2 Texture n Texture : a repeatable pattern of small elements § Stripes § Brick wall n Appearance related § Single leaf vs. foliage § Single stripe vs. the stripes on a zebra n 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 Elli Angelopoulou Texture and Image Pyramids

Page 3 Examples of Texture Elli Angelopoulou Texture and Image Pyramids

Page 4 Examples of Texture Elli Angelopoulou Texture and Image Pyramids

Page 5 Texture Filters n Sample texture filters n 2 dot filters n 6 bar filters n Original image n Squared response of each texture filter. Elli Angelopoulou Texture and Image Pyramids

Page 6 Texture Filters n Same sample texture filters n 2 dot filters n 6 bar filters n Original image at half size n Squared response of each texture filter. n Filtering was performed at coarser scale, since the filter size remained fixed but the image was half the size of the original. Elli Angelopoulou Texture and Image Pyramids

Page 7 Texture Filtering at Different Scales n Finer Scale n Enlarged coarser scale Elli Angelopoulou Texture and Image Pyramids

Page 8 The Gaussian Pyramid n Low-pass Pyramid § First smooth an image § Downsample smoothed image, typically by a factor of two. § Repeat n Each successive layer is a low-pass filtered image of the higher resolution image. Elli Angelopoulou Texture and Image Pyramids

Page 9 Gaussian Pyramid Example Elli Angelopoulou Texture and Image Pyramids

Page 10 The Laplacian Pyramid n 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. n Each successive layer stores the information lost (the error) between an expanded coarser level and its preceding finer level. n Caution: The Laplacian pyramid, does not compute the Laplacian of Gaussian (Lo. G) of an image. Elli Angelopoulou Texture and Image Pyramids

Page 11 Laplacian Pyramid Example Elli Angelopoulou Texture and Image Pyramids

Page 12 Shape from Texture n When the texture pattern is known, we can use its distortion to infer shape. n We can only compute the surface normals. The sphere on the left is projected on the image plane using perspective projection. The 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. Elli Angelopoulou Texture and Image Pyramids

Page 13 Sample Results of Shape from Texture Images courtesy of A. M. Loh Elli Angelopoulou Texture and Image Pyramids

Page 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” Elli Angelopoulou Texture and Image Pyramids