9Image Pyramids Known as a Gaussian Pyramid [Burt and Adelson, 1983] In computer graphics, a mip map [Williams, 1983]A precursor to wavelet transform
10Gaussian pyramid construction filter maskRepeatFilter (keep filter the same size)Subsample (by a factor of two)Until minimum resolution reachedcan specify desired number of levels (e.g., 3-level pyramid)Total number of pixels in pyramid?1 + ¼ + 1/16 + 1/32…….. = 4/3 Over-complete representation
11A bar in the big images is a hair on the zebra’s nose; in smaller images, a stripe; in the smallest, the animal’s nose
12What are they good for? Improve Search Pre-computation Compression Search over translationsClassic coarse-to-fine strategySearch over scaleTemplate matchingE.g. find a face at different scalesPre-computationNeed to access image at different blur levelsUseful for texture mapping at different resolutions (called mip-mapping)CompressionCapture important structures with fewer bytesDenoisingModel statistics of pyramid sub-bandsImage blending
13= * Gaussian pyramid Pixel domain Gaussian pyramid image Overcomplete representation. Low-pass filters, sampled appropriately for their blur.
21Can we reconstruct the original? Need this!interpolateinterpolateinterpolate
22The Laplacian Pyramid Synthesis Analysis preserve difference between upsampled Gaussian pyramid level and Gaussian pyramid levelband pass filter - each level represents spatial frequencies (largely) unrepresented at other levelsAnalysisreconstruct Gaussian pyramid, take top layer