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lecture08 - CAP5415 Computer Vision Spring 2003 Khurram...

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CAP5415 Computer Vision Spring 2003 Khurram Hassan-Shafique
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Scaled representations Big bars (resp. spots, hands, etc.) and little bars are both interesting Stripes and hairs, say Inefficient to detect big bars with big filters And there is superfluous detail in the filter kernel Alternative: Apply filters of fixed size to images of different sizes Typically, a collection of images whose edge length changes by a factor of 2 (or root 2) This is a pyramid (or Gaussian pyramid) by visual analogy
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Gaussian Pyramids Very useful for representing images Image Pyramid is built by using multiple copies of image at different scales. Each level in the pyramid is ¼ of the size of previous level The highest level is of the highest resolution The lowest level is of the lowest resolution
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Gaussian Pyramids
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A 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
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Aliasing Can’t shrink an image by taking every second pixel If we do, characteristic errors appear In the next few slides Typically, small phenomena look bigger; fast phenomena can look slower Common phenomenon Wagon wheels rolling the wrong way in movies Checkerboards misrepresented in ray tracing Striped shirts look funny on colour television
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Resample the checkerboard by taking one sample at each circle. In the case of the top left board, new representation is reasonable. Top right also yields a reasonable representation. Bottom left is all black (dubious) and bottom right has checks that are too big.
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Constructing a pyramid by taking every second pixel leads to layers that badly misrepresent the top layer
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Fourier Transform ( 29 ( 29 ( 29 ( 29 ( 29 dxdy e y x g v u y x g F vy ux i + - - - ∫ ∫ = π 2 , , , : Continuous Discrete
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Fgx , y ( 29 (29 u , v ( 29 = gx , y ( 29 e - i 2 π ux + vy ( 29 dxdy R 2 ∫∫ The Fourier Transform Represent function on a new basis Think of functions as vectors, with many components We now apply a linear transformation to transform the basis
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