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Algorithms and Applications in Computer Vision

Algorithms and Applications in Computer Vision. Lihi Zelnik -Manor lihi@ee.technion.ac.il Lecture 5: Pyramids. Image information occurs at all spatial scales. Image pyramids. Gaussian pyramid Laplacian pyramid. The Gaussian pyramid. Smooth with gaussians, because

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Algorithms and Applications in Computer Vision

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  1. Algorithms and Applications in Computer Vision LihiZelnik-Manor lihi@ee.technion.ac.il Lecture 5: Pyramids

  2. Image information occurs at all spatial scales

  3. Image pyramids • Gaussian pyramid • Laplacian pyramid

  4. The Gaussian pyramid • Smooth with gaussians, because • a gaussian*gaussian=another gaussian • Gaussians are low pass filters, so representation is redundant.

  5. The computational advantage of pyramids http://www-bcs.mit.edu/people/adelson/pub_pdfs/pyramid83.pdf

  6. http://www-bcs.mit.edu/people/adelson/pub_pdfs/pyramid83.pdf

  7. Gaussian pyramids used for • up- or down- sampling images. • Multi-resolution image analysis • Look for an object over various spatial scales • Coarse-to-fine image processing: form blur estimate or the motion analysis on very low-resolution image, upsample and repeat. Often a successful strategy for avoiding local minima in complicated estimation tasks.

  8. Image pyramids • Gaussian • Laplacian

  9. The Laplacian Pyramid • Synthesis • Compute the difference between upsampled Gaussian pyramid level and Gaussian pyramid level. • band pass filter - each level represents spatial frequencies (largely) unrepresented at other level.

  10. Laplacian pyramid algorithm

  11. Showing, at full resolution, the information captured at each level of a Gaussian (top) and Laplacian (bottom) pyramid. http://www-bcs.mit.edu/people/adelson/pub_pdfs/pyramid83.pdf

  12. Gaussian pyramid

  13. Laplacian pyramid

  14. Why use these representations? • Handle real-world size variations with a constant-size vision algorithm. • Remove noise • Analyze texture • Recognize objects • Label image features

  15. http://web.mit.edu/persci/people/adelson/pub_pdfs/RCA84.pdf

  16. http://www.hackerfactor.com/blog/index.php?/archives/440-The-Perfect-Blend.htmlhttp://www.hackerfactor.com/blog/index.php?/archives/440-The-Perfect-Blend.html

  17. http://www.hackerfactor.com/blog/index.php?/archives/440-The-Perfect-Blend.htmlhttp://www.hackerfactor.com/blog/index.php?/archives/440-The-Perfect-Blend.html

  18. Slide Credits • Trevor Darrell • Bill Freeman • and others, as noted…

  19. More on statistics of natural scenes • Olshausen and Field: • Natural Image Statistics and Efficient Coding, https://redwood.berkeley.edu/bruno/papers/stirling.ps.Z • Relations between the statistics of natural images and the response properties of cortical cells. • http://redwood.psych.cornell.edu/papers/field_87.pdf • Aude Olivia: • http://cvcl.mit.edu/SUNSlides/9.912-CVC-ImageAnalysis-web.pdf

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