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CV_2_Pyramids and Multiscale representations

Mohammed Hachama
March 01, 2025
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CV_2_Pyramids and Multiscale representations

Mohammed Hachama

March 01, 2025
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  1. Computer vision Image pyramids and multiscale representations (Week 2) NHSM

    - 4th year - Spring 2025 - Prof. Mohammed Hachama [email protected] http://hachama.github.io/home/
  2. Gaussian Scale-space Gaussian multiscale analysis • A continuous representation where

    an image is analyzed at different levels of blur (scale) L(x, y, σ) = I(x, y) ⋆ G(x, y, σ) NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 4/8
  3. Gaussian Scale-space Gaussian multiscale analysis • A continuous representation where

    an image is analyzed at different levels of blur (scale) L(x, y, σ) = I(x, y) ⋆ G(x, y, σ) NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 4/8
  4. Gaussian Scale-space Gaussian multiscale analysis • A continuous representation where

    an image is analyzed at different levels of blur (scale) L(x, y, σ) = I(x, y) ⋆ G(x, y, σ) NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 4/8
  5. Gaussian Scale-space Gaussian multiscale analysis • A continuous representation where

    an image is analyzed at different levels of blur (scale) L(x, y, σ) = I(x, y) ⋆ G(x, y, σ) NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 4/8
  6. Image Pyramids Image Pyramids • 1. Gaussian pyramid • 2.

    Laplacian pyramid • 3. Steerable Pyramid NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 5/8
  7. Gaussian Pyramid Gaussian Pyramid • Gaussian filtering as anti-aliasing filters

    • Details get smoothed out as we move to higher levels • Only mostly large uniform regions in the original image are preserved at the higher levels • Image reconstruction from the pyramid: Not possible NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 6/8
  8. Gaussian Pyramid Application 1: Template matching NHSM - 4th year:

    Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 6/8
  9. Gaussian Pyramid Applications • Multi-Scale Image Representation and Analysis •

    Scale-Invariant Image Features • Image Compression (Progressive Encoding and transmission) • Efficient Image Processing (Reducing Computation) • Optical Flow and Motion Estimation: track motion from coarse to fine resolution. • Prevents large displacements from being missed when only analyzing the full-resolution image • Deep Learning NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 6/8
  10. Laplacian Pyramid Laplacian Pyramid • Retain the residuals instead of

    the blurred images themselves NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 7/8
  11. Laplacian Pyramid Laplacian is a Bandpass Filter NHSM - 4th

    year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 7/8
  12. Laplacian Pyramid Laplacian is a Bandpass Filter NHSM - 4th

    year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 7/8
  13. Laplacian Pyramid Laplacian is a Bandpass Filter NHSM - 4th

    year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 7/8
  14. Laplacian Pyramid Constructing a Laplacian Pyramid NHSM - 4th year:

    Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 7/8
  15. Laplacian Pyramid Application 1: Image Blending • Blend two images

    smoothly by decomposing them into Gaussian and Laplacian pyramids, blending them at each level, and then reconstructing the final blended image. NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  16. Laplacian Pyramid Application 1: Image Blending • Blend two images

    smoothly by decomposing them into Gaussian and Laplacian pyramids, blending them at each level, and then reconstructing the final blended image. NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  17. Laplacian Pyramid Application 1: Image Blending • Blend two images

    smoothly by decomposing them into Gaussian and Laplacian pyramids, blending them at each level, and then reconstructing the final blended image. NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  18. Laplacian Pyramid Application 1: Image Blending NHSM - 4th year:

    Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  19. Laplacian Pyramid Application 1: Image Blending NHSM - 4th year:

    Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  20. Laplacian Pyramid Application 1: Image Blending • When blending two

    images directly, sharp edges at the boundary can be noticeable. By blending low-frequency components smoothly and high-frequency details selectively, the transition between images becomes natural. • The blending mask is also pyramidal, meaning it changes smoothly across scales. This ensures that low-frequency components are blended over a larger region, while high-frequency details are only blended near the boundary. NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  21. Laplacian Pyramid Application 1: Image Blending NHSM - 4th year:

    Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  22. Laplacian Pyramid Application 2: Image compression • Quantize Laplacian coefficients

    to reduce precision (e.g., rounding to integers). • Higher levels (coarser details) tolerate aggressive quantization, while finer levels require finer quantization to preserve details. NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  23. Laplacian Pyramid Application 2: Eulerian Video Magnification • Enhances small

    variations in color and motion • Pulse detection: monitoring tiny skin color changes due to blood flow • Breathing analysis: amplifying chest movements. • Material deformation detection: visualizing tiny vibrations in structures. NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8
  24. Laplacian Pyramid Application 2: Eulerian Video Magnification • Laplacian pyramid

    to separate different frequency bands. • Pixel values are filtered over time to enhance (by a factor ×α) specific frequency ranges (e.g., heartbeats at 0.5–1.5 Hz). NHSM - 4th year: Computer vision - pyramids (Week 2) - M. Hachama ([email protected]) 8/8