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SUBJECT -: FUNDAMENTAL OF IMAGE PROCESSING (2181102)
TOPIC -: IMAGE PYRAMIDS
FACUTLY -: Dr.SALMAN R. BOMBAYWALA
PEN NO. -: 170490111005
BRANCH -: ELECTRONICS AND COMMUNICATION ENGINEERING
Outlines :-
Gaussian Pyramid
 Laplacian Pyramid
 Applications
IMAGE PYRAMIDS
Image Pyramid = Hierarchical representation of an image
Low Resolution
High Resolution
No details in image
(blurred image)
Low frequencies
Details in image
Low+high frequencies
A collection of images at different resolutions.
GAUSSIAN PYRAMID
The Gaussian Pyramid: It is representation of images in multiple scales
Gaussian Pyramid Frequency
Composition
GAUSSIAN PYRAMID
 Applicatons:
• Scale invariant template
matching (like faces)
• Progressive image
transmission
• Image blending
• Efficient feature search
The goal is to define a representaton in which image informaton at different
scales is explicitly available (i.e. does not need to be computed when needed)
 The elements of a Gaussian Pyramids are smoothed copies of the
image at different scales.
 Input: Image I of size (2N+1)x(2N+i)
GAUSSIAN PYRAMID
 Output: Images g0, g1,…, gN-1
where the size of gi is: (2N-i+1)x(2N-i+1)
GAUSSIAN PYRAMID
Working
The "pyramid" is constructed by repeatedly calculating a weighted average of the
neighboring pixels of a source image and scaling the image down. It can be visualized
by stacking progressively smaller versions of the image on top of one another. This
process creates a pyramid shape with the base as the original image and the tip a
single pixel representing the average value of the entire image.
Gaussian – Image filter
LAPLACIAN PYRAMID
• Laplacian have decomposition based on difference-of-lowpass filters.
• The image is recursively decomposed into low-pass and highpass
bands.
• G0, G1, .... = the levels of a Gaussian Pyramid.
• Predict level Gl from level Gl +1 by expanding Gl +1 to G’l
• Denote by Ll the error in prediction: Ll = Gl – G’l
• L0 , L1, .... = the levels of a Laplacian Pyramid.
LAPLACIAN PYRAMID
 Laplacian of Gaussian can be
approximated by the difference
between two different
Gaussians
LAPLACIAN PYRAMID
 We create the Laplacian pyramid from the Gaussian
pyramid using the formula below :
g0, g1,…. are the levels of a Gaussian pyramid
L0, L1,…. are the levels of a Laplacian pyramid
LAPLACIAN PYRAMID Frequency
Composition
LAPLACIAN -- Image filter
Reconstruction of the original image from the
Laplacian Pyramid
APPLICATIONS
Image Blending and Mosaicing
Blending Apples and Oranges
Pyramid blending of Regions
Image Fusion
 Multi-scale Transform (MST) = Obtain Pyramid from Image
 Inverse Multi-scale Transform (IMST) = Obtain Image from Pyramid
Thank You

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Image pyramid

  • 1. SUBJECT -: FUNDAMENTAL OF IMAGE PROCESSING (2181102) TOPIC -: IMAGE PYRAMIDS FACUTLY -: Dr.SALMAN R. BOMBAYWALA PEN NO. -: 170490111005 BRANCH -: ELECTRONICS AND COMMUNICATION ENGINEERING
  • 2. Outlines :- Gaussian Pyramid  Laplacian Pyramid  Applications
  • 3. IMAGE PYRAMIDS Image Pyramid = Hierarchical representation of an image Low Resolution High Resolution No details in image (blurred image) Low frequencies Details in image Low+high frequencies A collection of images at different resolutions.
  • 4. GAUSSIAN PYRAMID The Gaussian Pyramid: It is representation of images in multiple scales
  • 6. GAUSSIAN PYRAMID  Applicatons: • Scale invariant template matching (like faces) • Progressive image transmission • Image blending • Efficient feature search The goal is to define a representaton in which image informaton at different scales is explicitly available (i.e. does not need to be computed when needed)
  • 7.  The elements of a Gaussian Pyramids are smoothed copies of the image at different scales.  Input: Image I of size (2N+1)x(2N+i) GAUSSIAN PYRAMID
  • 8.  Output: Images g0, g1,…, gN-1 where the size of gi is: (2N-i+1)x(2N-i+1) GAUSSIAN PYRAMID
  • 9. Working The "pyramid" is constructed by repeatedly calculating a weighted average of the neighboring pixels of a source image and scaling the image down. It can be visualized by stacking progressively smaller versions of the image on top of one another. This process creates a pyramid shape with the base as the original image and the tip a single pixel representing the average value of the entire image.
  • 11. LAPLACIAN PYRAMID • Laplacian have decomposition based on difference-of-lowpass filters. • The image is recursively decomposed into low-pass and highpass bands. • G0, G1, .... = the levels of a Gaussian Pyramid. • Predict level Gl from level Gl +1 by expanding Gl +1 to G’l • Denote by Ll the error in prediction: Ll = Gl – G’l • L0 , L1, .... = the levels of a Laplacian Pyramid.
  • 12. LAPLACIAN PYRAMID  Laplacian of Gaussian can be approximated by the difference between two different Gaussians
  • 13. LAPLACIAN PYRAMID  We create the Laplacian pyramid from the Gaussian pyramid using the formula below : g0, g1,…. are the levels of a Gaussian pyramid L0, L1,…. are the levels of a Laplacian pyramid
  • 16. Reconstruction of the original image from the Laplacian Pyramid
  • 20. Image Fusion  Multi-scale Transform (MST) = Obtain Pyramid from Image  Inverse Multi-scale Transform (IMST) = Obtain Image from Pyramid