Image pyramid

Pyramid, or pyramid representation, is a type of multi-scale signal representation developed by the computer vision, image processing and signal processing communities, in which a signal or an image is subject to repeated smoothing and subsampling. Pyramid representation is a predecessor to scale-space representation and multiresolution analysis.

1. SITARAMBHAI NARANJI PATEL INSTITUTE OF TECHNOLOGY & RESEARCH CENTER,UMRAKH 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

5. Gaussian Pyramid Frequency Composition

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 ( 2 N+1 )x( 2 N+i ) GAUSSIAN PYRAMID

8. Output: Images g0, g1,…, gN-1 where the size of g i is: ( 2 N-i +1)x( 2 N-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.

10. Gaussian – Image filter

11. LAPLACIAN PYRAMID Laplacian have decomposition based on difference-of-lowpass filters. The image is recursively decomposed into low-pass and highpass bands. G , G 1 , .... = the levels of a Gaussian Pyramid. Predict level G l from level G l +1   by expanding  G l +1  to G’ l Denote by L l the error in prediction: L l = G l – G’ l L  , L 1 , .... = 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

14. LAPLACIAN PYRAMID Frequency Composition

15. LAPLACIAN -- Image filter

16. Reconstruction of the original image from the Laplacian Pyramid

17. APPLICATIONS Image Blending and Mosaicing

18. Blending Apples and Oranges

19. Pyramid blending of Regions

20. Image Fusion Multi-scale Transform (MST) = Obtain Pyramid from Image Inverse Multi-scale Transform (IMST) = Obtain Image from Pyramid

21. Thank You