![Image Pyramid Gaussian Pyramid
Gaussian Pyramid
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g1 = REDUCE[gL-1]
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4.Do& Martion- Contourlet transform (Backup side-4)
- 1. Contourlet Transform Photo Source: http://commons.wikimedia.org/wiki/File:Contourlet_Transform_Double_Filter_Bank.jpg Department of Computer Science And Engineering Shahjalal University of Science and Technology Nashid Alam Registration No: 2012321028 annanya_cse@yahoo.co.uk Masters -2 Presentation (Paper Reading Backup Slides# 5)
- 3. Contourlet Transform GOAL Capture the intrinsic geometrical structure -A key feature in visual information (Dealing with enhancement.) Natural images are not simply stacks of 1-D piecewise smooth scan-lines; Discontinuity points (i.e. edges) are typically located along smooth curves (i.e. contours) owing to smooth boundaries of physical objects. Thus, natural images contain intrinsic geometrical structures
- 4. Contourlet Transform Main challenge Exploring geometry in images: - Duo to discrete nature of the data. --All we human can see is continuous --Image is discrete (Sampling and Quantization)
- 6. Contourlet Transform Approach starts with : 1.Constructing a discrete-domain : -Multiresolution and Multidirectional expansion -using non-separable filter banks (in much the same way that wavelets are derived from filter banks) This construction results : flexible multiresolution, and directional Image expansion (using contour segments) Thus it is named the contourlet transform. The concept of wavelet: University of Heidelburg Approach
- 7. flexible multiresolution • Multi resolution means that the same image content is available in two or more sizes (resolutions). L:M2workM2-implementation5.CT_realization(to_compare_with_NSCT) Original Image (mdb252.jpg) Contourlet Coefficients in multiresolution images (mdb252.jpg) More details on multiresolution Is provided in Laplacian pyramid concept Upcoming Slide ApproachContourlet Transform
- 8. Contourlet Transform Approach Decomposes The Image Into Several Directional Subbands And Multiple Scales
- 9. The CASCADE STRUCTURE allows: - The multiscale and directional decomposition to be independent - Makes possible to: Decompose each scale into any arbitrary power of two's number of directions(22=4, 23=8, 24=16, …) Contourlet Transform The CT is implemented by: Laplacian pyramid followed by directional filter banks (Fig-01) Input image Bandpass Directional subbands Bandpass Directional subbands Figure 01: Structure of the Laplacian pyramid together with the directional filter bank The concept of wavelet: University of Heidelburg Figure 01 Decomposes The Image Into Several Directional Subbands And Multiple Scales Approach Details ………….
- 11. Image Pyramid
- 12. Image Pyramid Content Courtesy: Prof.Mubarak Shah, PhD Director of the Center for Research in Computer Vision, UCF resolution (different in resolution)
- 13. Image Pyramid
- 15. Image Pyramid Gaussian Pyramid
- 16. Image Pyramid Gaussian Pyramid
- 17. Image Pyramid Gaussian Pyramid
- 18. Image Pyramid Gaussian Pyramid Gaussian Pyramid g0 = IMAGE g1 = REDUCE[gL-1] g0 g1 g2 0
- 19. Image Pyramid Gaussian Pyramid
- 20. Image Pyramid Gaussian Pyramid
- 21. Image Pyramid Gaussian Pyramid
- 22. Image Pyramid Gaussian Pyramid
- 23. Image Pyramid Gaussian Pyramid
- 24. Image Pyramid Gaussian Pyramid
- 25. Image Pyramid Gaussian Pyramid
- 26. Image Pyramid Gaussian Pyramid
- 27. Image Pyramid Gaussian Pyramid
- 28. Image Pyramid Gaussian Pyramid
- 29. Image Pyramid Gaussian Pyramid
- 30. Image Pyramid Gaussian Pyramid
- 31. Image Pyramid Gaussian Pyramid
- 32. Image Pyramid Gaussian Pyramid
- 33. Image Pyramid Gaussian Pyramid
- 34. Image Pyramid Gaussian Pyramid
- 37. Image Pyramid Laplacian Pyramid
- 38. Image Pyramid Laplacian Pyramid
- 39. Contourlet Transform Concept To perform multiscale decomposition we have applied LP : for generating a down sample version of the original image at each decomposition level. See paper page: 3 Sub-topic: Pyramid frames Each pyramid level creates only one bandpass image : without generating any scrambled frequencies; Pyramidal decomposition: In our approach we have only down sampled the low pass channel to get rid of this effect. which happens in the wavelet filter bank when: A highpass channel, after down sampling, is folded back into the low frequency band.
- 43. Contourlet Transform Concept Figure :The contourlet filter bank. Multiscale decomposition into octave bands is computed -by applying Laplacian pyramid and then a directional filter bank is used to each bandpass channel.
- 44. Contourlet Transform Approach Enhancement of the Directional Subbands
- 45. This DBF is implemented by using a k-level binary tree decomposition that leads to 2k subbands with wedge shaped frequency partition as shown (b). (a) (b) Frequency partitioning (l= 3, 2l = 8) wedge shaped frequency subbands. Directional filter bank. (a) Frequency partitioning: where l = 3 and there are 23 = 8 real wedge-shaped frequency bands. Subbands 0–3 correspond to the mostly horizontal directions, while subbands 4–7 correspond to the mostly vertical directions. (a) (b) Contourlet Transform Enhancement of the Directional Subbands
- 46. Contourlet Transform Concept See paper page: 4 Sub-topic: Iterated directional filter banks C. Directional filter bank
- 47. (a) Main image (b) Smooth Image (LP at highest level) (c) Contourlet coefficient at level 2 Contourlet Transform Example
- 48. Contourlet Transform Example (d) Contourlet coefficient (Horizontal direction) (e) Contourlet coefficient at (Vertical direction)
- 49. Contourlet Transform Example (f) Contourlet coefficient Angular direction (-60,-45, 45, 60)
- 50. (a) Main image Contourlet Transform Example
- 51. Contourlet Transform Decomposes The Image Into Several Directional Subbands And Multiple Scales Approach Figure 01: (a)Structure of the Laplacian pyramid together with the directional filter bank (b) frequency partitioning by the contourlet transform (c) Decomposition levels and directions. Input image Bandpass Directional subbands Bandpass Directional subbands Details…. Denote Each subband by yi,j Where i =decomposition level and J=direction (a) (b) (c)
- 52. Contourlet Transform Approach Enhancement of the Directional Subbands The processing of an image consists on: -Applying a function to enhance the regions of interest. In multiscale analysis: Calculating function f for each subband : -To emphasize the features of interest -In order to get a new set y' of enhanced subbands: Each of the resulting enhanced subbands can be expressed using equation 1. )(' , , jiyfjiy ………………..(1) -After the enhanced subbands are obtained:- The inverse transform is performed: to obtain an enhanced image. Denote Each subband by yi,j Where i =decomposition level and J=direction Details….More in main slide #56
- 53. Enhancement of the Directional Subbands Details…. The directional subbands are enhanced using equation 2. )( ,jiyf )2,1(,1 nnW jiy )2,1(,2 nnW jiy If bi,j(n1,n2)=0 If bi,j(n1,n2)=1 ………..(2) Denote Each subband by yi,j Where i =decomposition level and J=direction W1= weight factors for detecting the surrounding tissue W2= weight factors for detecting microcalcifications (n1,n2) are the spatial coordinates. bi;j = a binary image containing the edges of the subband Weight and threshold selection techniques are presented on upcoming slides Contourlet Transform Approach
- 54. Enhancement of the Directional Subbands The directional subbands are enhanced using equation 2. )( ,jiyf )2,1(,1 nnW jiy )2,1(,2 nnW jiy If bi,j(n1,n2)=0 If bi,j(n1,n2)=1 ………..(2) Binary edge image bi,j is obtained : -by applying an operator (prewitt edge detector) -to detect edges on each directional subband. In order to obtain a binary image: A threshold Ti,j for each subband is calculated. Contourlet Transform Approach
- 55. Image in different subbands