The document discusses the contourlet transform approach for image enhancement. It begins with the goal of capturing intrinsic geometrical structures in images. It then describes the contourlet transform's multi-resolution, multi-directional decomposition approach using a non-separable filter bank similar to wavelets. This results in a flexible multi-resolution expansion into contour segments. The approach uses a Laplacian pyramid followed by directional filter banks to decompose an image into multiple directional subbands across different scales. Directional subbands are then enhanced using weighting factors to emphasize features of interest for the final enhanced image.

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)

5. Approach
Contourlet Transform

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 ………….

10. Contourlet Transform
Laplacian Pyramid

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

14. Image Pyramid
Gaussian 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

35. Image Pyramid
Gaussian Pyramid
(Example)

36. Image Pyramid
Laplacian 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.

41. Contourlet Transform
Directional Filter
Bank

42. http://sazizi.ece.iut.ac.ir/content/accelerating-contourlet-transform
Contourlet Transform

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