1. Dendrochronology Sebastian Hegenbart Joachim Kerschbaumer
Dietmar Planitzer

2. Introduction Dendrochronology Motivation and target Preprocessing
Center point detection
Generating profiles and analysis

3. Dendrochronology Tree-ring dating
Analysis of tree-ring growth patterns
Annual rings of different properties depending on weather, rain, temperatur, etc. in different years
Used to date pieces of wood and when they were felled.

4. Motivation and target CT images of timber samples as input
Preprocessing for image enhancement
Skeletonizing
Detection of center point
Counting and analyzing annual rings

5. Implementation Three major steps: Preprocessing Finding the Center
Generating Profiles

6. Preprocessing Remove noise with a 3x3 Gauss filter
Local contrast enhancement
Isolate rings with a 5x5 Mexican Hat
Convert to binary with 50% threshold
Gabor Filtering
Skeletonization
Cleaning

7. Input Image

8. Local Contrast Enhancement
Adaptive algorithm from Yu & Bajaj
Operates on a 5x5 window
Computes local pixel min/max/avg values
Applies a stretching window
Applies an adaptive transfer function

9. Local Contrast Enhancement

10. Mexican Hat

11. Gabor Transformation Dennis Gábor (1946) Windowed Fourier Transform
Gaussian function as windowing function

12. Gabor Transformation contd.
Orientation 
Frequency f
Sigma (standard deviation of gaussian distribution)
Selection of sigma involves a tradeoff
Larger values: more robust to noise but more likely to create spurious rings
Smaller values:less likely produce spurious rings but less effective in removing noise

13. Gabor Transform contd. Timber CT images: Sigma = 4
3 different frequencies for detecting large,medium and small rings
Gabor Filter:

14. Gabor Transform contd.
Gabor filter applied to wood image

15. Gabor Implementation
Creation of gabor filters with different frequencies and orientations
Convolution operations with filters
Rotation from 0 to 180 degrees
Assemble output images

16. Gabor Transform

17. Gabor Transform

18. Skeletonization I Set white pixel if 4 conditions are fullfilled
Condition 1: pixel p[x,y] must presently be black. If the pixel is already white, no action needs to be taken
Condition 2: At least one of the pixels close neighbours must be white
Condition 3: the pixel must have more than one black neighbour. If it has only one, it must be the end of a line, and therefore shouldnt be removed.
Condition 4: a pixel cannot be removed if it results in its neighbours being disconnected.

19. Skeletonization II Thinning algorithm from Zhang & Suen
With improvements from Holt and Stentiford
Must guarantee that a line is exactly 1 pixel thick
Stair case removal

20. Skeletonization

21. Twig Removal Sometimes short curves (twigs) extend out of year rings
Those are artifacts of the scanning or skeletonization process
Danger of misinterpreting them as year rings
Consequently, they must be removed

22. Twig Removal Scan the image looking for T-junctions
Compute the length of all curves connected to a T-junction
A curve is a twig if its length is less a threshold
Remove the pixel which connects a twig to a year ring

23. Image Cleaner Removes short curves from the image
Those are often artifacts of the scanning process
All curves with length less a threshold are removed
This includes twigs

24. Image Cleaner Scan the image looking for curves
Trace the curve and measure its length
If the length is less a threshold, then remove it

25. Cleaned Image

26. Center point localization
Hough-Transform
Approximation by Curvature
Gradient Accumulation
Poincaré Index

27. Center point definition

28. Hough-Transform
Feature extraction technique used in digital image processing.
Used with binary images after edge detection.
The pixel space is transformed into parameter space by accumulation of all possible parameters (for a certain parameterized curve) for every edge pixel inside the pixel space.
3-Dimensional parameter space for circles.

29. Hough-Transform Figure 1. Successfull Detection
Figure 2. Failed Detection

30. Hough-Transform Summary: Complexity O(n³) Brute Force
No perfect circles
Sensitive to noise
Conclusion:
Not suited to find center in pure form

31. Approximating center by segment curvature.
Idea: Curvature increases heading to the center.
Curvature = 1 / Radius
Problems:
Need a way to calculate radius for a given Segment.

32. Approximating center by segment curvature.
Find a connected segment of pixels and follow it.
Calculate s as the euclid distance between start and end point of the circular arc.
Calculate normal Vector of AB and follow it to the next black pixel.
Validate if the pixel is part of the arc segment by following the segment to either A and B.
Calculate h as the euclid distance between the point of intersection and the center of AB.
Figure 4. Calculation of h and s.

33. Approximating center by segment curvature.
Tresholding on curvature to identify segments close to the center.
Use statistical methods to throw away stray „red“ segments.
Average segment‘s center points to estimate center.
Use hough transform on a 64 x 64 pixel window around estimated center to find the real center point.
Figure 5. Successfull Detection

34. Approximating center by segment curvature.
Summary:
works best with circular images (can use hough)
estimating center works best with a limited number of „red“ segments
twigs and distortions can fake a high curvature
requires connected segments
Conclusion:
works best combined with Hough-Transform
works best with cirular images
sensitive to twigs and cuts
Figure 6. Failed Detection

35. Gradient Accumulation
Idea: Gradients of segments point toward the center.
Problems:
Need a way to calculate the gradient for any given segment.
Need a way to evaluate the gradient‘s direction.

36. Gradient Accumulation
Gradient Calculation:
Compute Gradients either by derivative using Sobel/Prewitt Masks. (see Poincaré)
Follow line segments, identify tangent and calculate gradient from tangent.
Figure 7. Successfull Detection

37. Gradient Accumulation
Evaluating Gradient Direction:
Follow Gradient Orientation in either direction and accumulate each hit pixel in an array.
Use Maximum value inside the accumulator to identify center.
Alternatively calculate barycenter of accumulator or use box filtering.
Figure 8. Filled Accumulator

38. Gradient Accumulation
Summary:
Simple and fast
Insensitive to twigs and distortions
Finding the center inside the accumulator can be tricky
Works well with both kind of images
Conclusion:
Probably the best technique

39. Poincaré Index Used in fingerprint images to identify singularities.
Based on an Orientation image.
Idea: The total rotation of the vectors along a closed curve is 360°
Problems:
How to calculate the orientation image ?
How to average angles ?

40. Poincaré Index -1 1 -2 2 1 2 -1 -2 Generating the orientation image:
use Sobel Masks to calculate the derivatives in x and y -1 1 -2 2 1 2 -1 -2 Gx Gy
Problems with derivatives:
The derivative of a vertical line in x is 0 and vice versa
Also the derivative of a line with 45° of angle is 0

41. Poincaré Index
Solution: (Let‘s call the derivatives in x = Gx and in y = Gy )
If Gx = 0, assume a horizontal orientation (i.e. 0°)
If Gy = 0, assume a vertical orientation (i.e. 90°)
If both Gx and Gy = 0, throw the pixel away
Else calculate the orientation as:

42. Poincaré Index Averaging angles:
A single pixel orientation is not very strong, a way is needed to average pixel orientations over a window.
Angles can not be averaged arithmetically (e.g.: the angle between 175° and 5° is 0 °)
A solution to this problem is splitting the orientation into it‘s sine and cosine parts and then calculate their arithmetic mean.

43. Poincaré Index Averaging angles inside a window:
(note the division to account for 0° segments)

44. Poincaré Index
Once the orientation field is generated the poincaré index can be computed.
Care has to be taken to respect the orientation.
The Poincaré index then computes as:
Figure 9. Poincaré Index (source: Handbook of Fingerprint Recognition)
Figure 10. Orientation Field

45. Poincaré Index Figure 10. Failed Detection
Figure 11. Successfull Detection

46. Poincaré Index Summary: Tricky to implement Many practical problems
Center point accuracy depends on the size of the averaging window
Orientation accuracy depends on the size of the averaging window
Conclusion:
probably better than curvature approximation
does not work with images without a closed curve
can be modified to find -180° and 180° singularities

47. Profile Generation Trunk is scanned from the outside to the inside
Strictly along a straight line
Generating multiple profiles by going counter clockwise around the trunk
Only accept profile if the difference between year rings is less a threshold

48. Profile Generation
Scanning year rings along a straight line using the Bresenham algorithm
Scan window must be 2x1, otherwise a year ring might be missed
Profile records the distance between year rings
Profile data is normalized in the end

49. Application

50. Application

51. Standard preprocessing vs. Gabor preprocessing

52. Standard preprocessing vs. Gabor preprocessing

53. References
Handbook of Fingerprint Recognition (Maltoni,Maio,Jain,Prabhakar), 2003
An Adaptive Approach to Singular Point Detection in Fingerprint Images (Rahimi,Pakbaznia,Kasaei)
SingularPoints and Minutiae Detection in Fingerprint Images Using Principal Gabor Basis Functions (Lee,Yang,Jeng,Chen,Lin)
Gabor Filtering of Complex Hue/Saturation Images for Color Texture Classification (Palm,Keysers,Lehmann,Spitzer)
Graphic Gems (Glassner),1990
Fingerprint Matching using Gabor Filters (Munir,Javed),2004
C++ Gabor Filter Implementation, (Mian Zhou),2003

54. EOF