Dendrochronology

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.

• Gabor Transformation
• 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 valuesless 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 px,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 segments 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 gradients 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

• Generating the orientation image
• use Sobel Masks to calculate the derivatives in x
  and y

-1 0 1
-2 0 2
-1 0 1
1 2 1
0 0 0
-1 -2 -1
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 (Lets 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 its 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
Standard Preprocessing
Gabor Preprocessing
52
Standard preprocessing vs. Gabor preprocessing
Standard Preprocessing
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,
  http//www.personal.reading.ac.uk/sir02mz/ (Mian
  Zhou),2003

54

• EOF