Dendrochronology Sebastian Hegenbart Joachim Kerschbaumer Dietmar Planitzer

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

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.

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

Implementation Three major steps: Preprocessing Finding the Center Generating Profiles

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

Input Image

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

Local Contrast Enhancement

Mexican Hat

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

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

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

Gabor Transform contd. Gabor filter applied to wood image

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

Gabor Transform

Gabor Transform

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.

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

Skeletonization

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

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

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

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

Cleaned Image

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

Center point definition

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.

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

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

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.

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.

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

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

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.

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

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

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

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 ?

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

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:

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.

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

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

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

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

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

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

Application

Application

Standard preprocessing vs. Gabor preprocessing

Standard preprocessing vs. Gabor preprocessing

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

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