Contents Edge Linking and Boundar Detection
3 Edge Linking z Local processing link all points in a local neighbourhood (33, 55, etc.) that are considered to be similar similar response strength of a gradient operator similar direction of the gradient vector
3 Edge Linking z Local processing link all points in a local neighbourhood (33, 55, etc.) that are considered to be similar similar response strength of a gradient operator similar direction of the gradient vector z Global processing Hough transform
3 Edge Linking z Hough Transform a method for finding global relationships between piels eample: finding straight lines in an image appl edge enhancing filter (e.g., Laplace) set a threshold for deciding what is a true edge piel etract the piels that are on a straight line using the Hough transform original image edge enhanced image thresholded edge image
3 Edge Linking z Hough Transform i = a i + b b = -a i + i b a -space ab- or parameter space
3 Edge Linking z Hough Transform divide parameter space into accumulator cells A(p,q) initalise all cell values A(p,q) = 0 for all selected piels ( i, i ) in the image for all a-values a p ("draw a line in ab-space") calculate the corresponding b-value b q = -a p i + i increment accumulator value A(p,q) A(p,q) + 1 A(p,q) = Q Q points in -space ling on the line = a p + b q compleit = (number of a-increments) (number of points) result: the largest value A(p',q') = ma{a(p,q)} gives the line connecting the largest number of piels
3 Edge Linking z Hough Transform in realit we have a problem with =a+b because a reaches infinit for vertical lines use instead different variations of the Hough transform can also be used for finding other shapes of the form g(v,c)=0 cos sin v is a vector of coordinates c is a vector of coefficients possible to find an kind of simple shape e.g., circle: (3D parameter space) ( c ) ( c ) c 1 3
3 Edge Linking z Hough Transform Eample 5 points points of intersection A line through 1, 3, 5 B line through, 3, 4
3 Edge Linking z Hough Transform-based Edge Linking compute the image gradient threshold the image gradient specif subdivisions in the space eamine the counts of accumulator cells for high piel concentrations eamine continuit between the piels in a cell continuit tpicall based on computation of the distance between disconnected piels identified during traversal of a set of piels according to a given accumulator cell
3 Edge Linking z Hough Transform-based Edge Linking aerial infrared image thresholded gradient Hough transform set of piels in the 3 ma. accumulator cells linked over gaps < 6 piels
3 Edge Linking z Hough Transform-based Edge Linking from http://www.cs.tu-bs.de/rob/lehre/bv/hnf.html
3 Edge Linking z Hough Transform-based Edge Linking 7 maima from http://www.cs.tu-bs.de/rob/lehre/bv/hnf.html
3 Edge Linking z Hough Transform-based Edge Linking 7 maima from http://www.cs.tu-bs.de/rob/lehre/bv/hnf.html
Contents Thresholding
4 Thresholding z Global based on some kind of histogram: gre-level, edge, feature etc. lighting conditions are etremel important, will onl work under ver controlled circumstances fied threshold (the same value is used in the whole image) z Local (or Adaptive Thresholding) depends on the position in the image the image is divided into overlapping sections which are thresholded one b one
4 Thresholding z Global Thresholding Histograms to love and to hate
4 Thresholding z Global Thresholding Illumination solutions calibration of the imaging sstem measure illumination pattern g on a white reflective surface normalize images f obtained b dividing through g local/adaptive thresholding use a percentile filter with ver large mask to estimate illumination
4 z Thresholding Automatic Thresholding Algorithm 1. select an initial estimate for T. segment the image using T which produces groups: z G1, piels with value >T and G, with value <T 3. compute µ 1 and µ as average piel value of G 1 and G 4. new threshold: T=1/(µ 1 +µ ) 5. repeat steps to 4 until T stabilizes ver eas + ver fast assumptions: normal dist. + low noise
4 Thresholding z Automatic Thresholding
4 Thresholding z Optimal Thresholding based on the shape of the image histogram foreground background miture T miture distribution p(z) = P 1 p 1 (z) + P p (z) if P 1 = P then optimum threshold is at T
Thresholding z Otsu s Method Maimize between-class variance (10.3.3 GW) Based on the histogram (L-1 gre levels) Find Threshold k for which η is maimized: 4 1 0 1 1 ) ( ) ( L i i G G G G B G B p m i m m P m m P 1 1 0 1 1 1 0 ) ( 1 ) ( ) ( 1 ) ( L k i i k i i L i i G p i k P k m p i k P k m p i m
4 Thresholding T z Adaptive Thresholding
4 Thresholding z Chow-Kaneko Method subdivide image into overlapping regions test bimodalit for each region fit a bimodal Gaussian to the histograms of the bimodal regions select optimal threshold for each bimodal region compute thresholds for the non-bimodal regions b interpolating the thresholds of the bimodal regions interpolate thresholds for each piel ( nd interpolation) can ield ecellent results
4 Thresholding z Remarks on Thresholding problem: can leave holes in segmented objects solution: post-processing with morphological operators thresholding is a special case of piel classification classes: 0 or 1 (above or below threshold) z Histogram Improvement Using Boundar Information determine edges using the image gradient and Laplacian discard piels not on an edge (gradient < threshold) derive segmentation threshold from a histogram of the edge piels (gradient > threshold) similar height of histogram peaks for object and background peaks tend to be better separated (deeper valles)