September 28, SEGMENTATION ITERATIVE ALGORITHMS HOUGH TRANSFORM

September 28, ITERATIVE ALGORITHMS ON IMAGES Start with an initial image. Apply a rule which transforms individual pixel grey values according to neighboring grey values. At each step reapply this same rule. After ‘alot’ of iterations the effect of this rule on the resulting image should be negligible and the iterations are said to converge. FOR k=0 to 999 IMAGE = F( IMAGE ) k+1 k

September 28, ITERATIVE ALGORITHMS ON IMAGES A general example of the form of an iterative rule at the (k+1)st iteration: I1 I2 I3 I4 I0 I5 I6 I7 I8 Local Image Neighborhood I0 = F (I1,I2,I3,I4,I5,I6,I7,I8,I0 ) k+1 k k k k k k k k k As a purely illustrative example, the convolution operation is an example of an iterative rule

September 28, DISCRETE CONVOLUTION Template ‘Kernel’ T1 T2 T3 T4 T5 T6 T7 T8 T9 I1 I2 I3 I4 I5 I6 I7 I8 I9 Image I = T1 x I1 + T2 x I2 + T3 x I3 + T4 x I4 + T5 x I5 + T6 x I6 + T7 x I7 + T8 x I8 + T9 x I9 3x3 Template Local Image Neighborhood

September 28, ITERATIVE ALGORITHMS ON IMAGES Specific simple example of an iterative procedure on an image SUCCESSIVE CONVOLUTION AVERAGING (Caveat: This is an illustrative example and not necessarily useful) What Happens ?? ANSWER: Successive blurring at each iteration until eventually after a certain number of iterations the image becomes a constant grey value equal to the average of all pixels.

September 28, ITERATIVE ALGORITHMS ON IMAGES SOMETHING MORE USEFUL SIMULATED ANNEALING RELAXATION LABELING

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9 GRAYLEVEL HISTOGRAM PIXEL GRAYVALUE # OF PIXELS

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September 28, HOUGH ALGORITHM Choose an analytic form f(x,y,a1,a2,…,an) and choose a range of values for parameters a1, a2, a3,….,an. Create accumulator array A(a1,a2,…,an) which represents direct match of f(x,y,a1,a2,…,an) with binary image. Local for local maximum which exceeds certain threshold.

September 28, GENERALIZED HOUGH ALGORITHM (Xc,Yc)  R-TABLE    1 2 n r1,r2,…,,rn