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lecture08

# lecture08 - ELEC317 Digital Image Processing Image Analysis...

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ELEC317 Digital Image Processing Lecture 8 Image Analysis 2 5. Geometric Transformations & Boundary Matching In pattern recognition & computer vision, it is important to be able to identify figures/object with different orientation, size etc. (i) Translation (ii) Scaling α (iii) Rotation [ ] [ ] 0 u n u n u + [ ] [ ] [ ] k u k U k U δ 0 + [ ] [ ] k U k U for 0 k DFT u 0 = x 0 +jy 0 1 α [ ] [ ] n u n u α [ ] [ ] k U k U α [ ] [ ] k U k U

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[ ] [ ] [ ] [ ] [ ] [ ] k U k U e k U k U e n u n u j j φ φ (iv) Reindexing Of Starting Points [ ] [ ] [ ] [ ] [ ] [ ] k n N j k n N j e k U k U e k U k U n n u n u 0 0 2 2 0 π π Invariance Properties From (i)-(iv), we see that (a) [ ] k U k=1,2,…N-1 does not change with respect to translation, starting point index, rotation. (b) [ ] k U does not change with respect to scaling Thus the above properties can be used for detection of shapes. φ ( ) φ j ue y x y j x u = + = ~ , ~ ~ ~ ~ ( ) jy x u y x + = , φ φ φ φ cos sin ~ sin cos ~ y x y y x x + = = ( ) ( ) φ φ φ φ cos sin sin cos ~ ~ y x j y x y j x + + = + ( )( ) φ φ sin cos j jy x + + = Æ φ j e u u = ~
Boundary Matching Given two boundaries u[n] & v[n] , we can decide where they are of similar shape. Normally, we will have a number of templates u 1 [n] ; u 2 [n] ; (Circle) (Square) etc So if v[n] matches with u k [n] we will know its shape. To take care of Scaling, indexing, rotation & translation, we use the following matching criteria: ( ) [ ] ( ) + = = 2 1 0 0 0 , , , 0 0 0 0 0 0 0 min , , , N n j N u u e N n v n u N u d θ θ α α θ α Origin at centroid, [ ] [ ] = = = = 1 0 1 0 0 0 N n N n n v n u 0 u 0 * 0 = = optimal u optimal value of 0 θ α j e = * 0 * θ α j e [ ] ( ) ( ) = = + = 1 0 2 1 0 0 * N n N n n u n u N n v ( ) ( )( ) ] 0 2 [ 2 2 2 = = = = = i i i i i i i i i i i y y x a y a y x y ay x c a ay x c

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1) Start with a seed (or N seeds) 2) Region growing criterion -absolute difference in gray level between seed and candidate less than 10% of difference between min. and max. gray level in entire image j i y x x x > min max * 1 . 0 -candidate must be 8-connected To obtain the seed -analyze histogram & pick centroids of clusters.
P(Ri)=false 1. split into 4 disjoint regions, for any non-homogenous region Ri. 2. merge adjacent regions R i & R j for which P(R 1 U R 2 )=true 3. stop when no further merging or splitting possible. Thus ( ) ( ) ( ) ( ) ( ) + + = = = = 2 1 0 1 0 2 1 0 0 * 0 0 min N n N n N n N n u n u N n v N n v n u d The minimum can be found by searching for N 0 =0,1,2,…N-1 Region Representation As discussed above, boundary can be used to define a region. Other region representation methods also exists, such as using the indicator function ( ) ( ) = otherwise 0 region n m, if 1 , n m u Another method is to use run length code

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A third method is using quad-tree. Here the area is divided into 4 areas. Each area is examined.
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lecture08 - ELEC317 Digital Image Processing Image Analysis...

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