ece542-11 - ECE542-11 Digital Image Processing 9-...

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1 ECE542-11 Digital Image Processing 9- Morphological Image Processing-II Dr. Z. Aliyazicioglu Cal Poly Pomona Electrical & Computer Engineering 1 Cal Poly Pomona Electrical & Computer Engineering Office 9-143 Some Basic Morphological Algorithms Boundary Extraction The boundary of a set A can be obtained by first eroding A by B and then performing the set difference between A and its erosion Where B is a suitable structure element D(u,v) diat () ( ) AA A B  a) Set A b) Structuring element B ECE542 - 10 2 Cal Poly Pomona c) A eroded by B d) Boundary, given by the set difference between a and its erosion
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2 Example: A simple binary image, with 1’s represented in white Result of using Boundary extraction with the structure element B ECE542 - 10 3 Cal Poly Pomona Region Filling Based on set dilations, complementation and intersection a) Set A b) Complement of A c) Structuring element B d) Initial point inside the boundary X 0 e) Various steps of ECE542 - 10 4 Cal Poly Pomona (i) Final result 1 ( ) 1,2,3,. .. c kk XX B A k 
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3 Example a) Binary Image (the white dot inside one of the regions is starting point for the region-filling algorithm) b Result of filling that region b) c) Result of filling all region ECE542 - 10 5 Cal Poly Pomona Extraction of connected components Extraction of connected components in a binary image. Y represent a connected represent a connected contained in a set A and assume that a point p of is known The expression all the elements of Y Where X = and B is suitable 1 () 1 , 2 , 3 , . . . kk XX B A k  ECE542 - 10 6 Cal Poly Pomona Where 0 and is suitable structure element If k = k-1 , the algorithm has converged and we let = k
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4 Example a) X-ray Image b) Threshold image c) Image eroded with a 5x5 structuring elements of 1’s d) Number of pixel in the connected components of c ECE542 - 10 7 Cal Poly Pomona Convex hull A set A is said to be convex if the straight line segment joining any two points in lies entirely within . The convex hul H of an arbitrary set S is the smallest convex set The convex hull of an arbitrary set is the smallest convex set containing . The set difference - is called the convex deficiency of If B i , i=1,2,3,4 represent the four structuring elements The representation is ( ) 1,2,3,4 and 1,2,3,. .. ii i kk XX B A i k  ECE542 - 10 8 Cal Poly Pomona Where X i 0 =A. Now The convex hull of A is (When ) 4 1 () i i CA D i i convergence DX 1
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5 Example a) Structuring elements b) Set A c) Result of convergence with the structuring elements d) . e) . f) . g) Convex hull Convex hull showing the ECE542 - 10 9 Cal Poly Pomona h) Convex hull showing the contributing of each structuring element Thinning The thinning of A by a structuring element B () A BA AB AA B   C A sequence of structuring elements Where B i is a rotated version of B i-1 Defining thinning by a sequence of structure elements as 123 { } { , , ,..., } n BB B 12 {} ( ( ( ( ) ) ) n AB A B B B   ECE542 - 10 10 Cal Poly Pomona
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This note was uploaded on 10/24/2010 for the course ECE 542 taught by Professor Zeki during the Spring '10 term at Cal Poly Pomona.

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ece542-11 - ECE542-11 Digital Image Processing 9-...

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