Step 1. Mark pixels for deletion if the following conditions are true. a) 2 N ( p1 ) 6 (Apply to all border pixels) p9 p2 p3 b) T(p1) =1 p8 p1 p4 c) p2 p4 p6 0 p7 p6 p5 d) p4 p6 p8 0 Step 2. Delete marked pixels and go to Step 3. Step 3. Mark pixels for deletion if the following conditions are true. a) 2 N ( p1 ) 6 (Apply to all border pixels) b) T(p1) =1 c) p2 p4 p8 0 d) p2 p6 p8 0
0. Object boundary
3. Draw a polygon
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Distance-Versus-Angle Signatures Represent an 2-D object boundary in term of a 1-D function of radial distance with respect to q.
Turn Right OK! Turn Right OK! Turn Left NOK!
Convex Hull Algorithm (cont.)
For the lower side of a convex hull 7. Put the points pn and pn-1 in a list Llower w 8. For i = n-2 down to 1 9. Do append pi to Llower 10. While Llower contains more than 2 points in Llower do not make a right turn 11. Do delete the middle point of the 12. Remove the first and the last points fro 13. Append Llower to Lupper resulting in the lis 14. Return L
Turn Left NOK! Turn Right OK! Turn Right OK!
Skeletons Obtained from thinning or skeletonizing processes
Medial axes (dash lines)
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Digital Image Processing
Chapter 11: Image Description and Representation
12 September 2007
Image Representation and Description? Objective: To represent and describe information embedded in an image in other forms that are more suitable than the image itself. Benefits: - Easier to understand - Require fewer memory, faster to be processed - More “ready to be used” What kind of information we can use? - Boundary, shape - Region - Texture - Relation between regions
T(p1) = the number of transition 0-1 in the ordered sequence p2, p3, … , p8, p9, p2. 1 p1 0 1 0 1 N(p1) = 4 T(p1) = 3
Concept:
Thinning Algorithm (cont.)
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Polygon Approximation:Splitting Techniques
1. Find the line joining two extreme points 2. Find the farthest points from the line
Object boundary (resampling)
Boundary vertices
4-directional chain code
8-directional chain code
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Boundary Segments Concept: Partitioning an object boundary by using vertices of a convex hull.
The first difference of a chain code: counting the number of direction change (in counterclockwise) between 2 adjacent elements of the code. Example: 1 2 Chain code : The first Example: difference - a chain code: 10103322 01 1 - The first difference = 3133030 2 - Treating a chain code as a 0 02 03 3 circular sequence, we get 23 1 the first difference = 33133030 20 2 The first difference is rotational 21 3 invariant.
4-directional chain code
8-directional chain code
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
Examples of Chain Codes
Convex Hull Algorithm
Input : A set of points on a cornea boundar Output: A set of points on a boundary of a c 1. Sort the points by x-coordinate to get a s For the upper side of a convex hull 2. Put the points p1 and p2 in a list Lupper wit 3. For i = 3 to n 4. Do append pi to Lupper 5. While Lupper contains more than 2 points points in Lupper do not make a right 6. Do delete the middle point of th
Step 4. Delete marked pixels and repeat Step 1 until no change occurs.
Example: Skeletons Obtained fton
(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.
3
Polygon Approximation
Represent an object boundary by a polygon
Object boundary
Minimum perimeter polygon
Minimum perimeter polygon consists of line segments that minimize distances between boundary pixels.
The First Difference of a Chain Codes
Problem of a chain code: a chain code sequence depends on a starting point. Solution: treat a chain code as a circular sequence and redefine the starting point so that the resulting sequence of numbers forms an integer of minimum magnitude.
Shape Representation by Using Chain Codes Why we focus on a boundary? The boundary is a good representation of an object shape and also requires a few memory. Chain codes: represent an object boundary by a connected sequence of straight line segments of specified length and direction.