Representation image
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This document discusses various techniques for representing and describing images for image processing and segmentation. It covers chain codes, polygonal approximations using minimum perimeter polygons and merging/splitting techniques, signatures which provide a 1D functional representation of boundaries, boundary segments to extract information from concave parts of objects, and skeletons which reduce regions to graphs by obtaining medial axis transformations. It also provides examples of thinning algorithms used to obtain skeletons by iteratively deleting contour points while ensuring the overall shape is preserved.
![• 2nd pass
• Conditions (a) and (b) are the same as the 1st pass
• (c) and (d) are different [call these (c’) and (d’)]:
– (c’) p2 * p4 * p8 = 0
– (d’) p2 * p6 * p8 = 0
• Delete all points that are flagged from the 2nd pass
Repeat 1st pass and 2nd pass until no contour point is deleted
during an iteration
p4p8
p2
p2
p6
p8](https://image.slidesharecdn.com/representationimage-151210211848/85/Representation-image-22-320.jpg)
Representation image
- 1. Representation and Description for image Processing
- 2. Segmentation Raw data (pixels) Representations Computation of descriptors external characteristics (boundary) internal characteristics (pixels comprising the region) shape characteristics regional properties such as color & texture
- 4. Chain Codes Polygonal Approximations – Minimum perimeter polygons – Merging techniques – Splitting techniques Signatures Boundary Segments Skeletons Technique of representation
- 5. Chain Codes Problem1: - Long chains of codes - Easily disturbed by noise, and sidetracked Solution: - Resampling using larger grid spacing Problem2: - start point Solution: - Normalizations Before resample: 000000766…1111 After resampling: 076666…12
- 6. • normalized – circular sequence – Ex. First difference of 4-direction chain code 10103322 is 3133030. – 2 10103322 – 33133030
- 8. Polygonal Approximations • Determine which points on the boundary to use • Minimum perimeter polygons o Choose an appropriate grid - The boundary is enclosed by a set of concatenated cells o Allow the boundary to shrink as a rubber band The maximum error per grid cell is √2d, where d is the dimension of a grid cell
- 10. Merging Techniques • least square error line fit 1. Merge points along a boundary until the least square error line fit of the points merged so far exceeds a threshold 2. Record the the two end point of the line 3. Repeat Steps 1 and 2 until all boundary points are processed .
- 12. problem • Merging technique problem: – No guarantee for corner detection • Solution: – Splitting: to subdivide a segment successively into two parts until a given criterion is satisfied. – Objective: seeking prominent inflection points.
- 13. Splitting techniques: 1. Start with an initial guess, e.g., based on majority axes 2. Calculate the orthogonal distance from lines to all points 3. If maximum distance > threshold, create new vertex there 4. Repeat until no points exceed criterion
- 15. Signatures • Signature: a 1D functional representation of a boundary • To generate: – Plot the distance from the centroid to the boundary as a function of angles. • The signature is often unique for a region – We can distinguish the region by its signature • Independent of translation, but not rotation & scaling .
- 17. • r(ϴ)= D/cos ϴ 0<= ϴ<60 • = D/cos(120- ϴ) 60<= ϴ<120 • = D/cos(180- ϴ) 120<= ϴ<180 • = D/cos(240- ϴ) 180<= ϴ<240 • = D/cos(300- ϴ) 240<= ϴ<300 • = D/cos(360- ϴ) 300<= ϴ<360
- 19. Boundary segments • The boundary can be decomposed into segments. – Useful to extract information from concave تقعر parts of the objects. • A good way to achieve this is to calculate the convex Hull of the region enclosed by the boundary Hull • Can be a bit noise sensitive 1. Smooth prior to Convex hull calculation 2. Calculate Convex Hull on polygon approximation
- 20. Skeletons • To reduce a plane region to a graph - by e.g. obtaining the skeleton of the region via thinning. • Find medial axis transformation (MAT): The MAT of region R with border B is found as: • For each point p in R, we find its closest neighbor in B. • If p has more than one such neighbor, it belongs to the Medial Axis.
- 21. • Assume foreground pixels = “1” , Background = “0” • 1st pass Flag a contour point p for deletion if the following conditions are satisfied: • (a) 2 <= N(p1) <= 6 • (b) T(p1) = 1; • (c) p2 * p4 * p6 = 0 11.1.1 • (d) p4 * p6 * p8 = 0 N(p1) is the number of nonzero neighbors of p1 T(p1) is the number of 0-1 transitions in the ordered sequence of p2, p3, . . . , p8, p9,p2. If (a) – (d) are not violated, the point is marked for deletion • Points are not deleted until the end of the pass • This way the data stays intact until the pass is complete Thinning Algorithm 0 0 1 1 p1 0 1 0 1 p2 p4 p6 p4 p6 p8
- 22. • 2nd pass • Conditions (a) and (b) are the same as the 1st pass • (c) and (d) are different [call these (c’) and (d’)]: – (c’) p2 * p4 * p8 = 0 – (d’) p2 * p6 * p8 = 0 • Delete all points that are flagged from the 2nd pass Repeat 1st pass and 2nd pass until no contour point is deleted during an iteration p4p8 p2 p2 p6 p8
- 23. Examples NO NO
- 24. • In the first case • N(p) = 5, S(p) = 1, p2 · p4 · p6 = 0, and p4 · p6 · p8 = 0, then p is flagged for deletion. • In the second case • N(p) = 1, so( 2 :5 N(p,) <0 6) is violated and p is left unchanged. • In the third case • p2 · p4 · p6 = 1 and p4 · p6 · p8 = 1, so conditions (p2 · p4 · p6 = 0) and (p4 · p6 · p8 = 0) violated and p is left unchanged. • In the forth case • S(p) = 2, so condition (T ( p l) = 1) is violated and p is left unchange