Digital Image Processing Lecture 20: Representation & Description

1. Digital Image Processing Lecture 20: Representation & Description Prof. Charlene Tsai * Materials from Gonzales chapter 11

2. Representation • After segmentation, we get pixels along the boundary or pixels contained in a region. • Representing a region involves two choices: • Using external characteristics, e.g. boundary • Using internal characteristics, e.g. color and texture

3. Common Representation • Common external representation methods are: • Chain code • Polygonal approximation • Signature • Boundary segments • Skeleton (medial axis) • We’ll discuss the first 3.

4. Method 1: Chain Codes • Represent a boundary by a connected sequence of straight-line segments of specified length and direction. • Directions are coded using the numbering scheme 4-connectivity 8 connectivity

5. Generation of Chain Codes • Walking along the boundary in clockwise direction, for every pair of pixels assign the direction. • Problems: • Long chain • Sensitive to noise • Remedies? • Resampling using larger grid spacing.

6. Resampling for Chain Codes 0766…12 (8-directional) 0033…01 (4-directional) Spacing of the sampling grid affect the accuracy of the representation

7. Normalization for Chain Codes • With respect to starting point: • Make the chain code a circular sequence • Redefine the starting point which gives an integer of minimum magnitude • E.g. 101003333222 normalized to 003333222101 • For rotation: • Using first difference (FD) obtained by counting the number of direction changes in counterclockwise direction • E.g FD of a 4-direction chain code 10103322 is 3133030 • For scaling: • Altering the size of the resampling grid.

8. Method 2: Polygonal Approximation • Approximate a digital boundary with arbitrary accuracy by a polygon. • Goal: to capture the “essence” of the boundary shape with the fewest possible polygonal segments.

9. Minimum Perimeter Polygons • Two techniques: merging & splitting

10. Merging Technique • Repeat the following steps: • Merging unprocessed points along the boundary until the least-square error line fit exceed the threshold. • Store the parameters of the line • Reset the LS error to 0 • Intersections of adjacent line segments form vertices of the polygon. • Problem: vertices of the polygon do not always correspond to inflections (e.g. corners) in the original boundary.

11. Splitting Technique • Subdivide a segment successively into two parts until a specified criterion is met. • For example

12. Method 3: Signature • Reduce the boundary representation to a 1D function • For example, distance vs. angle

13. (con’d) • For the signature just described • Invariant to translation (everything w.r.t. the centroid) • Depending on rotation and scaling • How to remove the dependence on rotation? • Selecting point farthest from the centroid • Farthest point on the eigen axis (more robust) • Using the chain code • How to remove the dependence on scaling? • Scale all functions to span the range, say, [0,1] (not very robust) • Normalize by the variance

14. Descriptors • Boundary information can be used directly, or converted into features that describe properties of a region, such as • Length of the boundary • Orientation of straight line joining its extreme points • Number of concavities in the boundary

15. Boundary Descriptors (Properties) • Length: approximated by the # of pixels • Diameter: • Basic rectangle: defined by • Major axis: the line giving the diameter • Minor axis: the line perpendicular to major axis • Eccentricity: ratio of the 2 axes

16. Fourier Descriptor • Given a set of boundary points (x0, y0), (x1, y1), (x2, y2), …,. (xK-1, yK-1). • Represent the sequence of coordinates as s(k)=[xk, yk], for k=0, 1, 2, …, K-1. • Using complex representation for each point: s(k) = xk + jyk • Advantage: reducing 2D to 1D problem

17. 1D Fourier (Review) • DFT of s(k) is • The complex coefficients a(u), for u=0,1, 2, …, K-1, are called the Fourier descriptor of the boundary • The inverse Fourier restores s(k)

18. Fourier Approximation • Using only the first P coefficients (a(u)=0 for u>P) • Please note that k still ranges from 0 to K-1 • The smaller P becomes, the more detail that is lost on the boundary • There are ways to make the descriptor insensitive to translation, rotation, and scale changes. Please refer to Gonzalez pg 658-659 for details.

19. Example

20. Region Descriptors • Simple descriptors: • Area: # of pixels in the region • Perimeter: length of its boundary • Compactness: (perimeter)2/area • Q: What shape gives the minimal compactness • Mean and median of the gray levels. • Topological descriptors: • # of holes • # of connected components

21. Summary • Common external representation methods are: • Chain code • Polygonal approximation • Signature • Descriptors • Boundary descriptor • Fourier descriptor • Region descriptor