1. Image Representation and Description – Representation Schemes

2. Image Representation Outline
Tasks in image representation / description
Representation scheme

3. Representing a region involves two choices:
Image Representation
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

4. Tasks in image representation / description
Choose a representation scheme
Using external characteristics – Shape properties
Boundary
Chain codes
signatures
Using internal characteristics – Regional properties (color, texture, etc.)
Pixels comprise the region
Skeleton (medial axis)
Describe the region based on the scheme
Scaling (size) invariant
Translation invariant
Rotation invariant

5. Common Representation scheme
Image Representation
Common Representation scheme
Common external representation methods are:
Chain code
Polygonal approximation
Signature
Boundary segments
Skeleton (medial axis)
We’ll discuss the first 3 and the last one.

6. Directions are coded using the numbering scheme
Image Representation
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

7. Generation of Chain Codes
Image Representation
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.

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

9. Normalization for Chain Codes
Image Representation
Normalization for Chain Codes
With respect to starting point, normalization for starting position – shape number
Make the chain code a circular sequence
Redefine the starting point which gives an integer of minimum magnitude
E.g normalized to
Normalization for rotation – first difference (FD)
Counting (in counterclockwise direction) the number of direction changes that separate two adjacent element of the code
E.g FD of a 4-direction chain code is
The first difference of smallest magnitude, E.g normalized to
Normalization for size (scaling)
Multi-scaling resampling
Altering the size of the resampling grid.

10. Image Representation
Chain codes normalization example

11. Method 2: Polygonal Approximation
Image Representation
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.

12. Minimum Perimeter Polygons
Image Representation
Minimum Perimeter Polygons
Two techniques: merging & splitting

13. Repeat the following steps:
Image Representation
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 least-square (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.

14. Image Representation
Splitting Technique
Subdivide a segment successively into two parts until a specified criterion is met.
For example

15. A 1-D functional representation of a boundary
Image Representation
Method 3: Signature
A 1-D functional representation of a boundary
Basic idea : reduce the boundary representation to a 1-D function, which might be easier to describe than a 2-D boundary
One simple approach : use the distance from the centroid to the boundary as a function of angle. It is invariant to translation, but not to rotation and scaling.
Rotation : select the farthest point from the centroid as the starting point
Scaling : normalize the function by variance

16. Image Representation
Signature (con’d)
Reduce the boundary representation to a 1D function
For example, distance vs. angle

17. For the signature just described
Image Representation
Signature (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

18. Method 4:Skeleton of a region
Image Representation
Method 4:Skeleton of a region
Use skeleton to represent a region
Skeletonizing (thinning) a region
Medial axis transformation (MAT) : for each point (p) in a region R, find its closest neighbor in the boundary (B). If it has more than one closest neighbor in B, then this point belongs to the medial axis of the region (skeleton)
Computationally expensive
Refer to pp.651 for a fast MAT algorithm for binary image

19. Skeleton of a region - example
Image Representation
Skeleton of a region - example p9 p2 p3 p8 p1 p4 p7 p6 p5
Step 1:
2<=N(p1)<=6
T(p1)=1
p2·p4·p6=0
p4·p6·p8=0
Step 2:
(a),(b) as previous
(c) p2·p4·p8=0
(d) p2·p6·p8=0

20. Common external representation methods are:
Image Representation
Summary
Common external representation methods are:
Chain code
Polygonal approximation
Signature
Skeleton (medial axis)
Descriptors ---- next lecture
Boundary descriptor
Fourier descriptor
Region descriptor

21. Signatures – Bitangent Points
Image Representation
Signatures – Bitangent Points
Graham Scan
Andrew algorithm
Barber’s Qhull algorithm
C. Orrite, J. E. Herrero, Shape matching of partially occluded curves invariant under projective transformation, Compute. Vision Image Understanding, 93(2004) 34-64