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1. Lecture 12

2. Object boundary (resampling) Boundary vertices 4-directional chain code 8-directional chain code Boundary Descriptors Chain Codes & Shape Numbers

3. The chain code of boundary depends on the starting point. The shape number of a boundary, generally based on 4-directional Freeman chain codes, is defined as the first difference of smallest magnitude. The order n of a shape number is defined as the number of digits in its representation. Chain code can be made insensitive to the starting point by using circular sequence and the integer of minimum magnitude to rotations that are multiples of 90 o ) by using the first difference of the code, called shape number. Size normalization can be achieved by adjusting the size of the resampling grid. Boundary Descriptors Chain Codes & Shape Numbers

4. Ch12-p.368 Chain code: 0 3 0 3 2 2 1 1 Circular list: 0 3 0 3 2 2 1 1 0 c i +1 - c i : 3 -3 3 -1 0 -1 0 -1 ( c i +1 - c i ) mod 4: 3 1 3 3 0 3 0 3 Min magnitude: 0 3 0 3 3 1 3 3 (normalized) Chain code: 0 3 3 2 2 1 0 1 Circular list: 0 3 3 2 2 1 0 1 0 c i +1 - c i : 3 0 -1 0 -1 -1 1 -1 ( c i +1 - c i ) mod 4: 3 0 3 0 3 3 1 3 Min magnitude: 0 3 0 3 3 1 3 3 (normalized) Therefore shape number of both images is 03033133 of order 8 Boundary Descriptors Chain Codes & Shape Numbers: Example

5. Boundary Descriptors Chain Codes & Shape Numbers: Exercise

6. Boundary Descriptors Chain Codes & Shape Numbers: Example Circular chain code: 0 0 0 0 3 0 0 3 2 2 3 2 2 2 1 2 1 1 0 First difference mod 4: 0 0 0 3 1 0 3 3 0 1 3 0 0 3 1 3 0 3 Shape No. 0 0 0 3 1 0 3 3 0 1 3 0 0 3 1 3 0 3 1. Original boundary 2. Find the smallest rectangle that fits the shape 3. Create grid 4. Find the nearest grid

7. Convert a boundary segment into 1D graph View a 1D graph as a PDF function Compute the n th order moment of the graph Definition: the n th moment where Boundary segment 1D graph Example of moment: The first moment = mean The second moment = variance Statistical Moments

8. Purpose: to describe regions or “areas” 1. Some simple regional descriptors (discussed above) - area of the region - length of the boundary (perimeter) of the region - Compactness where A ( R ) and P ( R ) = area and perimeter of region R 2. Topological Descriptors 3. Texture 4. Moments of 2D Functions Example: a circle is the most compact shape with C = 1/4 p Regional Descriptors

9. White pixels represent “light of the cities” % of white pixels Region no. compared to the total white pixels 20.4% 64.0% 4.9% 10.7% Infrared image of America at night Regional Descriptors Examples

10. Used to describe holes and connected components of the region Euler number ( E ): C = the number of connected components H = the number of holes Regional Descriptors Topological

11. Regional Descriptors Topological E = -1 E = 0 Euler Formula V = the number of vertices Q = the number of edges F = the number of faces E = -2

12. Regional Descriptors Topological: Example Original image: Infrared image Of Washington D.C. area After intensity Thresholding (1591 connected components with 39 holes) Euler no. = 1552 The largest connected area (8479 Pixels) (Hudson river) After thinning

13. Regional Descriptors Texture Purpose: to describe “texture” of the region, e.g., optical microscope images. Superconductor (smooth texture) Cholesterol (coarse texture) Microprocessor (regular texture) A B C