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(11)(11) Representation and DescriptionRepresentation and Description

- Low-level image processing* Image enhancement, restoration, transformation

Image ImageEnhancement

EnhancedImage

Restored/Transformed

ImageRestoration/Transformation

- Mid-level image processing (image understanding)* Object representation, description

Restored/Transformed

ImageImageSegmentation

SegmentedImage

Representation/Description/Features

Object

Representation/Description

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- High-level image processing (recognition and interpretation)* Object recognition, interpretation of object relationships

ObjectRecognition

Objects

Meaning/

RelationshipsImageInterpretation

Representation/Description/

Features

(a)(a) Chain codeChain code

- Chain codes: represent a boundary by a connected sequence of straight-line segments of specified length and direction* Choose an appropriate grid to approximate objects

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0

3

2

1

4-direction: 8-direction:

04

1

2

3

56

7

2

0 0

3

3

3

3

3

3

22

12

1

1

10

01

1

07

6

6

6

5

53

3

2

1

2

20

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* Chain code (clockwise): 4-direction: 00333332322121110101, 8-direction: 07666553321202

* Problem 1: different starting points result in different chain codes# Solution: normalization redefine the starting point such that the chain

code forms a smallest number# E.g.: 6553320000 0000655332

* Problem 2: object rotation results in different chain codes# Solution: difference code coding with the difference of directions

(counter-clockwise)

# E.g.: 0000655332 0006706076 0006706076 (normalization)

(b)(b) Polygonal approximationPolygonal approximation

- Polygonal approximation: approximate a boundary using a polygon

- Minimum perimeter polygons* Choose an appropriate grid The boundary is enclosed by a set of concatenated cells

* Allow the boundary to shrink as a rubber band

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- Merging techniques

1. Merge points along a boundary until the least square error line fit ofthe points merged so far exceeds a threshold

2. Record the the two end point of the line3. Repeat Steps 1 and 2 until all boundary points are processed

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- Splitting techniques

Subdivide a boundary segment successively into two parts until aspecified criterion is satisfied

1. Find two points on the boundary that are farthest away and draw a line

Splitting line divides the boundary into two boundary segments2. For each boundary segment, find a point on the boundary that has a

maximum perpendicular distance to its corresponding line

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3. Draw two lines joining the point and the two end points, respectively,of the corresponding splitting line Subdivide the boundary segment into two parts

4. Repeat Steps 2~3 until the perpendicular distance is less than a

threshold

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(c)(c) SignatureSignature

- Signature: a 1D functional representation of a boundary* Plot the distance from the centroid to the boundary as a function of

angles:signature = r(), = 0 ~ 2

(d)(d) Boundary descriptorsBoundary descriptors

- Descriptions of boundary

* Perimeter: length of the chain code* Diameter: maxi,j(D(pi,pj))

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pi

pj

Ma= max

i,j(D(p

i,p

j))

Ma

ma

and forms a

basic rectangle

Ma

ma

* Major axis (Ma) and minor axis (ma)* Eccentricity: Ma/ma

- MATLAB p = bwperim(bw, conn): find perimeter pixels* bw: binary image* conn: 4 or 8 (connectivity)* Perimeter pixels: 1-valued pixels that are connected to at least one 0-

valued pixels* p

: returned perimeter binary image- MATLAB S = diameter(L): find descriptions of a boundary

* L: a labeled image

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* S: a structure with the following fields# S.Diameter, S.MajorAxis, S.MinorAxis, S.BasicRectangle

(e)(e) Regional descriptorsRegional descriptors

- Compactness: perimeter2/area

- Topological: Euler number,E= C H (number of connected component number of holes)

E= 1 3 = 2 E= 1 1 = 0 E= 1 2 = 1

- MATLAB D = regionprops(L, properties)

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* L: labeled image* Properties: 'Area', 'BoundingBox', 'Centroid'* D: a structure with the fields specified when invoking regionprops( )

* E.g., D.Area

- Texture* Statisticcal approaches

* Intensity mean: m=i=0

L1

zip zi ,

* nth moment about the mean: n=

i=0L1

zimnpzi

Moment Expression Description

Mean m=i=0L1

zipzi Measure of average intensity

Standard deviation =zz=2

Measure of average contrast

Smoothness R = 11/(1+2

) Measure of smoothness of intensity

Third moment 3=i=0L1

zim3pzi Measure of skewness of the

histogram; 0: symmetric, positive:skewed to the right; negative:

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skewed to the left

Uniformity U=i=0

L1

p2zi Measure of uniformity; maximum: all

graylevels are equal

Entropy e=i=0

L1

pzi log2 zi Measure of randomness

* Sprectral approach: based on Fourier spectrum* Structural approach: structure of the texture primitives

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(f)(f) High-level image processingHigh-level image processing

- High-level image processing (computer vision)* Recognition and interpretation

* Object recognition: identify objects based on object models* Interpretation: using artificial intelligence to infer the following

# Properties of objects: identity, size, material, 2D/3D position, orientation# Relationships among objects: occlusion, relative position

Further inference: planning of path, operations, control

- Applications: robotics, industrial automatic inspection, autonomousnavigation, document image analysis, bio-information recognition

11-13