# YUV _YC C _ Color Model by bestt571

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```									        July 13, 2007 (Class 4: 1/2007)

ENE 461 Introduction to Digital Image Processing
Werapon Chiracharit, Ph.D., ENE, KMUTT

YUV (YCbCr) Color Model
Y=R+G+B

U=B-Y
V=R-Y

Y is the lumimance (brightness)
U is the chrominance blue-luma difference
V is the chrominance red-luma difference

1
Otsu’s Thresholding
•   Probability distribution from histogram, Pi=ni/N
•   For any threshold = k for bimodal assumption
•   Frequency, ω1=Σ0→kPi and ω2=Σk+1→L-1Pi
•   Mean, µ1=Σ0→kiPi/ω1 and µ2=Σk+1→L-1iPi/ω2
Mean total, µt=ω1µ1+ω2µ2
•   Variance between classes, δ2b=ω1ω2(µ1- µ1)2
•   Variance total, δ2t= Σ0→L-1(i- µt)2Pi
•   Criterion function, η=δ2b/ δ2t
•   Choose threshold k that MAX η

Line – 1st Order Polynomial
The line from 2 points (x1,y1) and (x2,y2)
Ax + By + C = 0
Known x1, y1, x2, y2
Unknown A, B, C
Y
y2                            (x2,y2)

y1             (x1,y1)

0        x1             x2             X

2
Pseudo-Inverse Matrix
y = -(A/B)x – (C/B)
y1 = -(A/B)x1 – (C/B)
y2 = -(A/B)x2 – (C/B)

y1     = -x1 -1        A/B
y2       -x2 -1        C/B
2×1          2×2        2×1
-1
A/B = -x1 -1            y1
C/B   -x2 -1            y2
2×1         2×2        2×1

Slope – 1st Derivative

Number                         +                 -
of Pixel

+          -

0                                         255 Intensity
HISTOGRAM

3
Labeled Pixels
For X = 1:Height
For Y = 1:Weight
I(X,Y)
y-1                  y     y+1
Up                         Up
x-1      Left            Up        Right
(x-1,y-1)        (x-1,y)   (x-1,y+1)

x       Left          Here        Right
1       2       3                 (x,y-1)         (x,y)      (x,y+1)
Down                       Down
4                   5               Left           Down       Right
x+1   (x+1,y-1)        (x+1,y)   (x+1,y+1)
6       8
7

Cropping
Y               y1                   y2
0                                                x1

x2

I(x1:x2,y1:y2)

X

4
Scale-Down Interpolation
I(x′) = λ I(x1) + (1- λ) I(x2)

Intensity I(x1,y1)        Intensity                 I(x2)
0 y
1
x1
I(x1)
Pixel(x1,y1)           Y
X                                               λ    1-λ
0      x1                x2   X

Image Interpolation

X,Y                 I(X,Y′)                    X,Y+1

X′,Y′        I(X′,Y′)

X+1,Y                I(X+1,Y′)              X+1,Y+1

5
Scale-Up Interleave and Interpolation

X,Y             0             X,Y+1

0              0               0

X+1,Y            0             X+1,Y+1

Rotation
Y′
Y
Y

X
X         θ
X′

6
Rotated Axis
X′ = cosθ -sinθ X
Y′   sinθ cosθ Y
Y

X
0

Scaling              1.2y

y

0.7y
1.2x
0.7x

x

7
MATLAB Toolbox Functions
• imrotate(I,θ-degree) => counter-clockwise
• imresize(I,M-times) => M=[0,1] scale down
=> M>1 scale up
imresize(I,[height,width]) => fixed size
• zeroint(I)

No Assignment ☺

When you hear, you forget.
When you see, you remember.
When you do, you Understand.

8
Exercise
• By using no MATLAB scaling function,
rotate your image (clockwise and
anti-clockwise)
• Resize your image (smaller scaling and
enlargement)

HAVE FUN ☺

9

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