Pixel Operations: Histograms

1
Pixel Operations Histograms
8x8 picture, 3 bits 8 levels
intensity
n,x hist(G(),(07))
Frequency (pels)
Probability (freq/64)
0
7
0
0
2
2
6
6
6
6
25
2
2
2
2
6
6
6
6
0
0
6
6
7
7
7
7
0
3
3
0
6
6
7
15
Freq.
6
6
6
6
7
7
7
7
0
1
1
0
7
7
7
7
5
0
0
1
1
7
7
7
7
7
7
7
7
7
7
7
7
0
1
2
3
4
5
6
7
7
Intensity Level
2
Real Histogram 8 bit pic
784
1088
latex
3
Histogram Equalisation
i
Levels
H(i)
Target H(i)
m
To have 16 pels at intensity 1, take all from
I1,2 and 8 from I 3 and map onto intensity 1
because H(1) H(2) 8 16 To have 16 pels at
intensity 2 Take remainder (21-8)13 at level 3,
add to 3 from level 4 So intensity mapping is
1,2,3 -gt 1 3,4 -gt2 etc etc
latex
4
Hist. Equalisation with CuF
i
Levels
H(i)
CuF(i)
Target H(i)
m
Target CuF(i)
m
Resulting transformation
5
Histogram Equalisation
Matlab imadjdemo Try it
6
About that storyboard problem
Shot 1
Shot 2
Shot 3
Shot 4
Cut 1
Cut 2
Cut 3
7
Using Histograms
60
61
62
63
64
65
Frame Index
8
Detecting cuts using Histograms
n
64
H
64
n-1
18
18/64 gt 28 change
9
Detecting cuts using Histograms
10
Histograms better than Frame difference
Frame Difference
Histograms
11
The demo again just to remind you
Back to latex
12
Primitive functions in 2D
h
u(h,k)
h
(0,0)
k
(h,k)
d
(h-1,k-1)
d
(h,k-1)
d
k
Plan
Latex
13
Convolution in 2D
0
p(0,0)
p(0,1)
0
0
0
0
0
p(1,0)
p(1,1)
-1
.2
0
0
1
2
3
Input Image
.3
.5
0
0
4
5
6
I(h,k)
Impulse Response
p(h,k)
0
0
7
8
9
0
0
0
0
0
p(1,0)
p(1,1)
At each output Pixel overlay, find products then
add
0
Flip Impulse Response
p(0,0)
p(0,1)
n1 -h n2 -k
0
0
0
0
0
-1
0
0
0
0
g(h,k)
0
0
0
0
0
0
0
14
Convolution in 2D
0
p(0,0)
p(0,1)
0
0
0
0
0
p(1,0)
p(1,1)
-1
.2
0
0
1
2
3
Input Image
.3
.5
0
0
4
5
6
I(h,k)
Impulse Response
p(h,k)
0
0
7
8
9
0
0
0
0
0
p(1,0)
p(1,1)
At each output Pixel overlay, find products then
add
0
Flip Impulse Response
p(0,0)
p(0,1)
n1 -h n2 -k
0
0
0
0
0
-1
0
0
-.8
0
0
g(h,k)
0
0
0
0
0
0
0
15
Convolution in 2D
0
p(0,0)
p(0,1)
0
0
0
0
0
p(1,0)
p(1,1)
-1
.2
0
0
1
2
3
Input Image
.3
.5
0
0
4
5
6
I(h,k)
Impulse Response
p(h,k)
0
0
7
8
9
0
0
0
0
0
p(1,0)
p(1,1)
At each output Pixel overlay, find products then
add
0
Flip Impulse Response
p(0,0)
p(0,1)
n1 -h n2 -k
0
0
0
0
0
-1
0
0
-.8
Filter mask
0
0
g(h,k)
0
0
-3.1
0
0
0
0
0
Latex
16
Image Extension for boundary conditions
Zero extension
Image
Periodic Extension
Extension by reflection
Latex
17
Convolution identities
f(h,k)
Associativity
p(h,k) () g(h,k)
f(h,k)

Distributivity
18
Causality (examining impulse response support)
Non Causal
Output Location of mask
Causal
Filter Support
Semi-Causal
Latex
Or Causal if TV Raster used as causality reference
19
Filtering as a matrix operation
H is Block Diagonal, Symmetric
If i is extended using a periodic extension, then
H becomes circulant
Latex