Xiaochun Cao [email protected]
1
CAP5415 Computer Vision
Assignment # 5
1. Proof:
2. Proof:
Since:
So
(1)
(
)
( )( )
nnnn
nnn
mmnmx
xnmmn
−+=−
+
=
+
++
++
11
11
1
1 (2
=
=n
iin x
n
m
1
1
( )
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
+
+
=
+
=
+
+
=
+
=
+
+
+
=
+
+
+
=
−
+
+
n
n
ii
n
n
ii
n
n
nnn
m
x
n
x
n
x
n
x
nn
nm
mx
n
m
( )
=
−
−
=n
inin mx
n1
2
2
1
1
σ
( )
( ) ( )
[ ]
( ) ( ) ( )( )
( ) ( )( ) ( ) ( )
( ) ( )( ) ( )( )( )
( ) ( )( )
2
1
1
1
2
11
2
1
1
1
2
1
1
1
2
1
1
1
2
1
11
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
21
1
121
21
2
+
+
=
+++
+
=
+
=
++
+
=
+
=+
+
=+
+
=
+
=+
+
=++
−+−−=
−+−+−++−=
−−+−++−=
−−+−+−=
−+−=
−=
nn
n
ini
nnnnnn
n
ini
n
ininnnn
n
ini
n
innni
n
inn
n
ini
n
innni
n
inin
mmnmx
mmnmmmmnmx
mxmmmmnmx
mmmxmmmx
mmmx
mxn
σ
