# HOG- Processing

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```					                Dx = (−1 , 0 , 1)

Dy = (−1 , 0 , 1)T

I

Ix = I ∗ Dx
Iy = I ∗ Dy
￿ 2    2
| G |=    Ix + Iy

Iy
θ = arctan( Ix )
[0 , 40 )

[40 , 80 )

[80 , 120 )
v                       ￿ v ￿k   ε

v → v/(￿ v ￿1 +ε)
￿
v → v/ ￿ v ￿2 +ε2
2
(4 × 8) × (2 × 2) × 9 = 1152

{xk , yk } ∈ χ × {−1 , 1}   xk
yk
xk                        φ
f (x) = w · φ(x) + b   f (x)
φ(xi )                            x
f (x)
yi , i = 1, . . . , n

Hi

￿ n
ˆ            1                                 D2 [y, yi , Hi ]
f (y) =                | Hi |−1/2 t(wi ) exp(−                  )
n(2π)3/2 i=1                               2
D2 [y, yi , Hi ] = (y − yi )￿ Hi−1 (y − yi )

y      yi                  t(wi )

￿ n
ˆ            1                −1/2    −1                       D2 [y, yi , Hi ]
∇f (y) =                | Hi |      Hi (yi − y)t(wi ) exp(−                      )=
n(2π)3/2 i=1                                               2
￿ n                                                     ￿
1       ￿                                    D2 [y, yi , Hi ]
3/2
| Hi |−1/2 Hi−1 yi t(wi ) exp(−                  ) −
n(2π)        i=1
2
￿￿ n                                                     ￿ ￿
1         ￿                                   D2 [y, yi , Hi ]
3/2
| Hi |−1/2 Hi−1 t(wi ) exp(−                     ) y
n(2π)         i=1
2

￿i

2
| Hi |−1/2 t(wi ) exp(− D [y,yi ,Hi ] )
2
￿i (y) = ￿
n                           2 [y,y ,H ]
| Hi |−1/2 t(wi ) exp(− D 2 i i )
i=1

￿
n
￿i = 1
i=1

n
￿ n                     ￿
∇f (y) ￿
ˆ                                ￿
=  ￿i (y)Hi−1 yi −                     ￿i (y)Hi−1       y
ˆ
f (y)       i=1                        i=1

n
￿
−1
Hh (y) =           ￿i (y)Hi−1
i=1
Hi

￿ n              ￿
ˆ
∇f (y)           ￿
m(y) = Hh        ≡ Hh (y)     ￿i (y)Hi−1 yi − y
fˆ(y)
i=1

ˆ
∇f (y) = 0                 m(y) = 0

￿   n
￿
￿
ym = Hh (ym )              ￿i (y)Hi−1 yi
i=1

yi                   ym
yi , i =
1, . . . , n         ym

Hi Hi                                                           diag [Hi ]

￿                                            ￿
diag [Hi ] = (exp (si ) σx )2 , (exp (si ) σy ) , (σs )2

σx , σy , σs
#f alseN egatives
M issRate =    #trueP ositives+#f alseN egatives

#trueP ositives
P recision =   #trueP ositives+#f alseP ositives
#f alseN egatives

#trueP ositives

#f alseP ositives

ao   bp
bgt

area (bp ∩ bgt )
ao =
area (bp ∪ bgt )

ao
area (bp ∩ bgt ) = (396 − 305) × (411 − 127) = 91 × 284 = 25844
area (bp ∪ bgt ) = (443 − 259) × (458 − 90) = 184 × 368 = 67712

25844
ao =   67712
= 0.38

```
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Flavio Bernardotti Ing. www.bernardotti.it/portal
About Computer consultant since 1984. I wrote the software ITALINK (1985) to create the italian FIDONET (with some other sysop). I wrote 14 books all free distributed with fidonet, usenet and internet (http://www.bernardotti.it). For other info see my site.