Estimation of Homography Dynamics on the Special Linear Group - Visual Servoing via Advanced Numerical Methods - page 136

h 11 h 12 h 13

h 21 h 22 h 23

h 31 h 32 h 33

Fig. 8.1 Plain line: the measured homography matrix H . Dashed line: the observed homog-

raphy H

When ( H 0 , 0) ∈ E u , one has

2 I +( 1
λ

H 0 =

) vv T = H 0 +(

2

λ

2 − λ

λ − λ ) I .

Therefore, we deduce from (8.30) that

f (0)=

H (0) C

2 +

1)tr( C 2 ) λ ( λ − . (8.31)

Since ( H (0)

2 such that H (0)=

I +( 1
λ

) vv T .From , 0) ∈ E u , there exists v ∈ S λ − λ

2

3 2 + 1 = 0, one verifies that

this expression and using the fact that λ − λ

2 +( 1
λ

H (0) C

2 = 2

)tr( C T vv T C ) λ C

2 − λ

. (8.32)