Information Technology Reference
In-Depth Information
Linearize the vector d
(
x
)
at x
=
0 with a second-order Taylor series approximation:
1
2 x H
(
)=
(
)+
(
)
+
(
)
d
x
d
0
J
0
x
0
x
(9)
where J
0 , separately.
In the ESM algorithm, the Hessian matrix is replaced by a first-order Taylor Series
approximation of vector J
(
0
)
and H
(
0
)
are the Jacobian matrix and Hessian matrix at x
=
(
x
)
about x
=
0 :
x H
J
(
x
)=
J
(
0
)+
(
0
)
(10)
Then Eq. 9 becomes
1
2 (
d
(
x
)=
d
(
0
)+
J
(
0
)+
J
(
x
))
x
(11)
With some mathematical proofs by Malis [7], Eq. 11 can be simplified to follows:
d
(
x 0 )=
d
(
0
)+
J esm x 0 =
0
(12)
1
2
=
(
(
)+
(
x 0 ))
where J esm
J
0
J
. Therefore, the solution x 0 can be obtained by:
J esm d
x 0 =
(
)
0
(13)
where J esm is the pseudoinverse inverse matrix of J esm . The incremental transformation
Δ
can be calculated with x 0 by Eq. 5 and Eq. 6. Then a new homography G
solution can be obtained by such update:
G
(
x 0 )
= G
G
Δ
G
(
x 0 )
(14)
With this homography G , visual tracking can be implemented.
2.2
SIFT Algorithm
SIFT was proposed by Lowe in 1999[11]. Compared with other feature matching ap-
proaches, the SIFT algorithm has been demonstrated to have a better performance with
respect to variations in scale, rotation, and translation[8]. However, its computation in-
volves a high dimensional descriptor which is computational intensive and difficult to
apply for realtime processing. To improve its performance, various algorithms have
been proposed, including Affine SIFT [12], PCA-SIFT [13] and SURF[14] and so on.
2.3
GPU-Based Visual Tracking
The increasing programmability and computational capability of the GPU has shown
great potential for computer vision algorithms which can be parallelized[15]. For ex-
ample, a versatile framework for programming GPU-based computer vision tasks (ra-
dial distortion, corner detection etc) was recently introduced by [15][16]. There are
also GPU implementations for visual tracking, such as GPU-KLT tracker[17], GPU-
SIFT[17] [18][19]. These applications can get a 10
20 times speedup.
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