Digital Signal Processing Reference
In-Depth Information
2.3
Assign Orientation for Each Keypoint
In order to get rotation invariance for SIFT feature points, statistic each point's
gradient magnitude and direction within a region around the keypoint. For each image
sample,
Lxy
, in this kind of scale, the gradient magnitude,
mxy
, and
(, )
(, )
orientation,
θ
( ,
xy
)
, is recomputed using pixel differences:
2
2
(9)
mxy Lx y Lx y Lxy Lxy
(, )
=
(
(
+−−
1,
)
(
1,
))
+
(
( ,
+−
1)
( ,
−
1))
Lxy Lxy
(
,
+−
1)
( ,
−
1)
−
1
θ
(, )
xy
=
(
)
(10)
tan
Lx y Lx y
( 1,)
+−−
( 1,)
Fig. 2.
Assign orientation for each keypoint
Fig. 2: Indicating the gradient magnitude and orientation of each sample point within
keypoint neighborhood. These sample points are weighted by a Gaussian circular
window with σ that is 1.5 times of the keypoint scale. The ma
H
represents the
main direction of the feature point, we consider the energy that is higher
than 0.8
H
max
as the auxiliary direction.
2.4
Generate Keypoint Descriptor
The image is rotated to the main direction of this feature point. A
44
×
sub-region is
chosen around each keypoint. There are
44
pixel points in each sub-region. Then
the gradient orientation histogram of the 8 directions is calculated and sorted in each
sub-region. SIFT features descriptor is a
448 128
×
××=
dimensional feature vector.
Fig. 3.
The figure shows a
44
×
descriptor array computed from a
16
×
16
set of sample
3
Description of PCA-SIFT
The principal component analysis (PCA) is a linear transformation, which enables
high-dimensional samples to project onto low-dimensional space. Yan Ke (2004)
proposed PCA-SIFT which are the improved SIFT [5].
