Computational and Mathematical Methods in Medicine
two eigenvalues is greater than the minimum threshold value,
it will get strong corners. e method proposed by Shi and
Tomasi is relatively perfect and could obtain better results
under many conditions.
2.2. SIFT Feature Description. SIFT [] extracts invariant
feature based on invariant descriptor that was proposed by
Lowe in . SIFT feature fundamentally remains invariant
to image translation, rotation, scaling, brightness variation,
and noises. SIFT feature description mainly includes two
steps: () determine direction parameter of feature points; ()
use graphic information around feature points to construct
-dimensional descriptor.
2.2.1. e Determination of Direction Parameter. To ensure
rotatedinvarianceofdescriptoroffeaturepoints,itshall
calculate the main direction of feature points and create SIFT
feature descriptor at this main direction. For the detected
feature points, nite dierence calculation will be applied to
gure out pixel gradient module and angle of gradient
amplitude in the region with the feature point as center. e
formalists are as follows:
,=
2
1
+
2
2
,
1
=+1,−−1,,
2
=,+1−,−1,
,=arctan
,+1−,−1
+1,−−1,
,
()
in which (,) means pyramid image grayscale of the
feature point at (,) on its scale. en use histogram to
statistically state pixel gradient module and direction in
this region. e abscissa axis of histogram is the angle of
amplitude of gradient direction, and the ordinate axis is
theaccumulatedvalueofgradientmodulecorrespondingto
gradient direction angle. e graphic of gradient direction is
divided into columns according to the range of 0
∘
∼360
∘
that is each
∘
is for a column. e peak value of histogram
represents the direction of image gradient in neighborhood of
this feature point, which is the main direction of this point,
and selects % of peak value as auxiliary direction value.
erefore,onefeaturepointcouldbesetwithmanydirections
to enhance the robustness of matching.
2.2.2. e Construction of SIFT Descriptor. Rotate local
region around feature point by ;theangleisrepresented
by the main direction to maintain its rotational invariance.
Intherotatedregion,equallydividethe16×16rectangular
window with the feature point as center into 4×4subregions,
and in each subregion, gure out gradient histogram of eight
directions (
∘
,
∘
,
∘
,
∘
,
∘
,
∘
,
∘
,and
∘
). In
thesameway,itisnecessarytoconductGaussianweighting
processing to each pixel’s gradient magnitude. erefore, each
feature point will generate a -dimensional eigenvector.
3. Directed Line Segment Matching
e description method based on features of line segment not
only can acquire local information of images, such as textures
andgradients,butalsocanbeabletoobtainimagecontent
between line segments and other information. Our method
has two creative aspects: () it describes image features
through the description of connecting line between key
points, not through image blocks; () the description method
based on line segment can reect topological structures of
image and therefore it has relatively high robustness for
nonlinearly distorted and rotated images.
3.1. Line Segment Features. Given two images and
to be
matched, we use Harris operator to detect key points in these
two images and utilize detected key points to construct two
directed graphics, = (,) and
=(
,
).Dene
={
1
,
2
,...,
𝑛
}and
={
1
,
2
,...,
𝑚
}that mean key
points extracted from images and
,respectively,andand
are the edge sets of directed graphics and
,respectively,
where ={(
𝑖
,
𝑗
), =},
={(
𝑖
,
𝑗
), =}.Takethe
directed line segment between two key points as the object
of feature description. Set one edge of graph ,
𝑖𝑗
∈
(the starting point is
𝑖
, and the end point is
𝑗
). In order to
reduce computation time of describing features of the edge
𝑖𝑗
,weequidistantlysamplevepointsfromtheedge
𝑖𝑗
,
{
1
,
2
,
3
,
4
,
5
},inwhich
𝑘
=
𝑖
+((−1)/4)(
𝑗
−
𝑖
), =
1,...,5;
𝑖
refers to the image coordinate of point
𝑖
.Astothe
feature points {
1,
2
,
3
,
4
,
5
} sampled from the directed
line segment
𝑖𝑗
, extract their SIFT feature, respectively, =
(
1
,
2
,
3
,
4
,
5
). Each column in ,
𝑘
, = 1,2,...,5,is
a -dimensional vector, which represents SIFT feature of
point
𝑘
. ose feature points sampled uniformly from line
segment have strong robustness for image scaling, rotation,
and changes in resolution.
3.2. Nearest-Neighbor Matching of Line Segments. With the
purposeofroughmatching,alinesegment-matchingmethod
based on nearest-neighbor criterion is proposed. It is
assumed that image has
1
directed line segments, =
[
1
,
2
,...,
𝑛
1
],andimage
has
2
directed line segments,
=[
1
,
2
,...,
𝑛
1
],andastaticmatrix,∈
𝑛
1
×𝑛
2
,could
be dened as
,=
1
𝑗
is the nearest neighbor points of
𝑖
0 otherwise.
()
Because this paper uses a matrix to describe features of line
segments, it takes -norm of the matrix as measurement in
computation of nearest-neighbor points; that is, (
𝑖
,
𝑗
)=
𝑖
−
𝑗
𝐹
and
𝑖
means features of line segment
𝑖
;
𝑗
means
features of line segment
𝑗
. Computation procedure of matrix
isasshowninProcedure.
3.3. Matching of Points. In last section, we obtain match-
ingofdirectedlinesegmentsthroughtheruleofnearest-
neighborhood. It is necessary to get more accuracy of point