144
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
True w
σ
2
2.5
3
3.5
4
4.5
5
5.5
6
v
σ
0
0.2
0.4
0.6
0.8
1
r
0
0.5
1
1.5
2
2.5
3
(a) True
w
True a
2
2.5
3
3.5
4
4.5
5
5.5
6
v
σ
0
0.2
0.4
0.6
0.8
1
r
0
0.2
0.4
0.6
0.8
1
(b) True
a
Figure 3: True values of the line width
w
(a) and the asymmetry
a
(b).
algorithm (Press et al., 1992). To make the bias inversion efficient,
f
1
must be computed once offline and tabulated.
Because of the scale-invariance property, the resulting table is an array of only two dimensions (
v
and
r
), which makes
the table manageable in size.
In 2D, we can model lines as curves
s
(
t
)
that exhibit a characteristic 1D profile in the direction perpendicular to the
line, i.e., perpendicular to
n
(
t
) =
s
0
(
t
)
. Hence, we can extract lines points in 2D by requiring that the first directional
derivative in the direction
n
(
t
)
should vanish and the second directional derivative should be of large absolute value. The
direction
n
(
t
)
can be obtained for each pixel from the eigenvector corresponding to the eigenvalue of largest magnitude of
the Hessian matrix of the smoothed image. The Hessian and the gradient result in a second-degree Taylor polynomial in
each pixel, from which we can extract the line position with subpixel accuracy (Steger, 1998b). To extract the line width,
the edges on the right and left side of the line are extracted by extracting edge points on a search line of length
2
:
5
in
the direction
n
(
t
)
. The length of the search line is motivated by the restriction
>w=
p
3
. As mentioned above, edges
are regarded as bright lines in the gradient image. Therefore, to extract edge points we need the first and second partial
derivatives of the gradient image. The gradient image is given by
e
(
x; y
)=
q
f
x
(
x; y
)
2
+
f
y
(
x; y
)
2
=
q
f
2
x
+
f
2
y
(8)
where
f
(
x; y
)
is the image smoothed with
g
(
x; y
)
. The partial derivatives are given by:
e
x
=
f
x
f
xx
+
f
y
f
xy
e
(9)
e
y
=
f
x
f
xy
+
f
y
f
yy
e
(10)
e
xx
=
f
x
f
xxx
+
f
y
f
xxy
+
f
2
xx
+
f
2
xy
e
2
x
e
(11)
e
xy
=
f
x
f
xxy
+
f
y
f
xyy
+
f
xx
f
xy
+
f
xy
f
yy
e
x
e
y
e
(12)
e
yy
=
f
x
f
xyy
+
f
y
f
yyy
+
f
2
xy
+
f
2
yy
e
2
y
e
:
(13)
As can be seen, we need the third partial derivatives of the smoothed image, i.e., 8 convolutions in total. For efficiency
reasons, the coefficients
e
x
;:::;e
yy
are computed by convolving the image with
3
3
facet model masks (Steger, 1998b).
With this second-degree Taylor polynomial, the edge point extraction is exactly the same as the line point extraction above.
Note that in contrast to standard edge detection approaches, the direction perpendicular to the edge is obtained from the
Hessian of the gradient image, not from the gradient direction. We will see below what implications this definition has.
The individual line points are linked into lines by an extension of Canny’s hysteresis thresholding algorithm (Canny, 1986)
which takes the direction of the lines into account and correctly handles junctions (Steger, 1998b).
Figures 4(a) and (c) display the result of extracting lines and their width with bias removal from an aerial image with a
reduced resolution of 1 m. To assess the accuracy of the results, they are shown superimposed onto the original image of
resolution 0.25m. For comparison purposes, Figures 4(b) and (d) display the results without bias removal. Evidently, the
algorithm was able to correct the line positions and widths successfully with high accuracy.
2.3 Extraction of Lines with Different Polarity
We would now like to use the same scale-space analysis techniques as for lines with equal polarity to design an algorithm
that is able to extract lines with different polarity, which returns unbiased line positions and widths. This type of lines
Steger Carsten
剩余15页未读，继续阅读
qq_35516708
- 粉丝: 2
- 资源: 9
我的内容管理
展开
最新资源
- ASP.NET数据库高级操作：SQLHelper与数据源控件
- Windows98/2000驱动程序开发指南
- FreeMarker入门到精通教程
- 1800mm冷轧机板形控制性能仿真分析
- 经验模式分解：非平稳信号处理的新突破
- Spring框架3.0官方参考文档：依赖注入与核心模块解析
- 电阻器与电位器详解：类型、命名与应用
- Office技巧大揭秘：Word、Excel、PPT高效操作
- TCS3200D: 可编程色彩光频转换器解析
- 基于TCS230的精准便携式调色仪系统设计详解
- WiMAX与LTE：谁将引领移动宽带互联网?
- SAS-2.1规范草案：串行连接SCSI技术标准
- C#编程学习：手机电子书TXT版
- SQL全效操作指南：数据、控制与程序化
- 单片机复位电路设计与电源干扰处理
- CS5460A单相功率电能芯片：原理、应用与精度分析
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
