MATLAB实现亚像素精度边缘与线条提取算法
1星 需积分: 45 170 浏览量
更新于2024-07-20
8
收藏 2.71MB PDF 举报 "本文主要介绍了在MATLAB环境下实现亚像素精度的边缘和线条提取算法，旨在提高图像处理中的定位精度。作者Carsten Steger提出了新颖的方法来从二维图像中提取曲线结构，即线条和边缘，并关注了亚像素精度的问题。文章涉及到的关键技术包括边缘检测、线检测、亚像素精度、偏差校正以及对边缘和线条接合点的提取。"
在图像处理领域，边缘和线条的精确提取是至关重要的，特别是在高分辨率和精确测量的应用中。MATLAB作为一种强大的数学计算和可视化工具，被广泛用于图像处理任务。亚像素提取算法能够提升边缘定位的精度，从而提高整体图像分析的准确性。
文章首先探讨了线条的亚像素精确提取。通过利用几何模型分析线条剖面在尺度空间中的行为，作者开发了算法来提取线条及其宽度，这些算法能在亚像素级别运行。然而，由于在提取过程中使用的平滑处理，线的位置和宽度不可避免地受到偏置。通过研究这种偏置的映射关系，作者发现可以反向操作以消除这种偏置，从而获得无偏且准确的结果。
对于边缘提取，它们被视为梯度图像中的亮线。通过对尺度空间的分析，揭示了为什么边缘和线条接合点常常难以精确提取。基于这一理解，作者提出了一种新的方法来提取完整的接合信息，这有助于更完整地理解和重建图像中的复杂结构。
这篇论文为MATLAB环境中的亚像素边缘和线条提取提供了理论基础和实际应用案例，对于从事图像处理和计算机视觉研究的人员具有很高的参考价值。通过应用这些算法，研究人员和工程师可以提高图像分析的精确度，特别是在需要高精度测量或识别的场景中。
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
点击了解资源详情
点击了解资源详情
点击了解资源详情
2021-10-14 上传
2021-04-25 上传
2013-03-01 上传
2022-09-23 上传
2015-12-16 上传
2023-05-25 上传
qq_35516708
- 粉丝: 2
- 资源: 9
我的内容管理
展开
