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References
[1] Marr D. and E. Hildreth, Theory of edge detection, Proc. R. Soc. Lond., 207:187-217 (1980).
[2] Clark, J. J., Authenticating edges produced by zero-crossing algorithms, IEEE Transactions on Pattern Analysis and Machine
Intelligence, 11(1):43-57 (1989).
[3] Bergholm, F., Edge focusing, IEEE Trans. Pattern Analysis and Machine Intelligence, 19:726--741 (1987).
[4] Canny, J., A computational approach to edge detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679-714
(1986).
[5] Goshtasby, A. 2-D and 3-D Image Registration, Wiley Press, 2005.
[1] Marr D. and E. Hildreth, Theory of edge detection, Proc. R. Soc. Lond., 207:187-217 (1980).
[2] Clark, J. J., Authenticating edges produced by zero-crossing algorithms, IEEE Transactions on Pattern Analysis and Machine
Intelligence, 11(1):43-57 (1989).
[3] Bergholm, F., Edge focusing, IEEE Trans. Pattern Analysis and Machine Intelligence, 19:726--741 (1987).
[4] Canny, J., A computational approach to edge detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679-714
(1986).
[5] Goshtasby, A. 2-D and 3-D Image Registration, Wiley Press, 2005.
2-D edge detection |
| Image Registration and Fusion Systems |
____________________________________________________________________________________
Purpose of edge detection
Most information in an image resides along edges. Therefore, it
makes sense to select the features used in image registration along
edges. Edge detection can be considered a preprocessing
operation that narrows down the search in feature detection and
feature correspondence.
Edge detection methods
Various edge detection methods have appeared in the literature,
each with its own strengths and weaknesses. A number of popular
edge detection methods have been included in an easy-to-use
interactive software. Implemented methods are: Laplacian of
Gaussian (LoG) [1], Authentic LoG [2], Canny [4], and functional
approximation [4]. These methods find edges based on intensity
differences. A method based on intensity ratios [5] is also included
in this software. Moreover, an edge focusing capability [3] to
gradually increase resolution of an image to localize edges more
accurately while avoiding noisy edges to enter the process is
provided. Finally, a method to detect edges in color images is
included.
Examples
Edge detection examples on an outdoor scene image, an aerial
urban scene image, and a radar image (Fig. 1) are shown below.
Fig. 2 shows edges detected by the LoG operator after removal of
weak and noisy edges. Standard deviation of the Gaussian for the
outdoor scene image and the aerial image was 1.5 pixels, while that
for the radar image was 2.5 pixels to reduce more noise.
Authentic LoG method removes the false edges from the LoG
edges, and since false edges are usually weak, edges detected by
the Authentic LoG edges after removal of weak edges are almost the
same as those obtained by the LoG operator after removal of weak
edges.
Canny method avoids detection of false edges, so, detected edges
are similar to those detected by Authentic LoG. Canny methods finds
locally maximum gradient points in the gradient direction, while
Authentic LoG finds zero-crossings of the image second derivative
and from among the zero-crossings removes those that correspond
to locally minimum gradient magnitudes, thus, removing the false
edges.
If the objective is to detect strong edges in an image, LoG, Authentic
LoG, and Canny methods all detect very similar edges.
Most information in an image resides along edges. Therefore, it
makes sense to select the features used in image registration along
edges. Edge detection can be considered a preprocessing
operation that narrows down the search in feature detection and
feature correspondence.
Edge detection methods
Various edge detection methods have appeared in the literature,
each with its own strengths and weaknesses. A number of popular
edge detection methods have been included in an easy-to-use
interactive software. Implemented methods are: Laplacian of
Gaussian (LoG) [1], Authentic LoG [2], Canny [4], and functional
approximation [4]. These methods find edges based on intensity
differences. A method based on intensity ratios [5] is also included
in this software. Moreover, an edge focusing capability [3] to
gradually increase resolution of an image to localize edges more
accurately while avoiding noisy edges to enter the process is
provided. Finally, a method to detect edges in color images is
included.
Examples
Edge detection examples on an outdoor scene image, an aerial
urban scene image, and a radar image (Fig. 1) are shown below.
Fig. 2 shows edges detected by the LoG operator after removal of
weak and noisy edges. Standard deviation of the Gaussian for the
outdoor scene image and the aerial image was 1.5 pixels, while that
for the radar image was 2.5 pixels to reduce more noise.
Authentic LoG method removes the false edges from the LoG
edges, and since false edges are usually weak, edges detected by
the Authentic LoG edges after removal of weak edges are almost the
same as those obtained by the LoG operator after removal of weak
edges.
Canny method avoids detection of false edges, so, detected edges
are similar to those detected by Authentic LoG. Canny methods finds
locally maximum gradient points in the gradient direction, while
Authentic LoG finds zero-crossings of the image second derivative
and from among the zero-crossings removes those that correspond
to locally minimum gradient magnitudes, thus, removing the false
edges.
If the objective is to detect strong edges in an image, LoG, Authentic
LoG, and Canny methods all detect very similar edges.
Fig. 1. (Top) An outdoor scene image. (Middle) An aerial
image of an urban scene. (Bottom) A radar image. The
Middle and Bottom images are courtesy of USGS.
image of an urban scene. (Bottom) A radar image. The
Middle and Bottom images are courtesy of USGS.
Fig. 2. Edges detected by the LoG operator after interactive removal of weak and noisy edges. Similar edges are obtained by the
Authentic LoG and Canny methods after removal of weak and noisy edges.
Authentic LoG and Canny methods after removal of weak and noisy edges.
Edge detection by intensity ratios
Edges represent image pixels with locally maximum intensity
changes. Change is measured by intensity difference. Change
can be quantified using intensity ratio also. Certain sensors do
not convert scene properties to image intensities linearly, so use
of intensity difference to detect edges may not be appropriate. In
sensors where recorded intensities relate to scene properties
exponentially, locally maximum change in intensity ratio may be
a better method than locally maximum intensity difference when
detecting the edges. This edge detector uses the properties of
the human visual system to detect edges in an image. Edge
detection results by intensity ratios are shown in Fig 4. Intensity
ratio method tends to detect more edges in dark areas
compared to intensity difference method, and intensity difference
method tends to detect more edges in bright areas compared to
intensity ratio method.
Edges represent image pixels with locally maximum intensity
changes. Change is measured by intensity difference. Change
can be quantified using intensity ratio also. Certain sensors do
not convert scene properties to image intensities linearly, so use
of intensity difference to detect edges may not be appropriate. In
sensors where recorded intensities relate to scene properties
exponentially, locally maximum change in intensity ratio may be
a better method than locally maximum intensity difference when
detecting the edges. This edge detector uses the properties of
the human visual system to detect edges in an image. Edge
detection results by intensity ratios are shown in Fig 4. Intensity
ratio method tends to detect more edges in dark areas
compared to intensity difference method, and intensity difference
method tends to detect more edges in bright areas compared to
intensity ratio method.
| Fig. 4. Edges detected by intensity ratios. |
Edge detection by functional approximation
Considering intensities in an image samples from a 2-D
continuous signal, edges in an image can be obtained by
approximating a surface to the image intensities and detecting
surface points with second derivatives that are zero. Since the
process deals with a continuous surface, the location of edges
can be determines with subpixel accuracy. Examples of edge
detection by functional approximation are given in Fig. 3.
Detected edges are similar to those obtained by the LoG and
Canny methods after removal of weak and noisy edges.
Considering intensities in an image samples from a 2-D
continuous signal, edges in an image can be obtained by
approximating a surface to the image intensities and detecting
surface points with second derivatives that are zero. Since the
process deals with a continuous surface, the location of edges
can be determines with subpixel accuracy. Examples of edge
detection by functional approximation are given in Fig. 3.
Detected edges are similar to those obtained by the LoG and
Canny methods after removal of weak and noisy edges.
| Fig. 3. Edges detected by functional approximation. |
Edge detection in color images
Pixel values in a color image represent vectors. Here, the
objective is to detect locally maximum color changes in the
image domain. More detail about this method can be found in
[5]. Edges in a color image after removal of weak and noisy
edges are shown in Fig. 5.
This software can read a variety of image formats and can
save the edges in a variety of formats, including jpg, gif, png,
pgm, and ppm.
Pixel values in a color image represent vectors. Here, the
objective is to detect locally maximum color changes in the
image domain. More detail about this method can be found in
[5]. Edges in a color image after removal of weak and noisy
edges are shown in Fig. 5.
This software can read a variety of image formats and can
save the edges in a variety of formats, including jpg, gif, png,
pgm, and ppm.
| Fig. 5. Edges detected in a color image. |
