Evaluation of Front Detection Methods for Satellite-Derived SST and Chl-a
Data Using Edge Detection Algorithms
1.
Introduction
The knowledge of sea surface temperature (SST) and chlorophyll-a over large
spatial areas in a continuous temporary base is necessary from the perspectives of both
physical and biological oceanography. Satellite remote sensing is the only tool that can
provide these SST and chl-a fields with high spatial and temporal resolution in a practical
way. Many studies that make use of satellite-derived data depend upon the precise location
of edges associated with oceanographic features (Pratt et al., 1991; Podesta et al. 1993). As
in costal seas, thermal frontal regions have been shown to be associated with high primary
production and corresponding large standing stocks of phytoplankton; while the chl-a
fronts might reveal the events of red tides or unusual land discharge [ref?].
For many years, in spite of intensive labor, the location of edges in oceanographic
images was performed manually [ref? This is before when?]. With the rapid expansion of
the available data, it becomes impossible to for the processing and analysis to be done by
human operators. In addition, the results obtained are subjective and lack of consistency,
and therefore could not be compared by different researchers. By contrast, a single
computer algorithm will always process images the same way and obtain the same results
and, thus, can provide a standard of comparison.
Over the last few years, various edge detection methods have been developed and
applied to oceanographic satellite images. Although the significant improvements have
been made, there still remain the following challenges when using the algorithms for front
detection from satellite SST and ocean color images. The method should be robust enough
to overcome the impulsive noise and thus detect the smaller-scale features. Furthermore, a
detected front should be defined from a point of spatial structures of the front rather than
seasonally/regionally varying geophysical parameters in order to analyze the fronts
consistently throughout the year [not sure what this means].
Widely used edge detection algorithm is derivative-based operators. The intensity
gradient (first derivative) detectors (such as Sobel, Prewitt, Roberts, Kirsch [what are
these?]) are used, for example, in oceanographic texture analysis (Sauter and Parson, 1994),
in automatic detection of Gulf Stream rings (Janowitz, 1985). Second-derivative detectors,
such as Laplacian/Laplacian of the Gaussian [what is this? Need brief explanation] are
used in fish detection (Savage et al., 1994). These derivative-based edge operators are very
sensitive to impulsive noise. They usually require a previous filtering to eliminate the
noise. But the filtering inevitablely blurs the edges of the images and makes it more
difficult to detect finer-scale frontal features.
Canny (1986) proposed an ‘optimal’ edge detector based on three criteria: good
detection, good localization and low error rate. The algorithm first smoothes the image
using a filter very close to the first derivative of a Gaussian [explain this]. It then finds the
image gradient to highlight regions with high spatial derivatives and applies nonmaxima
suppression to the gradient magnitude [explain this, too]. Finally, a double thresholding
algorithm is used to detect and link edges. Although the Canny is a modern “standard” [for
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oceanographic features?], in the sense that papers describing new edge detectors often
compare the results to those of the Canny [ref?], its application to marine satellite images
has been scarce [then who used the Canny method? For what type of features?].
Recently, wavelet transform based edge detectors have been applied to satellite
images to separate processes [features?] at various scales, including relative phase/location
information for coastal monitoring applications (Liu et al., 1997a), for ice edge and ice floe
tracking (Liu et al., 1997b), for ocean surface layer drift tracking (Liu et al, 2002), and for
monitoring snowmelt using satellite passive microwave measurements (Liu et al., 2005).
Wavelet transform (WT) is naturally a multiscale analysis [explain more]. Mallat and
Zhong (1992) constructed a dyadic wavelet, a quadratic spline, which approximates the
first derivative of Gaussian [explain more]. The corresponding dyadic wavelet transform
(DWT) is equivalent to the Canny edge detection. In DWT domain, it is represented that
the edge structures present observably at each subband while the noise decreases rapidly
along the scales [not clear]. It has also been shown that multiplying the adjacent scales
could enhance edges while suppressing noise (Xu et al., 1994; Sadler and Swami, 1999).
Zhang and Bao (2002) proposed a wavelet based edge detection scheme by scale
multiplication. [all these above methods need to be explained more on their principles]
Several recent studies have adopted an edge detection method developed by Cayula
and Cornillon (1992, 1995), and have obtained good results in presenting frontal views of
the regional seas (e.g., Kahru et al., 1995; Mavor & Bisagni, 2001; Ullman and Cornillon,
1999, 2001; Miller, 2004). The algorithm, originally developed for SST images (?),
operates at three levels: picture, window, and local/pixel levels. The edge detection is
based on the analysis of the temperature histogram of each window in the image, using
unsupervised learning methods and statistically deciding on the existence of boundaries.
[explain more on how an “edge” is found] The edge contour is then completed by
region-based algorithms. The algorithm is affected by impulsive noise; therefore, previous
median filtering is needed.
SUSAN edge detector (Smith and Brady, 1997) calculates the edge strength using
the number of edges with similar brightness within circular masks [not clear]. The edge
direction is calculated using moment calculation and nonmaxima suppression is used to
thin edges [not clear]. In one work on comparison of edge detector performance through
use in an object recognition task (Shin et al., 2001) [what is this object?], SUSAN edge
detector was found to perform best. Holyer and Peckinpaugh (1989) applied an algorithm
based on the gray level co-occurrence (GLC) to ocean satellite images [what type of
image?] to detect mesoscale features. Recently, an edge detection algorithm, based on an
entropic approach using Jensen-Shannon divergence [what is this], has been used to detect
sea surface temperature (SST) fronts in satellite images (Vazquez and Allah, 1999;
Shimada et al., 2005). [Having read this far I have no clue on how each method works]
Assessing the performance of edge detection algorithms is a difficult task because
the performance depends on several factors. At a minimum, they include (Heath et al.,
1997): the algorithm itself, the type of images used to measure the performance of the
algorithm, the edge detector parameters used in the evaluation, and the method for
evaluating the edge detectors. Any conclusions based on synthetic images have limited
value since there is no simple extrapolation to real world images. Most methods for
evaluating an edge detector rely on the specification of ground truth. This is very difficult
for real images of common scenes, even more so for marine satellite images of SST and
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Chl-a fields. It is possible for people to label some of the edges in an image, but the
difficulty in labeling all of the edges is clear to anyone who has tried. Some methods
proposed (Kitchen and Rosenfeld, 1981; Zhu, 1996; Yitzhaky and Peli, 2003) can operate
on real images and do not required ground truth [what are these methods? Are these new
methods in addition to the ones you already described?]. As pointed out in Health et al.
(1997), each of these methods leaves something to be desired [don’t know what this
means]. Most significantly, some kind of estimated ground truth (EGT) produced in these
methods might not necessary reflect the true edges in the images [how do we know if an
edge is “true”?].
Given the various edge-detection methods, it is desirable to know which one performs
better on realistic satellite imagery of SST and ocean color, and how they compare with
each other under various circumstances. Unfortunately, to our knowledge such a
comparison study does not exist in the current literature. Therefore, in this paper, we
evaluated four edge detection algorithms to satellite images of SST and Chl-a fields on the
West Florida Shelf. These algorithms include (1) the Canny edge detector (Canny, 1986),
(2) the histogram algorithm (Cayula and Cornillon, 1992), (3) dyadic wavelet transform
(DWT) based edge detection by scale multiplication (Zhang and Bao, 2002), (4) SUSAN
edge detector (Smith and Brady, 1997). The gradient-based detectors were not included in
this comparison, because they are sensitive to noise and can not adequately detect and
retain finer-scale frontal features, based on our preliminary tests over satellite SST and
ocean color images. We use human judgment [why human judgment? No other better
way?] for obtaining a practical evaluation on how well the above algorithms detect both
mesoscale fronts and fine features in a dynamic coastal area.
2. Data
The SST satellite data were obtained from the Advanced Very High Resolution
Radiometer (AVHRR) of the TIROS-N series satellites. The images cover the West
Florida Shelf, between 24° N - 30.5° N and 87.5° W - 80.5° W, with a spatial resolution of
1.4 km x 1.5 km. The presentation of temperatures in the images is 5 digital counts for 1 oC.
Data products of SeaWiFS were created in IMaRS (University of South Florida) with the
SeaDAS software (version 4) developed at NASA. The OC4 bio-optical algorithm of
O'Reilly et al. (2000) is used to derive chlorophyll concentrations. Chl-a images in the
West Florida Shelf covers the area 22° N - 31° N and 91° W - 79° W, with a spatial
resolution of 1 km x 1 km.
[If you introduce the various edge-detection methods very briefly in the “Introduction”
section, this section can be “Data and Methods” where you can detail those methods to
make it very clear to a reader how they work. Perhaps some of the text in the next section
can be moved to this “Method” section, too]
3. Result and discussion
3.1 Parameter Selection
Selecting the input parameters of each algorithm is a critical step in edge detector
performance evaluation because the resulting edge quality varies greatly with the choice of
parameters. A fixed number set of parameters [do you mean several sets? The word
3
“fixed” is confusing] for each algorithm is used to find a final set of parameter which gives
optimal result based on visual assessment as well as checking the gradient across the
detected edges. While this approach does not guarantee that the optimal parameter set was
identified, it does avoid biasing the results toward particular algorithm (Heath et al., 1997)
[what does this mean?].
The Canny edge detector allows the user to specify three parameters. The first is
sigma, the standard deviation of the Gaussian filter specified in pixels. The second
parameter, low, and the third parameter, high, are the low and high hysteresis thresholds,
respectively. The parameters tested are combinations of sigma, low and high threshold
values, where sigma  {0.8, 1.0, 1.5}, low  {0.05, 0.1, 0.2}, high  {0.1, 0.15, 0.2, 0.4,
0.6}. Low threshold values are tested for the detection of fine features. [not clear what
these parameters mean. This should be in the “Method” section]
The histogram algorithm (Cayula and Cornillon, 1992), the parameter (opt) is the
criterion used to decide whether one or two populations are present in a given window
[what is a population? What is a window?]; the parameters C1, C2 and C3 measure the
cohesion of each population with a given window. The combinations of parameters tested
are: (opt)  {0.68, 0.72, 0.76}, C1, C2 and C  {0.88, 0.9, 0.92, 0.94}, the pixel window
size  {16 x 16, 32 x 32, 64 x 64}. [what do these parameters mean?]
In DWT based edge detection scheme by scale multiplication, the scale product
function of f(x,y) is defined as the correlation of two adjacent DWT scales, Pjf,1(x, y) =
Wj1f(x,y) * Wj+11f(x, y) and Pjf,2(x, y) = Wj2f(x,y) * Wj+12f(x, y). Subscript j means that the
correlation is computed at scales 2j and 2j+1. A single threshold t applied to module map to
remove the noise and detect edge points. The parameters tested are j  {1, 2, 3, 4, 5}, t 
{0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0}. [similarly, what do they mean?]
SUSAN edge detector allows user to specify two parameters: (1) spatial control for
flat mask – either 37 pixels arranged in a “circle”, or a 3 by 3 mask which gives finer detail;
(2) brightness control t, determining the maximum difference in greylevels between two
pixels which allows them to be considered part of the same ‘region’ in the image. The
values of t tested in this study is t  {2,3,4,5,6,7,8,9,10}. [need to explain these as well. All
these should be in “Method” section]
[do these 4 methods apply to the floating point data array, or the byte-value image? If it is
the latter, how are these byte images derived from SST (floating point) and chl (floating
point)? Why?]
3.2 SST results
Four algorithms were tested on the SST image of March 12, 2005 to select
‘optimal’ parameters, again by visual assessment. The ‘optimal’ parameters were those
that gave the most and obvious fronts and not introducing significant false and noisy edges.
The results are shown in Figure 1. The parameters obtained and used to produce the results
shown in Figure 1 are as follow: (1) Canny detector, sigma = 1.0, low = 0.05, high = 0.10;
(2) histogram algorithm, window size = 32 x 32, (opt) = 0.72, C = 0.92, C1 = C2 = 0.90; (3)
DWT scale multiplication, j = 3 (lower scales are sensitive to noise, while higher scales
result in poor edge localization), t =1.0; (4) SUSAN algorithm, flat mark = 37 pixels
“circle”, t = 2.
As shown in Figure 1, Canny detector, histogram algorithm and DWT scale
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multiplication give similar performance, and do obviously better than SUSAN detector.
Further discussions does not include SUSAN detector. Canny detector seems to give better
finer features near the costal area than histogram algorithm and DWT (Figure 1a, 1b, 1c).
Front labeled as #1 in Figure 1a is the one detected by Canny and DWT detectors but not by
histogram algorithm. Figure 2(1) shows the SST transact across the fronts #1 in Figure 1a,
which corresponds to a 0.8 oC temperature gradient across the detected front edge. Fronts
labeled as #2 and #3 were detected by Canny but not by histogram algorithm and DWT.
Figures 2(2) and 2(3) show the SST transacts across the fronts #2 and #3 in Figure 1a,
which correspond to a 0.4 oC temperature gradient across the detected front edges. Fronts
labeled as #4 and #5 in Figure 1b are detected by histogram algorithm and DWT but not by
Canny. The SST transacts across the fronts #4 and #5 are shown in Figure 2(4) and 2(5),
which corresponds to a 0.6 oC and 0.8 oC temperature gradient, respectively. [so?]
The same set of parameters derived from image of March 12, 2005 above is
applied to images collected for different dates. Figure 3 shows similar results for SST
image of February 11, 2005. All algorithms detect most of the visually obvious strong
front edges. Canny performs better in detecting the finer features near the costal area,
while fails to detect some relatively strong fronts (i.e. the arrow pointed front edge in
Figure 3b). One problem with the Canny operator is to do with Y-junctions i.e. places
where three ridges meet in the gradient magnitude image [no clear what this means]. For
histogram algorithm, as pointed out in Cayula and Cornillon (1992), the window size must
be sufficiently large to obtain reliable statistics; on the other hand, a too large window may
include interference features in the area under study. In the original configuration of
Cayula and Cornillon (1992), the size of the windows was set to 32 x 32. Our testing also
shows that window size of 32 x 32 gives better results than that of 16 x 16 and 64 x 64.
However, if there are more than two fronts within a 32 x 32 window, the algorithm will
miss the front representing a smaller portion of the window. This might partially explain
its failure to detect finer features near the costal area. [this discussion is the best so far as I
read]
#1
#2 #3
#4
#5
5
(a)
(b)
(1)
(2)
6
7
(a)
(b)
Again, three algorithms produce similar results on SST image of May 25, 2005, which has
quite uniform surface temperature within the study area (Figure 4).
(a)
(b)
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Figure 4. SST fields on West Florida Shelf, May 25, 2005, with edges overlaid. (a) edges
detected by Canny, (b) edges detected by histogram algorithm, (c) edges detected by
DWT, (d) edges detected by SUSAN.
[How are clouds handles? How do they perform on images with lots of scattered clouds?
What about coastlines? Can you have some statistics in addition to visual and gradient
evaluations, such as total # of frontal pixels from each method? Otherwise the above
comparison is really qualitative]
3.3 Chl-a results
The same four algorithms were tested on the Chl-a image of March 12, 2005 to
select ‘optimal’ parameters, again by visual assessment. The ‘optimal’ parameters were
those that gave the most and obvious fronts and not introducing significant false and noisy
edges [how do you know they are obvious fronts or false/noisy fronts? Do you have some
quantitative measure?]. The results are shown in Figure 5. The parameters obtained and
used to produce the results shown in Figure 5 are as follow: (1) Canny detector, sigma = 1.0,
low = 0.1, high = 0.15; (2) histogram algorithm, window size = 32 x 32, (opt) = 0.72, C =
0.92, C1 = C2 = 0.90; (3) DWT scale multiplication, j = 3 (lower scales are sensitive to
noise, while higher scales result in poor edge localization), t =1.0; (4) SUSAN algorithm,
flat mark = 37 pixels “circle”, t = 5.
Contract to the results of SST images, Canny detector produce quite different
9
results from histogram algorithm and DWT scale multiplication. Again SUSAN detector
performs most poorly. Further discussions exclude SUSAN detector. Canny detector
gives much better finer features near the costal area than histogram algorithm and DWT
(Figure 5a, 5b, 5c). Front labeled as #1 in Figure 5a [I can’t see the front] is detected by
Canny but not by histogram algorithm and DWT. Figure 6(1) shows the SST [Chl-a?]
transact across the fronts #1 in Figure 5a, which corresponds to a 0.2 Chl-a gradient across
the detected front edge. Front labeled as #2 is detected by Canny and DWT but not by
histogram algorithm. Figures 6(2) show the Chl-a transact across the fronts #2 in Figure 5a,
which correspond to a 0.25 Chl-a gradient across the detected front edge. Canny detector
fails to detect low Chl-a fronts in the center of study area. Fronts labeled as #3, #4 and #5
in Figure 5b are detected by histogram algorithm and DWT but not by Canny. Even when
the parameters for Canny are lowered to low = 0.01, high = 0.02, Canny still does not detect
the edges such as #3, #4 and #4 in Figure 5b. The Chl-a transacts across the fronts #3, #4
and #5 are shown in Figure 6(4) and 6(5), which corresponds to a 0.07, 0.03 and 0.05 chl-a
gradient, respectively. The magnitudes of these chl-a gradients correspond to a change of
2-3 pixel values across the detected fronts. DWT algorithm seems to perform best in
detecting low chl-a fronts. For example, front labeled as #6 in Figure 5c was not detected
by Canny and histogram algorithm. The Chl-a gradient across front #6 is about 0.05
(Figure 6(6)).
The same set of parameters derived from image of March 12, 2005 above is
applied to images collected for different dates. Figure 7 shows similar results for chl-a
image of April 4, 2005. Canny performs better in detecting the fronts near the costal area,
while histogram algorithm and DWT are sensitive enough to detect the low Chl-a fronts in
the center of study area.
#1
#3
#2
#4
#5
10
(1)
(2)
11
12
(1)
(2)
Figure 7. Chl-a fields on West Florida Shelf, April 4, 2005, with edges overlaid. (a)
edges detected by Canny, (b) edges detected by histogram algorithm, (c) edges detected
by DWT, (d) edges detected by SUSAN.
4. Summary
All the algorithms evaluated in this study, except SUSAN detector, gives similar
overall performance on SST images [how many images have been evaluated?] off the West
Florida Shelf. Canny detector performs better than other detectors in detecting and
retaining finer scale [give measure, < 5 km? 10km?] fronts near the coastal area. [what is
the “optimal” parameter set for each algorithm?] [Does Canny have some shortcomings? If
not this must be the best candidate, right? If yes what are they?]
For Chl-a images, Canny detector performs better in detecting edges near the shore
where chl-a has high values (sometimes erratically high), but performs poorly in detecting
low chl-a fronts in the center of study area [where is the center?]. On the contrary,
histogram algorithm and DWT perform better in low chl-a area than in the high chl-a costal
area. [the words “high”, “low” etc. without context are not scientific languages. Need to
give some specific numbers, for example, > 5 mg m-3 <0.5 mg m-3, etc.] [this is very
qualitative summary. Give some specifics]
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For practical point of view, it is difficult, if not impossible, to select a single
algorithm which can provide same high level of performance in detecting various type of
fronts, i.e. mesoscale fronts vs fine scale fronts, strong fronts vs weak fronts. Selection of a
particular edge detection algorithm for marine satellite images is most likely a task-based
choice. [this last paragraph makes the entire paper nearly useless – what can a reader learn
from your work? Can you recommend something(s)? For example, under such and such
circumstances, use this method with this parameter set…. For SST, do this…. For Chl do
that….]
[Visual judgment is not a good evaluation, because color is illusive. I can tweak color to
show whatever feature you want to see or not want to see. So, this must be pointed out in
the discussion, and most importantly, add some quantitative measure for evaluation, such
as your detailed gradient analysis, some statistics on the frontal pixels for large and small
features respectively, some more tests on other images where contrast is not as strong as in
the given examples, cloud edge problems, etc.]
[Overall this is a good start, but major improvement is needed. If I can summarize: 1.
Methods. Describe each method concisely yet let an average reader like me understand the
principle, and what those parameters mean (if you change x from 0.5 to 0.6 what does the
algorithm do).
Results. Have you tested many more images under all circumstances? Is the “optimal” set,
chosen from one image only, always “optimal” for all other images? Give quantitative
measures – this is important
Discussion. What do these results mean? What are the remaining issues? If an algorithm
miss one front, so what?
Summary. Make it a real summary to include some quantitative numbers and some
recommendations, so other people don’t need to spend months again trying to find the
“best” edge-detection method]
Reference
Canny, J., 1986. A computational approach to edge detection. IEEE Trans. PAMI, 8,
679-698.
Cayula, J. F. and Cornillon, P., 1992. Edge detection algorithm for SST images. J. Atmos.
Oceanic Technol., 9, 67-80.
Cayula, J. F. and Cornillon, P., 1995. Multi-image edge detection for SST images. J.
Atmos. Oceanic Technol., 12, 821-829.
Heath, M. D., Sarkar, S., Sanocki, T., Bowyer, K. W., 1997. A robust visual method for
assessing the relative performance of edge-detection algorithm, IEEE Trans. PAMI, 19,
1338-1359.
14
Holyer, R. J. and Peckinpaugh, S, H., 1989. Edge detection applied to sea surface
temperature fields, IEEE Trans. On Geoscience and Remote Sensing, GE-27, 46-56.
Janowitz, M. F., 1985. Automatic detection of gulf stream rings, Office of Naval Research
Tech. Rep. TR-J8501, Contr. N-00014-79-C-0629, 44 pp.
Kahru, M., Hakansson, B., Rud, O., 1995. Distributions of the sea-surface temperature
fronts in the Baltic sea as derived from satellite imagery, Continental Shelf Research, 15,
663-679.
Kitchen, L. and Rosenfeld, A., 1981. Edge evaluation using local edge coherence, IEEE
Trans. System, Man, and Cybernetics, 11, 597-605.
Liu, A. K., Peng, C. Y., Chang, S. Y.-S., 1997a. Wavelet analysis of satellite images for
coastal watch, IEEE J. Oceanic Eng., 22, 9-17.
Liu, A. K., Martin, S., Kwok, R., 1997b. Tracking of ice edge and ice floes by wavelet
analysis of SAR images. J. Atmos. Oceanic Technol., 14, 1187-1198.
Liu, A. K., Zhao, Y., Esaias, W. E., Campbell, J. W., Moore, T. S., 2002. Ocean surface
layer drift revealed by satellite data. Eos, Transactions, AGU, 83, pages 61-62, 64.
Liu, H., Wang, L., Jezek, K. C., 2005. Wavelet-transform based edge detection approach
to derivation of snowmelt onset, end, and duration from satellite passive microwave
measurements, Internale J. Remote Sensing, 26, 4639-4660.
Mallat, S. and Zhong, S., 1992. Characterization of signals from multiscale edges. IEEE
Trans. PAMI, 14, 710-732.
Mavor, P. T. and Bisagni, J. J., 2001. Seasonal variability of sea-surface temperature
fronts on Geores Bank, Deep-Sea Research, 48, 215-243.
Miller, P., 2004. Multi-spectral front maps for automatic detection of ocean color features
from SeaWiFS, International J. Remote Sensing, 25, 1437-1442.
O'Reilly, J. E., Maritorena, S., O'Brien, M. C., Siegel, D. A., Toole, D., Mitchell, B. G.,
Kahru, M., Chavez, F. P., Strutton, P., Cota, G. F., Hooker, S. B., McClain, C. R.,
Carder, K. L., Muller-Karger, F. E., Harding, L., Magnuson, A., Phinney, D.,
Moore, G. F., Aiken, J., Arrigo, K. R., Letelier, R., and Culver, M. (2000), Ocean
color chlorophyll a algorithms for SeaWiFS, OC2, and OC4: version 4. In:
SeaWiFS Postlaunch Technical Report Series (S. B. Hooker & E. R. Firestone
Eds.), NASA Technical Memorandum 2000-206892, Vol. 11. Greenbelt,
Maryland: NASA Goddard Space Flight Center (51pp).
Sadler, B. M., Swami, A., 1999. Analysis of multiscale products for step detection and
estimation. IEEE Trans. Information Theory, 45, 1043-1051.
15
Sauter, D. and Parson, L., 1994. Spatial filtering for speckle reduction contrast
enhancement, and texture analysis of GLORIA images. IEEE Journal of Oceanic
Engineering, 19, 563-576.
Savage, C. R., Petrell, R. J., Neyfeld, T. P., 1994. Underwater fish video images: Image
quality and edge detection techniques. Canadian Agricultural Engineering, 19, 563-576.
Shin, M. C., Goldgof, D. B., Bowyer, K. W., 2001. Comparison of edge detector
performance through use in an object recognition task, Computer Vision and Image
Understanding, 84, 160-178.
Smith, S. and Brady, J. M., 1997. SUSAN – a new approach to low level image processing.
International Journal of Computer Vision, 23, 45-78.
Ullmann, D. S. and Cornillon, P. C., 1999. Satellite-derived sea surface temperature fronts
on the continental shelf off the northeast U.S. coast, J. Geophysical Research, 104,
459-478.
Ullmann, D. S. and Cornillon, P. C., 2001. Continental shelf surface thermal fronts in
winter off the northeast US coast, Continental Shelf Research, 21, 1139-1156.
Vazquez, D. P., Atae-Allah, C., Escamilla, P. L. L., 1999. Entropic approach to edge
detection for SST images, J. Atmos. Oceanic Technol., 16, 970-979.
Xu, Y. et al., 1994. Wavelet transform domain filter: a spatially selective noise filtration
technique. IEEE Trans. Image Process., 3, 747-758.
Yitzhaky and Peli, 2003.
Zhang, L and Bao, P., 2002. Edge detection by scale multiplication in wavelet domain.
Pattern Recognition Letters, 23, 1771-1784.
Zhu, Q., 1996. Efficient evaluations of edge connectivity and width uniformity, Image and
Vision Computing, 14, 21-34.
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