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A. K. Lm AND C. Y. PENG
winds, waves, and ocean currents, the ice edge in general consists of ice floes of multiple scales with a complex edge configuration. In such cases the use of a single-scale
wavelet transform may not be applicable. Therefore, in these cases, it is difficult to delineate a representative ice edge by locating the zero crossing of the Mexican-hat wavelet
transform as a single-scale band-pass filter. If one uses a large-scale wavelet transform
to suppress the noisy small-scale features, a simple approximate boundary can be located, but it may deviate from the true ice edge considerably. On the other hand, if a small
scale is chosen, the wavelet transform yields so many edge elements of zero-crossing
that it is hard to sort out by threshold techniques those belonging to the true boundary.
To overcome these deficiencies of the edge segmentation with a single-scale wavelet
transform, we use a more general algorithm to locate the ice edge in the SAR images by
assembly of the edge elements from the results of a multiscale wavelet transform which
include both large and small scales. In the algorithm, some of the techniques developed
in the field of computer vision are used, such as the method of "proximity to an approximation" (Ballard and Brown 1982) to locate a more accurate boundary through use of
a distance criterion (evaluation function) to obtain a new point for an approximate
boundary. The distance operator measures the minimum distance of the new point to
the approximate boundary. With the ice edge detected from the large-scale wavelet
transform used as the approximate boundary, the edge elements from the small-scale
wavelet transform are then used as boundary points for a more accurate boundary.
Thus, the linking of these edge elements can serve as an approximate boundary for an
even smaller-scale wavelet transform. Several scales can be used to delineate the ice
edge as accurately as required.
Thus, in the case of the St. Lawrence Island polynya a wavelet transform with a median scale, a =16 units of pixel spacing, is computed as a band-pass filter. The edge elements are not obtained directly from the contours of zero-crossing of wavelet transform.
As mentioned above, because the smoothing effect of the Mexican-hat wavelet is reduced
as its scale becomes smaller, the zero-crossing associated with noise proliferates in the
whole image, and it becomes difficult to sort out the true boundary even by threshold.
Here we obtain the edge elements by selecting a contour value of the wavelet transform
equal to a fraction of its maximum, as shown in Fig. 7a indicated by white contours. A
threshold value of 5% was used in this case. The result is the appearance of a number of
small closed contours, most of them located in the neighborhood of the approximate ice
edge given by tlIe dashed line. Because of the fragmented nature of the marginal ice zone,
a few of the closed contours may appear anywhere in the image. These closed contours
can be effectively eliminated by the method of proximity mentioned above.
The center of mass of these closed contours is computed first. Then the distance from
the point of the center of mass Xc to the approximate boundary is calculated. If the distance is below a certain threshold value, the point (xoYc) is considered to be a new point
on a refined boundary of the ice edge. A threshold value of 100 m was used in this case.
These new points still have to be linked to form an integral boundary corresponding
to the large-scale ice edge. There are a number of methods for edge linking, such as the
method of "divide and conquer" (Selfridge et al.1979). Since the boundary points given by the median scale are in general sparse and well separated, the boundary can be
delineated by successively connecting each center of mass to its nearest neighbor.
Finally, a wavelet transform with a scale of a = 4 units of pixel spacing is computed.
Repeating the same procedure as above, we obtain a new boundary closer to the true ice
A. K. Lm AND C. Y. PENG
winds, waves, and ocean currents, the ice edge in general consists of ice floes of multiple scales with a complex edge configuration. In such cases the use of a single-scale
wavelet transform may not be applicable. Therefore, in these cases, it is difficult to delineate a representative ice edge by locating the zero crossing of the Mexican-hat wavelet
transform as a single-scale band-pass filter. If one uses a large-scale wavelet transform
to suppress the noisy small-scale features, a simple approximate boundary can be located, but it may deviate from the true ice edge considerably. On the other hand, if a small
scale is chosen, the wavelet transform yields so many edge elements of zero-crossing
that it is hard to sort out by threshold techniques those belonging to the true boundary.
To overcome these deficiencies of the edge segmentation with a single-scale wavelet
transform, we use a more general algorithm to locate the ice edge in the SAR images by
assembly of the edge elements from the results of a multiscale wavelet transform which
include both large and small scales. In the algorithm, some of the techniques developed
in the field of computer vision are used, such as the method of "proximity to an approximation" (Ballard and Brown 1982) to locate a more accurate boundary through use of
a distance criterion (evaluation function) to obtain a new point for an approximate
boundary. The distance operator measures the minimum distance of the new point to
the approximate boundary. With the ice edge detected from the large-scale wavelet
transform used as the approximate boundary, the edge elements from the small-scale
wavelet transform are then used as boundary points for a more accurate boundary.
Thus, the linking of these edge elements can serve as an approximate boundary for an
even smaller-scale wavelet transform. Several scales can be used to delineate the ice
edge as accurately as required.
Thus, in the case of the St. Lawrence Island polynya a wavelet transform with a median scale, a =16 units of pixel spacing, is computed as a band-pass filter. The edge elements are not obtained directly from the contours of zero-crossing of wavelet transform.
As mentioned above, because the smoothing effect of the Mexican-hat wavelet is reduced
as its scale becomes smaller, the zero-crossing associated with noise proliferates in the
whole image, and it becomes difficult to sort out the true boundary even by threshold.
Here we obtain the edge elements by selecting a contour value of the wavelet transform
equal to a fraction of its maximum, as shown in Fig. 7a indicated by white contours. A
threshold value of 5% was used in this case. The result is the appearance of a number of
small closed contours, most of them located in the neighborhood of the approximate ice
edge given by tlIe dashed line. Because of the fragmented nature of the marginal ice zone,
a few of the closed contours may appear anywhere in the image. These closed contours
can be effectively eliminated by the method of proximity mentioned above.
The center of mass of these closed contours is computed first. Then the distance from
the point of the center of mass Xc to the approximate boundary is calculated. If the distance is below a certain threshold value, the point (xoYc) is considered to be a new point
on a refined boundary of the ice edge. A threshold value of 100 m was used in this case.
These new points still have to be linked to form an integral boundary corresponding
to the large-scale ice edge. There are a number of methods for edge linking, such as the
method of "divide and conquer" (Selfridge et al.1979). Since the boundary points given by the median scale are in general sparse and well separated, the boundary can be
delineated by successively connecting each center of mass to its nearest neighbor.
Finally, a wavelet transform with a scale of a = 4 units of pixel spacing is computed.
Repeating the same procedure as above, we obtain a new boundary closer to the true ice