How to define a metric for similarity between two lines in radon form?
$begingroup$
I have a line given by r, theta, where
theta corresponds to the line's angle from the X axis
r corresponds to the distance from a given point "the center" to the line.
A clear plot of the paramaterization of such a line is given here
I have n such lines
I want to find the line(s) which are most 'similar' to the given line, from the given set.
I figured the Euclidean distance in the r, theta space won't catch the similarity between the lines well.
I figured a good metric would be one that takes the area between the lines into account (small area would be similar lines)
I'm sure there is a somewhat standard way for problems like this.
Please give me some formula that gives the similarity.
I would specify more requirements, but I don't really know what they are yet before seeing any appropriate metric.
geometry metric-spaces linear-transformations
asked Jan 7 at 16:33
GulzarGulzar
1013
$endgroup$
add a comment |
$begingroup$
I have a line given by r, theta, where
theta corresponds to the line's angle from the X axis
r corresponds to the distance from a given point "the center" to the line.
A clear plot of the paramaterization of such a line is given here
I have n such lines
I want to find the line(s) which are most 'similar' to the given line, from the given set.
I figured the Euclidean distance in the r, theta space won't catch the similarity between the lines well.
I figured a good metric would be one that takes the area between the lines into account (small area would be similar lines)
I'm sure there is a somewhat standard way for problems like this.
Please give me some formula that gives the similarity.
I would specify more requirements, but I don't really know what they are yet before seeing any appropriate metric.
geometry metric-spaces linear-transformations
asked Jan 7 at 16:33
GulzarGulzar
1013
$endgroup$
add a comment |
$begingroup$
I have a line given by r, theta, where
theta corresponds to the line's angle from the X axis
r corresponds to the distance from a given point "the center" to the line.
A clear plot of the paramaterization of such a line is given here
I have n such lines
I want to find the line(s) which are most 'similar' to the given line, from the given set.
I figured the Euclidean distance in the r, theta space won't catch the similarity between the lines well.
I figured a good metric would be one that takes the area between the lines into account (small area would be similar lines)
I'm sure there is a somewhat standard way for problems like this.
Please give me some formula that gives the similarity.
I would specify more requirements, but I don't really know what they are yet before seeing any appropriate metric.
geometry metric-spaces linear-transformations
asked Jan 7 at 16:33
GulzarGulzar
1013
$endgroup$
I have a line given by r, theta, where
theta corresponds to the line's angle from the X axis
r corresponds to the distance from a given point "the center" to the line.
A clear plot of the paramaterization of such a line is given here
I have n such lines
I want to find the line(s) which are most 'similar' to the given line, from the given set.
I figured the Euclidean distance in the r, theta space won't catch the similarity between the lines well.
I figured a good metric would be one that takes the area between the lines into account (small area would be similar lines)
I'm sure there is a somewhat standard way for problems like this.
Please give me some formula that gives the similarity.
I would specify more requirements, but I don't really know what they are yet before seeing any appropriate metric.
geometry metric-spaces linear-transformations
geometry metric-spaces linear-transformations
asked Jan 7 at 16:33
GulzarGulzar
1013
asked Jan 7 at 16:33
GulzarGulzar
1013
asked Jan 7 at 16:33
GulzarGulzar
1013
asked Jan 7 at 16:33
GulzarGulzar
1013
asked Jan 7 at 16:33
GulzarGulzar
1013
1013
add a comment |
add a comment |
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