Monday, January 2, 2017

Polar representation for lines

Let’s take an arbitrary point in the xy-plane, and consider all the possible lines passing through it . Each of these lines can be represented as subject to in the mb-plane. The mb-plane is called the Hough space:

The problem is when the line is vertical, is infinite and completely off the chart, not a nice property if you ask me. The solution is to use polar representation of the lines instead of slope-intercept representation.

In the figure below, AB is the line we want represent with polar coordinates , where is the distance from the origin to the line () and is angle between the x-axis and the normal vector of the line ().

Let E be an arbitrary point on AB, then , , , , , . Using the fact , you can derive that , the polar representation we were looking for.


Oliver Maurice said...

Maybe you could check out the mobistealth soft, because its awesome