The straight line $y=mx+b$ can be expressed in polar coordinates as:
$$\rho=x\cos(\theta) + y\sin(\theta)$$
Where $(\rho,\theta)$ defines a vector from the origin to the nearest point on the line. Thus the Hough transform of a straight line in $x-y$ space is a point in $(\rho,\theta)$ space.
Find $(\rho, \theta)$ for the following straight line $y=-x+5$.
I'm trying to go through a simple exercise for the Hough transform where I have a simple straight line in the form of $\;y=-x+5\;$ and I want to obtain polar coordinates $\;(\rho,\theta)$. I know polar coordinates can be represented by $\;\rho = x⋅\cos(\theta) + y⋅\sin(\theta).$
What are the steps I'm supposed to take to solve this problem? I have searched around and couldn't really find any examples I can follow in this exact format.
Best Answer
$$\frac{\left|c\right|}{\sqrt{a^2+b^2}}$$ Gives you the normal distance from the origin to the straight line which is $\rho$
So if you multiply $$ax+by=c$$ by $\rho/c$ you get $$mx+ny=\rho$$ where $m=\cos(\theta)$ and $n=\sin(\theta)$ and getting $\theta$ given this should be easy.