The other day I got very interested in learning about Hough Transform that is used to detect edges in images.
After going through OpenCV documentation, I still couldn't piece together an understanding for myself.
So I found this great video that provides a (very welcome) visual example of the interaction between the image space and the Hough space.
However before jumping straight to polar coordinates with rho and theta, a simpler example is shown: the relationship between X and Y; and a and b (the intercept and the slope).
Can somebody explain why a single Xi,Yi translates to a whole line in a/b space (if looking at cartesian coordinates)?
(x/y space to a/b space graphs)
By the way, here's the complete yt video that I am referring to in the snippet above.
I think after getting this down pat, the general translation between image space and Hough space will come easier to me.
Thank you for helping.
The equation $y=ax+b$ has various solutions in $a$ and $b$. Given only one point, $(x_i,y_i)$, we don't know what the values of $a$ and $b$ are, but we can constrain them to lie on a line given by $b=x_i-ay_i$. The point to note here is that we've gone from regarding $x$ and $y$ as variables to regarding $a$ and $b$ as variables.
The transform in question in the video looks at all pairs of points in an image in a quest to find entire sets of points which all lie on a particular line, in other words where the $a$ and $b$ values for many points coincide.