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Jan 4, 2019 at 15:02 comment added DrManhattan Nice, I'm starting to understand. If you move this explanation in detail from the commens to the main answer I will give you the right answer tag :)
Jan 4, 2019 at 14:59 comment added Marcus Müller well, yes/no! When you've actually got a line, not just two points on a line, the fact that many pixels map onto the same $\rho, \theta$ makes it very robust. If you only got single pixels on each end of a line, there's nothing to accumulate, and yes, then it can only work on exact lines.
Jan 4, 2019 at 14:45 comment added DrManhattan So, the problem is that the Hough Transform is not able to deal with unprecise alignment of the points and it is expected to detect only ideal lines?
Jan 4, 2019 at 14:37 comment added Marcus Müller well, good key word: in your $(\rho, \theta)$ space, the upper four points fall onto one point – and everything is fine; however, the last centroid is offset enough from the theoretical line you're looking for that all connections between that centroid and any other centroid maps to a significantly different point in the $(\rho, \theta)$ plane. Hence, there's not enough power accumulating in these four accumulator space points individually for the Hough algorithm you're using to detect a peak.
Jan 4, 2019 at 14:32 comment added DrManhattan Could you please explain this better? If my understanding of the math behind the Hough trasform is correct if I have no other signal in my image except my 5 points even if the peaks in the $\rho\theta$ space will be dim they will still be very well recognizable, because there is no noise at all to cover the signal of my line.
Jan 4, 2019 at 14:14 comment added Marcus Müller Well, it doesn't perform well because it's designed to do something different than what you're trying to make it do. There really is only a hint of a line, not a line in your image.
Jan 4, 2019 at 13:36 comment added DrManhattan Yes, what I already did is exactly a linear fit of the coordinates of these centroids. My question was not about finding an alternative method to the hough transform, but I wanted to understand why the hough trasform method was not working, if there is any kind of improvement I can apply and why there is a difference why I apply it on the simply binarized image and when I apply it with the image with the centroids.
Jan 4, 2019 at 13:23 history answered Marcus Müller CC BY-SA 4.0