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opencvcomputer-visioncomputer-sciencehough-transform

How exactly does dp parameter in cv::HoughCircles work?

I read similar question in Stack Overflow. I tried, but I still can not understand how it works.

I read OpenCV document cv::HoughCircles, here are some explanation about dp parameter:

Inverse ratio of the accumulator resolution to the image resolution. For example, if dp=1 , the accumulator has the same resolution as the input image. If dp=2 , the accumulator has half as big width and height.

Here are my question. For example, if dp = 1, the size of accumulator is same as image, there is a consistent one-to-one match between pixels in image and positions in accumulator, but if dp = 2, how to match?

Thanks in advance.

Solution

  • There is no such thing as a one-to-one match here. You do have an image with pixels and a hough space, which is used for voting for circles. This parameter is just a convenient way to specify the size of the hough space relatively to the image size.

    Please take a look at this answer for more details.

    EDIT:

    Your image has (x,y)-coordinates. Your circle hough space has (a,b,r)-coordinates, whereas (a,b) are the circle centers and r are the radii. Let's say you find a edge pixel. Now you vote for each circle, which could go through this edge pixel. I found this nice picture of hough space with a single vote i.e. a single edge pixel (continuous case). In practice this vote happens within the 3D accumulator matrix. You can think of it as rasterization of this continuous case.

    Now, as already mentioned the dp parameter defines the size of this accumulator matrix relatively to your image size. The bigger the dp parameter the lower the resolution of your rasterization. It's like taking photos with different resolutions. If you downsize your photo multiple pixels will reduce to a single one. Same happens if you reduce your accumulator matrix respectively increase your dp parameter. Multiple votes for different circle centers (which lie next to each other) and radii (which are of similar size) are now merged, i.e. you do get less accurate circle parameters, but a more "robust" voting.

    Please be aware that the OpenCV implementation is a little bit more complicated (they use the Hough gradient method instead of the standard Hough transform) but the considerations still apply.