对Canny边缘检测器的一个有趣的优化

Sat 08 Sep 2012

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That's why I took a few days toimplement it in FFmpeg. Following is a screenshot ofa Lynx video by Stefan Sobottafiltered with theedgedetectfilter:

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For those not familiar with the algorithm, it is essentially a few successive filters applied on a gray scale image:

For more details, I'd recommend theCanny edge detector Wikipedia pageand its external links.

This article will focus on the second step, and especially thedirections computation, since it involves some little math and can be expensive. The other steps are either trivial or widely documented so they won't be the topic of this post.

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The kernel forGxis:

And the kernel forGyis:

The interesting thing aboutGxandGyis that they allow to define an edge direction angleΘ = atan2(|Gx|,|Gy|). In the Canny Edge Detector algorithm, this angle must be rounded to one of the four directions:

These directions, defined for each pixel, will be used in the next step when looking for maximums.

Let's write a piece of code to test our direction rounder:

That code takes alimitparameter used to limit the range of thexandyvalues. Basically,get_direction()will be called for all the integer values forxin[-limit;limit]and foryin[-limit;limit]. Each pixel will be attributed a color describing the direction (blue for horizontal, yellow for vertical, etc).

The usage is pretty simple:

% gcc -Wall -lm a.c && ./a.out 100 > out.ppm && feh out.ppm

The resulting outputout.ppmis a picture of size2xlimitx2xlimitfull of colors.

Here is a naiveget_direction()implementation, where we computeΘto compare it to reference angles (π/8and3π/8), and use the signs ofGxandGy:

The resultingout.ppmwithlimit=100:

So this is exactly what we want to achieve. Unfortunately, the call toatan2()for each pixel is quite troublesome.

Note: ifGx = 0andGy = 0, we are at the center of the picture.

If we want to get get rid of theatan2()we can just usetan(): basically the tangent of the angleΘdefined byGxandGyisGy/Gx:tan(Θ) = Gy/Gx. So we just have to compareGy/Gxagainst the tangent of the reference angle, which are the following constants:

And to avoid the division ofGy/Gx, we can simply compareGyagainstGxmultiplied by these constants. Here is a new proposition of theget_direction()function:

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