This is my situation. It involves aligning a scanned image which will account for incorrect scanning. I must align the scanned image with my Java program.
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Edge detection is something that is typically done by enhancing the contrast between neighboring pixels, such that you get a easily detectable line, which is suitable for further processing.
To do this, a "kernel" transforms a pixel according it the pixel's inital value, and the value of that pixel's neighbors. A good edge detection kernel will enhance the differences between neighboring pixels, and reduce the strength of a pixel with similar neigbors.
I would start by looking at the Sobel operator. This might not return results that are immediately useful to you; however, it will get you far closer than you would be if you were to approach the problem with little knowledge of the field.
After you have some crisp clean edges, you can use larger kernels to detect points where it seems that a 90% bend in two lines occurs, that might give you the pixel coordinates of the outer rectangle, which might be enough for your purposes.
With those outer coordinates, it still is a bit of math to make the new pixels be composted with the average values between the old pixels rotated and moved to "match". The results (especially if you do not know about anti-aliasing math) can be pretty bad, adding blur to the image.
Sharpening filters might be a solution, but they come with their own issues, mainly they make the picture sharper by adding graininess. Too much, and it is obvious that the original image is not a high-quality scan.