Motion blur convolution matrix given an angle and magnitude

Question

I have Java code that takes a convolution matrix (just a 2D double[][]) and applies it to an image. I'm trying to figure out how to create a matrix that will give a motion blur, given an angle (in degrees) and a magnitude for the blur.

An example matrix for a blur with magnitude = 1 (the middle pixel is blurred by one pixel in each direction), 45 degree motion blur is:

0      0    1/3
0     1/3    0
1/3    0     0

The magnitude determines the size of the matrix (size = 2*magnitude + 1) and a single line of cells is non-zero in the direction of motion.

What I'm having trouble with is the math/code necessary to figure out which cells to have non-zero in the matrix given the angle.

Pseudo (or actual) code would be immensely helpful!

bogle · Answer 1 · 2013-03-22T21:16:17.110

1

For a motion blur the non-zero elements show all lie along a single line. That's why your example works. [1/n 1/n (ntimes)... 1/n] would blur in the horizontal direction while the transpose would blur vertically. For an arbitrary angle just fill in the non-zero elements that best approximate a line at the angle you want.

edit.

For example, you might try to minimize some function of the pixel indices to determine whether that pixel should be non-zero. |(i - 3*j)| < small number, would find pixels along a line of slope 3.

edited Mar 22 '13 at 21:16

answered Mar 22 '13 at 21:09

bogle

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Yes, I understand that. What I don't know how to do is figure out which cells best approximate a line at the given angle. – scaevity Mar 22 '13 at 21:10
ahh, sorry. ammended my answer with a heuristic solution. – bogle Mar 22 '13 at 21:17
@scaevity Did you find a solution to the problem? – zanbri Aug 24 '17 at 13:41

score 1 · Answer 2 · answered Jul 10 '20 at 16:03

In Matlab and Octave, there is a build in function called "fspecial" for creating kernels for convolution. By passing the 'motion' flag along with the magnitude and angle, it will output a constitutional kernel (matrix) that you can use to apply motion blur to your image. https://octave.sourceforge.io/image/function/fspecial.html

Unfortunately, there does not appear to be such a function in other languages, that I can find anyway for creating this kernel. The best that I can think of is to convert the angle and magnitude into the start and end (x,y) points of a line. Then you could draw a grayscale, anti-aliased line using Xiaolin Wu algorithm https://rosettacode.org/wiki/Xiaolin_Wu%27s_line_algorithm

You would have to divide all the elements by the sum of the elements to ensure that the kernel is normalised before convolving it with your image.

Motion blur convolution matrix given an angle and magnitude

2 Answers2