learn-blur

Learning about various blurring filters and how to optimize them by exploiting caching and separability.

Contents

• box filter
• gaussian filter
• median filter
• bilateral filter

Box Blur Optimisation

Implemented a naive Box blur filter and an optimized one that uses separablity to make runtime independent of the filter size. Running test_box_speedup.png generates the below plot.

For a filter size of 15, I can get a speedup factor of 75!

Box Blur vs Gaussian Blur

We can approximate a Gaussian filter with about 3 passes of a Box blur filter. This follows from the Central Limit Theorem.

Here's some qualitative results:

Numba Optimization

I added numba optimization to both the Gaussian filter and the Box blur filter. This is as simple as adding an @njit decorator to the class's staticmethod _filter1d.

Because the Gaussian Filter loop is less complex than that of the Box blur filter, we can get the optimized Gaussian filter to run faster than the Box blur filter for certain kernel sizes. Note that this won't be the case for lower-level languages if both filters are implemented in C for example.

Filter	No Numba	With Numba
Gaussian	68.04	2.5
Box (x3)	5.31	3.7
Speedup	12.82	0.68

Median Filter

Bilateral Filter

Blur Animation

Just for fun, here's a visualization of how the blurred image is generated pixel by pixel.

References

• Speeding Up Box Blur