Separable N-Dimensional Convolution

N-dimensional convolution for separable kernels, similar to functionality of "conv2(hcol, hrow, A)"


Updated 26 Feb 2011

View License

This function is an implementation of N-dimensional convolution for the special case when the convolution kernel is separable.

A continuous function f(x1, x2, ... xN) is considered separable if there exist N functions f1, f2, ... fN such that f(x1, x2, ... xN) = f1(x1)f2(x2)f3(x3)...fN(xN).

In two dimensions, a discrete version of the separability condition is as follows: a 2D matrix is separable if it can be expressed as an outer product of two 1D vectors:

a=[-1 0 1]; b=[1 0 -1]; H=a'*b

In this case, supplying Matlab's conv2 function with the two vectors a & b (one to convolve the rows with, the second to convolve the columns with) results in a faster computation than supplying conv2 with the outer product H.

Convnsep.m extends this functionality to an arbitrary number of dimensions.

This may be useful for applications such as:
1. Smoothing a 3D image with separable filters
2. Bilateral filtering (requires 4D convolution for filtering a 3D image)

Notes and caveats:

- As the total size of the variable being convolved increases towards the largest size allowable by Matlab (platform/architecture dependent), performance significantly degrades due to memory limitations, and may become worse than that of convn. Because Matlab requires a contiguous block of memory to allocate space for a variable, the maximum size for which performance is reasonable may be significantly lower than the "theoretical" size limit (which is 1.5 GB on my platform).

- For convolution types other than 'full' (no discarding of any samples), only odd-sized kernels are currently working properly.

Cite As

Igor Solovey (2023). Separable N-Dimensional Convolution (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010a
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes

Fixed a reference to num2str