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Determine whether filter coefficients are separable


S = isfilterseparable(H)
[S, HCOL, HROW] = isfilterseparable(H)


S = isfilterseparable(H) takes in the filter kernel H and returns 1 (true) when the filter is separable, and 0 (false) otherwise.

[S, HCOL, HROW] = isfilterseparable(H) uses the filter kernel, H, to return its vertical coefficients HCOL and horizontal coefficients HROW when the filter is separable. Otherwise, HCOL and HROW are empty.

Input Arguments


H numeric or logical, 2-D, and nonsparse.

Output Arguments


HCOL is the same data type as input H when H is either single or double floating point. Otherwise, HCOL becomes double floating point. If S is true, HCOL is a vector of vertical filter coefficients. Otherwise, HCOL is empty.


HROW is the same data type as input H when H is either single or double floating point. Otherwise, HROW becomes double floating point. If S is true, HROW is a vector of horizontal filter coefficients. Otherwise, HROW is empty.


Logical variable that is set to true, when the filter is separable, and false, when it is not.


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Determine if the Gaussian filter created using the fspecial function is separable.

Create a Gaussian filter.

twoDimensionalFilter = fspecial('gauss');

Test the filter.

[isseparable,hcol,hrow] = isfilterseparable(twoDimensionalFilter)
isseparable =



hcol =


hrow =

   -0.1065   -0.7870   -0.1065

More About

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Separable two dimensional filters

Separable two-dimensional filters reflect the outer product of two vectors. Separable filters help reduce the number of calculations required.

A two-dimensional convolution calculation requires a number of multiplications equal to the width × height for each output pixel. The general case equation for a two-dimensional convolution is:


If the filter H is separable then,


Shifting the filter instead of the image, the two-dimensional equation becomes:


This calculation requires only (width + height) number of multiplications for each pixel.


The isfilterseparable function uses the singular value decomposition svd function to determine the rank of the matrix.

Introduced in R2006a