# [SciPy-User] Convolving an ndarray by a function

Solbrig, Mr. Jeremy Jeremy.Solbrig@nrlmry.navy....
Thu Sep 27 13:20:57 CDT 2012

```David,

Thanks, that is exactly what I was looking for.  I had looked at ndimage, but apparently I didn't look deeply enough.

Jeremy

From: scipy-user-bounces@scipy.org [mailto:scipy-user-bounces@scipy.org] On Behalf Of David Baddeley
Sent: Wednesday, September 26, 2012 9:17 PM
To: SciPy Users List
Subject: Re: [SciPy-User] Convolving an ndarray by a function

Hi Jeremy,

what you are after is scipy.ndimage.generic_filter. For your particular case (std. deviation), there is also a neat approximate solution using just standard uniform filters, which, although not strictly accurate, might be close enough for many applications and is considerably faster (a quick test gives a speedup of ~ 300x). Assuming your data array is called x:

from scipy import ndimage

#calculate the mean of a 3x3 ROI round each point
xm = ndimage.uniform_filter(x, 3)

#the standard deviation is the mean of the sum of squared differences to the mean
#note that here we are subtracting the mean of the local neighbourhood of each pixel, rather than that of the central pixel
sigma = np.sqrt(ndimage.uniform_filter((x - xm)**2, 3)

cheers,
David

________________________________
From: "Solbrig, Mr. Jeremy" <Jeremy.Solbrig@nrlmry.navy.mil<mailto:Jeremy.Solbrig@nrlmry.navy.mil>>
To: "'scipy-user@scipy.org'" <scipy-user@scipy.org<mailto:scipy-user@scipy.org>>
Sent: Thursday, 27 September 2012 8:25 AM
Subject: [SciPy-User] Convolving an ndarray by a function

Hi all,

I have run into a situation where I need to calculate the standard deviation for each NxM box within an ndarray.  I am wondering if there is a function available that would allow me to convolve (may not be the correct word here) an ndarray by a function and return an array of the same size as the original array.  Something like this:

>>> foo = np.arange(10000).reshape([100,100])
>>> stddev_arr = foo.funcconvolve([3, 3], np.std)
>>> stddev_arr.shape == foo.shape
True

Such that each point within stddev_arr is the standard deviation of a 3x3 box around each point in foo.

I'm sure I could code this in a loop, but I expect that there is a better solution.

Jeremy

Jeremy Solbrig
NRL Monterey
jeremy.solbrig@nrlmry.navy.mil<mailto:jeremy.solbrig@nrlmry.navy.mil>
(831) 656-4885

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