a question about image filtering: what should be the scaling factor after image filtering?

Hi all,

I am facing a headache question in image filtering...

I want to apply a low pass filter to an RGB image... I used Gaussian filter, 
using Matlab "fspecial" command

h=fspecial('gaussian', [31, 31], 5);

... and I am setting the cutoff frequency quite low because I really want to 
blur the images quite heavily...

I applied the filter to each of the RGB planes, using the Matlab "imfilter" 
command.

My input image was made sure to be within [0, 1] for each plane. So for each 
RGB plane, the range is [0, 1], [0, 1], [0, 1]. The mean of each channel 
are: R: 0.2018;  G: 0.2805;  B: 0.2892.

After the filtering, the output image has a reduced dynamic range:

R: [0.0282, 0.2089]
G: [0.0659, 0.2909]
B: [0.0429, 0.2980]

and the mean of each channel are kept almost the untouched: R: 0.1971; G: 
0.2748; B: 0.2825.

The filtered image is definitely too dark...

I have to scale it back to [0, 1]...

but do I just do scaling/normalizing to 1 in each channel individually, or 
do I normalize with respect to the overall maximum in all three channels?

But why does this filter change the relative peak ratio for each plane from 
1:1:1 to 0.2089:0.2909:0.2980? Is there any low pass filter which can 
preserve the relative peak ratio to be still 1:1:1?

And is this scaling factor an arbitrary thing as long as I make the maximum 
value to be 1, or it has some theory behind it and it can be derived 
theoratically?

Thanks a lot!

lucy wrote:

> Hi all,
> 
> I am facing a headache question in image filtering...
> 
> I want to apply a low pass filter to an RGB image... I used Gaussian filter, 
> using Matlab "fspecial" command
> 
> h=fspecial('gaussian', [31, 31], 5);
> 
> ... and I am setting the cutoff frequency quite low because I really want to 
> blur the images quite heavily...
> 
> I applied the filter to each of the RGB planes, using the Matlab "imfilter" 
> command.
> 
> My input image was made sure to be within [0, 1] for each plane. So for each 
> RGB plane, the range is [0, 1], [0, 1], [0, 1]. The mean of each channel 
> are: R: 0.2018;  G: 0.2805;  B: 0.2892.
> 
> After the filtering, the output image has a reduced dynamic range:
> 
> R: [0.0282, 0.2089]
> G: [0.0659, 0.2909]
> B: [0.0429, 0.2980]
> 
> and the mean of each channel are kept almost the untouched: R: 0.1971; G: 
> 0.2748; B: 0.2825.
> 
> The filtered image is definitely too dark...
> 
> I have to scale it back to [0, 1]...
> 
> but do I just do scaling/normalizing to 1 in each channel individually, or 
> do I normalize with respect to the overall maximum in all three channels?
> 
Do the same thing to all three channels, or your color balance will be 
out of whack.

> But why does this filter change the relative peak ratio for each plane from 
> 1:1:1 to 0.2089:0.2909:0.2980?

You should know the answer to this, really you should.  If you have a 
signal that goes 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ... and you low-pass 
filter it, your filter will take those peaks and spread them out, 
flattening them in the process.  If the filter has a DC gain of 1 the 
average will be preserved, however.

> Is there any low pass filter which can 
> preserve the relative peak ratio to be still 1:1:1?

In general no.
> 
> And is this scaling factor an arbitrary thing as long as I make the maximum 
> value to be 1, or it has some theory behind it and it can be derived 
> theoratically?

What happens to the signal when you low-pass filter it depends on the 
signal and the filter.  In general you are removing the high-frequency 
content from the signal which is what is flattening and spreading out 
the peaks.  I don't know of any general theory, particularly since with 
some signals and some filters you'd actually see your peaks getting 
higher (not with video and Gaussian filters, I'm sure).

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com