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Calculation of snr

 
 
Marc Wossner
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      05-22-2008

Hi ng,

Iīd like to know about the signal to noise ratio of my digital camera.
According to a website I found this value is the ratio of total signal
to total noise expressed in decibels (dB) and can be calculated with
the following formula:

SNR = 20 log (Signal RMS / Noise RMS)

As math was always a horror for me, I have only a slight idea of "root
mean square" but donīt know how to deduce those values from simple
digital images. Can someone please help me with that?

Best Regards!
Marc Wossner


 
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ransley
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      05-22-2008
On May 22, 5:28*am, Marc Wossner <(E-Mail Removed)> wrote:
> Hi ng,
>
> Iīd like to know about the signal to noise ratio of my digital camera.
> According to a website I found this value is the ratio of total signal
> to total noise expressed in decibels (dB) and can be calculated with
> the following formula:
>
> SNR = 20 log (Signal RMS / Noise RMS)
>
> As math was always a horror for me, I have only a slight idea of "root
> mean square" but donīt know how to deduce those values from simple
> digital images. Can someone please help me with that?
>
> Best Regards!
> Marc Wossner


db is sound not what your eve sees, what is "this wedsite" for you id
say tb, trollbell
 
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Marc Wossner
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      05-22-2008
On 22 Mai, 12:36, ransley <(E-Mail Removed)> wrote:
> On May 22, 5:28*am, Marc Wossner <(E-Mail Removed)> wrote:
>
> > Hi ng,

>
> > Iīd like to know about the signal to noise ratio of my digital camera.
> > According to a website I found this value is the ratio of total signal
> > to total noise expressed in decibels (dB) and can be calculated with
> > the following formula:

>
> > SNR = 20 log (Signal RMS / Noise RMS)

>
> > As math was always a horror for me, I have only a slight idea of "root
> > mean square" but donīt know how to deduce those values from simple
> > digital images. Can someone please help me with that?

>
> > Best Regards!
> > Marc Wossner

>
> db is sound not what your eve sees, what is "this wedsite" for you id
> say tb, trollbell


Yes, but "db" is also quite often used in electronic context as well
so I thought id would be correct.
If it isn`t, can you tell me the right way?

Best regards!
Marc Wossner
 
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ransley
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Posts: n/a
 
      05-22-2008
On May 22, 6:10*am, Marc Wossner <(E-Mail Removed)> wrote:
> On 22 Mai, 12:36, ransley <(E-Mail Removed)> wrote:
>
>
>
>
>
> > On May 22, 5:28*am, Marc Wossner <(E-Mail Removed)> wrote:

>
> > > Hi ng,

>
> > > Iīd like to know about the signal to noise ratio of my digital camera.
> > > According to a website I found this value is the ratio of total signal
> > > to total noise expressed in decibels (dB) and can be calculated with
> > > the following formula:

>
> > > SNR = 20 log (Signal RMS / Noise RMS)

>
> > > As math was always a horror for me, I have only a slight idea of "root
> > > mean square" but donīt know how to deduce those values from simple
> > > digital images. Can someone please help me with that?

>
> > > Best Regards!
> > > Marc Wossner

>
> > db is sound not what your eve sees, what is "this wedsite" for you id
> > say tb, trollbell

>
> Yes, but "db" is also quite often used in electronic context as well
> so I thought id would be correct.
> If it isn`t, can you tell me the right way?
>
> Best regards!
> Marc Wossner- Hide quoted text -
>
> - Show quoted text -


I went to www.dpreview.com and typed in a search of Decibel, and it is
one measure used. But db was developed as a rating of sound. I have
no idea how its transfered to a visual rating, or number, if it even
is as sound can be easily rated in S/N and db numbers, which are easy
to understand and industry accepted. I dont see any db ratings at
dpreview, just visual detail charts and descriptions. It would make
buying equipment easy if numbered ratings on a large known scale were
assigned to cameras and lenses as is done in audio equipment. Is it
done with dvds on the video portion? It is done with sound ratings. To
compare your camera find sites that reviewed it, what camera is it.
 
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Don Stauffer in Minnesota
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      05-22-2008
On May 22, 5:28 am, Marc Wossner <(E-Mail Removed)> wrote:
> Hi ng,
>
> Iīd like to know about the signal to noise ratio of my digital camera.
> According to a website I found this value is the ratio of total signal
> to total noise expressed in decibels (dB) and can be calculated with
> the following formula:
>
> SNR = 20 log (Signal RMS / Noise RMS)
>
> As math was always a horror for me, I have only a slight idea of "root
> mean square" but donīt know how to deduce those values from simple
> digital images. Can someone please help me with that?
>
> Best Regards!
> Marc Wossner


Unfortunately, the handling of logrithmic values is not the hardest
part of the job. In order to really look at signal to noise, you need
to make a very carefully controlled exposure, and look at lots of
pixels in order to get a statistical value of each part (signal and
noise). Also, there are a couple of types of snr definitions (large
signal vs small signal snr).

You should also be looking at a RAW file, since the jpeg compression
affects snr of an image.

the root mean square part is easy.

Look at a large range of noise pixels, say at least 10. Compute the
average. Then go back to the individual readings, and subtract the
average from each. Then square the differences. Add together all
these "squares". Now take the square root of the sum of the squares.
Many calculators can do this part. In fact, some scientific and most
statistical calculators can compute the RMS by entering a series of
readings.

Now you can convert your ratio into dbs.

 
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David J Taylor
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      05-22-2008
John O'Flaherty wrote:
[]
>> - 4096 for 12-bit or 16384 for 14-bit. This program will take the
>> drudgery out of the calculations, if not out of getting the careful
>> exposures.


However, do be aware that a simple SNR calculation will tell you very
little about the performance of the camera, unless you take the MTF into
account. You could make a camera with a low high-frequency MTF which you
have a very high SNR, but produce very blurry images. You really need to
measure the SNR for a known input at a known spatial frequency, and then
weight that measurement according to the perception characteristics of the
viewer.....

Cheers,
David


 
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Marc Wossner
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      05-22-2008

Thanks a lot to all of you for your valuable input!
But I guess the calculation of the snr for a given camera would only
be the first step.
At least for high signal levels there should also be a scale of a
theoretical minimum noise to judge it against.
Could that be photon noise, because itīs unavoidable? And if so, what
values would be necessary to construct such a model?

Best regards!
Marc Wossner
 
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Marc Wossner
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      05-23-2008
On 22 Mai, 16:21, Don Stauffer in Minnesota <(E-Mail Removed)>
wrote:
> On May 22, 5:28 am, Marc Wossner <(E-Mail Removed)> wrote:
>
> > Hi ng,

>
> > Iīd like to know about the signal to noise ratio of my digital camera.
> > According to a website I found this value is the ratio of total signal
> > to total noise expressed in decibels (dB) and can be calculated with
> > the following formula:

>
> > SNR = 20 log (Signal RMS / Noise RMS)

>
> > As math was always a horror for me, I have only a slight idea of "root
> > mean square" but donīt know how to deduce those values from simple
> > digital images. Can someone please help me with that?

>
> > Best Regards!
> > Marc Wossner

>
> Unfortunately, the handling of logrithmic values is not the hardest
> part of the job. In order to really look at signal to noise, you need
> to make a very carefully controlled exposure, and look at lots of
> pixels in order to get a statistical value of each part (signal and
> noise). *Also, there are a couple of types of snr definitions (large
> signal vs small signal snr).
>
> You should also be looking at a RAW file, since the jpeg compression
> affects snr of an image.


Can this effect be roughly quantified? This would be very helpful in
the comparison of .raw files and scanned silver film. Or could it be
overcome by using .tif for the scanned silver image?

Best regards!
Marc Wossner
 
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Marc Wossner
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Posts: n/a
 
      05-23-2008
On 22 Mai, 19:01, "David J Taylor" <(E-Mail Removed)-
this-bit.nor-this-bit.co.uk> wrote:
> John O'Flaherty wrote:
>
> []
>
> >> - 4096 for 12-bit or 16384 for 14-bit. This program will take the
> >> drudgery out of the calculations, if not out of getting the careful
> >> exposures.

>
> However, do be aware that a simple SNR calculation will tell you very
> little about the performance of the camera, unless you take the MTF into
> account. *You could make a camera with a low high-frequency MTF which you
> have a very high SNR, but produce very blurry images. *You really need to
> measure the SNR for a known input at a known spatial frequency, and then
> weight that measurement according to the perception characteristics of the
> viewer.....


This is what Norman Korens hypothesis about Shannons information
theory does. He uses the equation C=W log2(SNR+1), that defines the
capacity of a data channel, to define image quality (IQ) as IQ=W
log2(SNR+1), where W is the image visual capacity in one dimension. He
choose to use the product of MTF 50 and image sensor size for this
value. Look at http://www.imatest.com/docs/shannon.html.

Best regards!
Marc Wossner




 
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Chris Malcolm
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      05-23-2008
Marc Wossner <(E-Mail Removed)> wrote:
> On 22 Mai, 16:21, Don Stauffer in Minnesota <(E-Mail Removed)>
> wrote:
>> On May 22, 5:28 am, Marc Wossner <(E-Mail Removed)> wrote:
>>
>> > Hi ng,

>>
>> > I?d like to know about the signal to noise ratio of my digital camera.
>> > According to a website I found this value is the ratio of total signal
>> > to total noise expressed in decibels (dB) and can be calculated with
>> > the following formula:

>>
>> > SNR = 20 log (Signal RMS / Noise RMS)

>>
>> > As math was always a horror for me, I have only a slight idea of "root
>> > mean square" but don?t know how to deduce those values from simple
>> > digital images. Can someone please help me with that?

>>
>> > Best Regards!
>> > Marc Wossner

>>
>> Unfortunately, the handling of logrithmic values is not the hardest
>> part of the job. In order to really look at signal to noise, you need
>> to make a very carefully controlled exposure, and look at lots of
>> pixels in order to get a statistical value of each part (signal and
>> noise). ?Also, there are a couple of types of snr definitions (large
>> signal vs small signal snr).
>>
>> You should also be looking at a RAW file, since the jpeg compression
>> affects snr of an image.


> Can this effect be roughly quantified? This would be very helpful in
> the comparison of .raw files and scanned silver film. Or could it be
> overcome by using .tif for the scanned silver image?


In the case of audio we're talking about a signal which can be sampled
from a single signal measuring device, i.e. a microphone. In that case
signal to noise ratio has a simple and useful definition.

An image is sampled by millions of sensors fed extremely different
signals which have been imperfectly seperated by means of a sequence
of sophisticated and complex optical devices. We therefore not only
have the kind of signal to noise ratio in each sensor (pixel) of the
same kind as an audio signal, each one of them different, but extra
noise added in a very irregular manner by the imperfections of the
optics.

If you want to derive a single signal to noise ratio for the whole
image from this complex plethora of widely variable SNRs then you're
going to have to make quite a number of simplifying assumptions, and
those will depend very specifically on what kind of purposes you want
that single number for.

So what are your purposes?

--
Chris Malcolm http://www.velocityreviews.com/forums/(E-Mail Removed) DoD #205
IPAB, Informatics, JCMB, King's Buildings, Edinburgh, EH9 3JZ, UK
[http://www.dai.ed.ac.uk/homes/cam/]

 
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