Reply by Ronald H. Nicholson Jr.●March 26, 20042004-03-26
In article <svfej1-vm3.ln1@lazy.lzy>,
Piergiorgio Sartor <piergiorgio.sartor@nexgo.REMOVETHIS.de> wrote:
>Jerry Avins wrote:
>> Now that you point that out explicitly, it's retrospectively obvious.
>> On the other hand, if the sensitive elements are just a little narrower
>> then the spacing, then some DC is possible with inputs of n*Fs.
>
>Currently that's the situation with CCD color sensor,
>since a pixel is made usually by four sub-pixels:
>
>RG
>GB
>
>so between each color of the _same_ type there is quite a lot of space.
>
>Not to mention the physical space between the single color sensors.
However, part of the "secret soup" used by some single-CCD digicams is
a degree of intentional physical blurring between sub-pixels of the color
mosiac to both low pass filter the pixel image and to gather some light
from between the CCD sensor rectangles. But with this method you get
less usable resolution than the rated "megapixels" of the camera.
Some cameras which don't physically blur the focal plane image run
demosaicing algorithms on the sub-pixels before handing you interpolated
RGB or color-subsampled YUV data, which can alias certain colored
patterns of just the right 2D spatial frequency. This gives higher
perceived "resolution" for some images at the cost of aliasing annoying
certain bright plaid shirts at just the right distance, etc. Also note
that some sensors psuedo-randomize the CCD color mosaic filter to make
it statistically unlikely that anyone has a shirt garish enough to
cause aliasing over a significant area.
Is there a theory of randomized sampling applicable to DSP processing?
(where something like the maximum sample spacing is specified?)
IMHO. YMMV.
--
Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/
#include <canonical.disclaimer> // only my own opinions, etc.
Reply by Piergiorgio Sartor●March 26, 20042004-03-26
Jerry Avins wrote:
> Now that you point that out explicitly, it's retrospectively obvious.
> On the other hand, if the sensitive elements are just a little narrower
> then the spacing, then some DC is possible with inputs of n*Fs.
Currently that's the situation with CCD color sensor,
since a pixel is made usually by four sub-pixels:
RG
GB
so between each color of the _same_ type there is quite
a lot of space.
Not to mention the physical space between the single
color sensors.
bye,
--
piergiorgio
Reply by Jerry Avins●March 26, 20042004-03-26
Fred Marshall wrote:
...
> Jerry,
>
> I might have said: "where X is the *original* spatial sampling interval."
>
> If T is the temporal sample interval, then 1/T is the sample frequency and
> 1/2T is the Nyquist frequency and the bandwidth is < 1/2T. If I want to
> decimate by 2, then I need to reduce the bandwidth to < 1/4T.
>
> If X is the spatial sample interval, then 1/X is the sample frequency and
> 1/2X is the Nyquist frequency and the bandwidth is < 1/2X. If I want to
> decimate by 2, then I need to reduce the spatial bandwith to < 1/4X.
>
> The "new" sample interval will be 2X or 2T. So, the Nyquist frequency is
> 1/(2*2X) or 1/(2*2T)
>
> Fred
Fred,
I get it. Sorry I asked!
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●March 26, 20042004-03-26
Fred Marshall wrote:
...
> Jerry,
>
> I might have said: "where X is the *original* spatial sampling interval."
>
> If T is the temporal sample interval, then 1/T is the sample frequency and
> 1/2T is the Nyquist frequency and the bandwidth is < 1/2T. If I want to
> decimate by 2, then I need to reduce the bandwidth to < 1/4T.
>
> If X is the spatial sample interval, then 1/X is the sample frequency and
> 1/2X is the Nyquist frequency and the bandwidth is < 1/2X. If I want to
> decimate by 2, then I need to reduce the spatial bandwith to < 1/4X.
>
> The "new" sample interval will be 2X or 2T. So, the Nyquist frequency is
> 1/(2*2X) or 1/(2*2T)
>
> Fred
Fred,
I get it. Sorry I asked!
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Fred Marshall●March 26, 20042004-03-26
"Jerry Avins" <jya@ieee.org> wrote in message
news:405f43e6$0$3039$61fed72c@news.rcn.com...
> Fred Marshall wrote:
>
> ...
>
> > You have to filter the image frequencies to be not greater than 1/4X
where X
> > is the spatial sampling interval. Same as 1/4fs in frequency/time
spaces.
> > This means you will be throwing out information - so perfect
reconstruction
> > of the original is out of the question. But, you can reasonably
reconstruct
> > the *bandlimited version from the subsamples*.
> >
> > Just apply a lowpass filter of appropriate character.....
> >
> > Fred
>
> Fred,
>
> I assume that by 1/4X you mean X/4. Why 4, rather than 2?
>
> Jerry
> --
Jerry,
I might have said: "where X is the *original* spatial sampling interval."
If T is the temporal sample interval, then 1/T is the sample frequency and
1/2T is the Nyquist frequency and the bandwidth is < 1/2T. If I want to
decimate by 2, then I need to reduce the bandwidth to < 1/4T.
If X is the spatial sample interval, then 1/X is the sample frequency and
1/2X is the Nyquist frequency and the bandwidth is < 1/2X. If I want to
decimate by 2, then I need to reduce the spatial bandwith to < 1/4X.
The "new" sample interval will be 2X or 2T. So, the Nyquist frequency is
1/(2*2X) or 1/(2*2T)
Fred
Reply by Jerry Avins●March 26, 20042004-03-26
jim wrote:
...
> The point was that gathering energy for each pixel over the
> entire sample interval acts like a filter that removes the
> frequencies that would otherwise alias to DC. Any additional
> filtering will not change that.
Now that you point that out explicitly, it's retrospectively obvious.
On the other hand, if the sensitive elements are just a little narrower
then the spacing, then some DC is possible with inputs of n*Fs.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by jim●March 26, 20042004-03-26
Jerry Avins wrote:
>
> Images usually have only positive brightness values. Black is usually
> assigned zero and white, MAXINT. Setting zero at neutral gray isn't the
> usual way, but it is more consistent with audio practice. I get your
> drift now.
>
Yes, usually images are assigned values so that they have a
built in DC bias.
> >>The semantic difficulty here lies in thinking in lines when line pairs
> >>are called for. When you think about it, it can make clear why we need
> >>two samples per cycle. Fs is the line spacing. Fs/2 is the cycle (or
> >>line pair) spacing.
> >
> >
> > But in nature we can have frequencies at Fs. And Fs and its
> > multiples are the frequencies that will alias to DC (unless
> > there be a filter that removes them).
> >
> > -jim
>
> I don't understand this point. Without filtering, there can be energy at
> Fs and higher. Why stop there?
The point was that gathering energy for each pixel over the
entire sample interval acts like a filter that removes the
frequencies that would otherwise alias to DC. Any additional
filtering will not change that.
-jim
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Reply by Jerry Avins●March 26, 20042004-03-26
jim wrote:
>
> Jerry Avins wrote:
>
>
>>As I see it, the period of the grating is not one, but two pixel sizes.
>>If the center of a stripe lies on the center of a pixel, full contrast
>>appears. If the center of a stripe lies between adjacent pixels, all
>>contrast is gone and a value half way between light and dark appears on
>>all pixels. Whether you call it aliasing to DC or not, that is a
>>constant output produced by a high-frequency input.
>
>
> Well yes, but that constant output is what we usually call zero.
> If black is minimum and white is the max of a sinusoid then
> where is zero?
Images usually have only positive brightness values. Black is usually
assigned zero and white, MAXINT. Setting zero at neutral gray isn't the
usual way, but it is more consistent with audio practice. I get your
drift now.
>>The semantic difficulty here lies in thinking in lines when line pairs
>>are called for. When you think about it, it can make clear why we need
>>two samples per cycle. Fs is the line spacing. Fs/2 is the cycle (or
>>line pair) spacing.
>
>
> But in nature we can have frequencies at Fs. And Fs and its
> multiples are the frequencies that will alias to DC (unless
> there be a filter that removes them).
>
> -jim
I don't understand this point. Without filtering, there can be energy at
Fs and higher. Why stop there?
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by jim●March 25, 20042004-03-25
Jerry Avins wrote:
>
> As I see it, the period of the grating is not one, but two pixel sizes.
> If the center of a stripe lies on the center of a pixel, full contrast
> appears. If the center of a stripe lies between adjacent pixels, all
> contrast is gone and a value half way between light and dark appears on
> all pixels. Whether you call it aliasing to DC or not, that is a
> constant output produced by a high-frequency input.
Well yes, but that constant output is what we usually call zero.
If black is minimum and white is the max of a sinusoid then
where is zero?
>
> The semantic difficulty here lies in thinking in lines when line pairs
> are called for. When you think about it, it can make clear why we need
> two samples per cycle. Fs is the line spacing. Fs/2 is the cycle (or
> line pair) spacing.
But in nature we can have frequencies at Fs. And Fs and its
multiples are the frequencies that will alias to DC (unless
there be a filter that removes them).
-jim
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Reply by Jerry Avins●March 25, 20042004-03-25
jim wrote:
>
> Piergiorgio Sartor wrote:
>
>>Jerry Avins wrote:
>>
>>
>>>Consider the sinc. It has zeros at evenly spaced multiples _except_ at
>>>zero; there, it is unity.
>>
>>Ah, OK, now it's clear.
>>
>>
>>>As for stripes at Fs/2 imaged onto rectangular pixels, it can come out
>>>as alternating black and white, uniform gray, or anything between,
>>>depending on how the image is aligned on the image. In other words, the
>>>modulation transfer function (MTF) can take any value from zero to one.
>>
>>Well, but this means there is aliasing at DC, or, at least,
>>there is potential aliasing at DC.
>
>
> First of all the notion of sampling with a rectangle is a
> simplification. But using that as the model then any frequency
> with a period of one sample space is completely attentuated as
> would be any frequency with integer multiples of thet period. So
> assuming perfect rectangular sampling and defining frequency
> content as axis aligned with that same rectangular matrix then
> no aliasing will occur at DC.
>
> -jim
Jim,
As I see it, the period of the grating is not one, but two pixel sizes.
If the center of a stripe lies on the center of a pixel, full contrast
appears. If the center of a stripe lies between adjacent pixels, all
contrast is gone and a value half way between light and dark appears on
all pixels. Whether you call it aliasing to DC or not, that is a
constant output produced by a high-frequency input.
The semantic difficulty here lies in thinking in lines when line pairs
are called for. When you think about it, it can make clear why we need
two samples per cycle. Fs is the line spacing. Fs/2 is the cycle (or
line pair) spacing.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������