Integrated Density and Image Scale

[lechristophe]

Dear all,

I have a question about the "Integrated Density" measurement. In the ImageJ
docs it is stated:
*"Integrated Density* - The sum of the values of the pixels in the image or
selection. This is equavalent to the product of *Area* and *Mean Gray Value*
."
This is fine for unscaled images, where the area is expressed in pixels. But
what about scaled images ?

- If i have a 10x10 pixel image with a uniform value of 255 unscaled,
Mean=255, Area=100, Integrated Density=25500. Good.

- The same image with a scale "one pixel=0.1 microns" gives Mean=255,
Area=100, Integrated Density=255. But then ID is not "the sum if the values
of the pixels in the image" as stated in the definition ? So what is the
definition of the integrated density ? I could'nt find a good reference for
this.

Thank you for your help,

Christophe Leterrier

[Gabriel Landini]

On Monday 31 March 2008 16:16:18 Christophe Leterrier wrote:
> I have a question about the "Integrated Density" measurement. In the ImageJ
> docs it is stated:
> *"Integrated Density* - The sum of the values of the pixels in the image or
> selection. This is equavalent to the product of *Area* and *Mean Gray
> Value* ."
> This is fine for unscaled images, where the area is expressed in pixels.

> But what about scaled images ?

The ID is about samples, not area. The number of samples in a scaled image is
the same than in a non-scaled image.

The integrated density is calculated as the sum of all the sample values.

This happens to be the same as area*mean density because the mean density is
calculated as the sum of all the samples divided the number of samples. But
to calculate the mean density you have first to compute the integrated
density anyway, so you know this value.

G.

[lechristophe]

I'm not sure I understand.
If the ID is about "samples" (what are samples ?) and not pixels, and the
number of samples is the same in a scaled and unscaled image, then why is
the ID output by ImageJ different for the same image before and after
scaling ?

christophe

On Mon, Mar 31, 2008 at 5:57 PM, Gabriel Landini <[hidden email]>
wrote:

> On Monday 31 March 2008 16:16:18 Christophe Leterrier wrote:
> > I have a question about the "Integrated Density" measurement. In the
> ImageJ
> > docs it is stated:
> > *"Integrated Density* - The sum of the values of the pixels in the image
> or
> > selection. This is equavalent to the product of *Area* and *Mean Gray
> > Value* ."
> > This is fine for unscaled images, where the area is expressed in pixels.
>
> > But what about scaled images ?
>
> The ID is about samples, not area. The number of samples in a scaled image
> is
> the same than in a non-scaled image.
>
> The integrated density is calculated as the sum of all the sample values.
>
> This happens to be the same as area*mean density because the mean density
> is
> calculated as the sum of all the samples divided the number of samples.
> But
> to calculate the mean density you have first to compute the integrated
> density anyway, so you know this value.
>
> G.
>

[Saveliev, Peter]

ID (and the area) is measured in pixels or in microns squared. Two different numbers.

Peter



-----Original Message-----
From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of Christophe Leterrier
Sent: Monday, March 31, 2008 12:03 PM
To: [hidden email]
Subject: Re: Integrated Density and Image Scale

I'm not sure I understand.
If the ID is about "samples" (what are samples ?) and not pixels, and the
number of samples is the same in a scaled and unscaled image, then why is
the ID output by ImageJ different for the same image before and after
scaling ?

christophe

On Mon, Mar 31, 2008 at 5:57 PM, Gabriel Landini <[hidden email]>
wrote:

> On Monday 31 March 2008 16:16:18 Christophe Leterrier wrote:
> > I have a question about the "Integrated Density" measurement. In the
> ImageJ
> > docs it is stated:
> > *"Integrated Density* - The sum of the values of the pixels in the image
> or
> > selection. This is equavalent to the product of *Area* and *Mean Gray
> > Value* ."
> > This is fine for unscaled images, where the area is expressed in pixels.
>
> > But what about scaled images ?
>
> The ID is about samples, not area. The number of samples in a scaled image
> is
> the same than in a non-scaled image.
>
> The integrated density is calculated as the sum of all the sample values.
>
> This happens to be the same as area*mean density because the mean density
> is
> calculated as the sum of all the samples divided the number of samples.
> But
> to calculate the mean density you have first to compute the integrated
> density anyway, so you know this value.
>
> G.
>

[lechristophe]

Err... thanks, I already knew that. My question is : what is the meaning of
the ID in case of a scaled image ? This is not "The sum of the values of the
pixels in the image or selection" anymore, right ? And what intensity is
taken for each square micrometer to compute such a scaled ID ?

On Mon, Mar 31, 2008 at 6:38 PM, Saveliev, Peter <[hidden email]>
wrote:

> ID (and the area) is measured in pixels or in microns squared. Two
> different numbers.
>
> Peter
>
>
>
> -----Original Message-----
> From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
> Christophe Leterrier
> Sent: Monday, March 31, 2008 12:03 PM
> To: [hidden email]
> Subject: Re: Integrated Density and Image Scale
>
> I'm not sure I understand.
> If the ID is about "samples" (what are samples ?) and not pixels, and the
> number of samples is the same in a scaled and unscaled image, then why is
> the ID output by ImageJ different for the same image before and after
> scaling ?
>
> christophe
>
> On Mon, Mar 31, 2008 at 5:57 PM, Gabriel Landini <[hidden email]>
> wrote:
>
> > On Monday 31 March 2008 16:16:18 Christophe Leterrier wrote:
> > > I have a question about the "Integrated Density" measurement. In the
> > ImageJ
> > > docs it is stated:
> > > *"Integrated Density* - The sum of the values of the pixels in the
> image
> > or
> > > selection. This is equavalent to the product of *Area* and *Mean Gray
> > > Value* ."
> > > This is fine for unscaled images, where the area is expressed in
> pixels.
> >
> > > But what about scaled images ?
> >
> > The ID is about samples, not area. The number of samples in a scaled
> image
> > is
> > the same than in a non-scaled image.
> >
> > The integrated density is calculated as the sum of all the sample
> values.
> >
> > This happens to be the same as area*mean density because the mean
> density
> > is
> > calculated as the sum of all the samples divided the number of samples.
> > But
> > to calculate the mean density you have first to compute the integrated
> > density anyway, so you know this value.
> >
> > G.
> >
>

[Rigo Pantoja]

You're correct, pixels are the elementary units. You need to calibrate your
pixels to your scale.  For example, if your scale (which is arbitrary) is 1
micron.  Then, how many pixels are equal to 1 micron.  Basically, you
understand the fundamental concept regarding ID.  Now you you need to
understand your imaging system.

On Mon, Mar 31, 2008 at 10:27 AM, Christophe Leterrier <
[hidden email]> wrote:

> Err... thanks, I already knew that. My question is : what is the meaning
> of
> the ID in case of a scaled image ? This is not "The sum of the values of
> the
> pixels in the image or selection" anymore, right ? And what intensity is
> taken for each square micrometer to compute such a scaled ID ?
>
> On Mon, Mar 31, 2008 at 6:38 PM, Saveliev, Peter <[hidden email]>
> wrote:
>
> > ID (and the area) is measured in pixels or in microns squared. Two
> > different numbers.
> >
> > Peter
> >
> >
> >
> > -----Original Message-----
> > From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
> > Christophe Leterrier
> > Sent: Monday, March 31, 2008 12:03 PM
> > To: [hidden email]
> > Subject: Re: Integrated Density and Image Scale
> >
> > I'm not sure I understand.
> > If the ID is about "samples" (what are samples ?) and not pixels, and
> the
> > number of samples is the same in a scaled and unscaled image, then why
> is
> > the ID output by ImageJ different for the same image before and after
> > scaling ?
> >
> > christophe
> >
> > On Mon, Mar 31, 2008 at 5:57 PM, Gabriel Landini <[hidden email]>
> > wrote:
> >
> > > On Monday 31 March 2008 16:16:18 Christophe Leterrier wrote:
> > > > I have a question about the "Integrated Density" measurement. In the
> > > ImageJ
> > > > docs it is stated:
> > > > *"Integrated Density* - The sum of the values of the pixels in the
> > image
> > > or
> > > > selection. This is equavalent to the product of *Area* and *Mean
> Gray
> > > > Value* ."
> > > > This is fine for unscaled images, where the area is expressed in
> > pixels.
> > >
> > > > But what about scaled images ?
> > >
> > > The ID is about samples, not area. The number of samples in a scaled
> > image
> > > is
> > > the same than in a non-scaled image.
> > >
> > > The integrated density is calculated as the sum of all the sample
> > values.
> > >
> > > This happens to be the same as area*mean density because the mean
> > density
> > > is
> > > calculated as the sum of all the samples divided the number of
> samples.
> > > But
> > > to calculate the mean density you have first to compute the integrated
> > > density anyway, so you know this value.
> > >
> > > G.
> > >
> >
>

[Gabriel Landini]

On Monday 31 March 2008 19:27:58 Christophe Leterrier wrote:
>  My question is : what is the meaning of
> the ID in case of a scaled image ? This is not "The sum of the values of
> the pixels in the image or selection" anymore, right ?

I had a look at this and noted that the values returned are scaled by the
factor that converts the pixels to area units, so the differences in ID
between different particles are still maintained despite that the values are
different.

> And what intensity
> is taken for each square micrometer to compute such a scaled ID ?

I think that it is still the pixel values (if there is no greyscale
calibration).
I had also a look at an old Optimas manual, and found that the grey value can
also be specified in engineering units.  So I checked this in IJ and indeed
if one does greyscale calibration, then the ID will have a different value as
well.

Cheers

G.

[lechristophe]

Rigo, I think you did not read my question... This is precisely about the
difference of the ID value output by ImageJ between the same image before
and after applying a scale, so thank you, I don't need an explanation of
what a scale is :)

On Mon, Mar 31, 2008 at 9:52 PM, Rigo Pantoja <[hidden email]> wrote:

> You're correct, pixels are the elementary units. You need to calibrate
> your
> pixels to your scale.  For example, if your scale (which is arbitrary) is
> 1
> micron.  Then, how many pixels are equal to 1 micron.  Basically, you
> understand the fundamental concept regarding ID.  Now you you need to
> understand your imaging system.
>
> On Mon, Mar 31, 2008 at 10:27 AM, Christophe Leterrier <
> [hidden email]> wrote:
>
> > Err... thanks, I already knew that. My question is : what is the meaning
> > of
> > the ID in case of a scaled image ? This is not "The sum of the values of
> > the
> > pixels in the image or selection" anymore, right ? And what intensity is
> > taken for each square micrometer to compute such a scaled ID ?
> >
> > On Mon, Mar 31, 2008 at 6:38 PM, Saveliev, Peter <[hidden email]>
> > wrote:
> >
> > > ID (and the area) is measured in pixels or in microns squared. Two
> > > different numbers.
> > >
> > > Peter
> > >
> > >
> > >
> > > -----Original Message-----
> > > From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
> > > Christophe Leterrier
> > > Sent: Monday, March 31, 2008 12:03 PM
> > > To: [hidden email]
> > > Subject: Re: Integrated Density and Image Scale
> > >
> > > I'm not sure I understand.
> > > If the ID is about "samples" (what are samples ?) and not pixels, and
> > the
> > > number of samples is the same in a scaled and unscaled image, then why
> > is
> > > the ID output by ImageJ different for the same image before and after
> > > scaling ?
> > >
> > > christophe
> > >
> > > On Mon, Mar 31, 2008 at 5:57 PM, Gabriel Landini <[hidden email]
> >
> > > wrote:
> > >
> > > > On Monday 31 March 2008 16:16:18 Christophe Leterrier wrote:
> > > > > I have a question about the "Integrated Density" measurement. In
> the
> > > > ImageJ
> > > > > docs it is stated:
> > > > > *"Integrated Density* - The sum of the values of the pixels in the
> > > image
> > > > or
> > > > > selection. This is equavalent to the product of *Area* and *Mean
> > Gray
> > > > > Value* ."
> > > > > This is fine for unscaled images, where the area is expressed in
> > > pixels.
> > > >
> > > > > But what about scaled images ?
> > > >
> > > > The ID is about samples, not area. The number of samples in a scaled
> > > image
> > > > is
> > > > the same than in a non-scaled image.
> > > >
> > > > The integrated density is calculated as the sum of all the sample
> > > values.
> > > >
> > > > This happens to be the same as area*mean density because the mean
> > > density
> > > > is
> > > > calculated as the sum of all the samples divided the number of
> > samples.
> > > > But
> > > > to calculate the mean density you have first to compute the
> integrated
> > > > density anyway, so you know this value.
> > > >
> > > > G.
> > > >
> > >
> >
>

[lechristophe]

Gabriel, thank you for your reply, I have a comment inline :

On Tue, Apr 1, 2008 at 12:37 AM, Gabriel Landini <[hidden email]>
wrote:

> On Monday 31 March 2008 19:27:58 Christophe Leterrier wrote:
> >  My question is : what is the meaning of
> > the ID in case of a scaled image ? This is not "The sum of the values of
> > the pixels in the image or selection" anymore, right ?
>
> I had a look at this and noted that the values returned are scaled by the
> factor that converts the pixels to area units, so the differences in ID
> between different particles are still maintained despite that the values
> are
> different.
>

> > And what intensity
> > is taken for each square micrometer to compute such a scaled ID ?
>
> I think that it is still the pixel values (if there is no greyscale
> calibration).


If the image is scaled, the scale unit (microns for exemple) can have an
area of several pixels (10x10 in my first exemple), or even worst an area of
a fraction of a pixel (if for exemple 1pixel=10microns). So what "pixel
value" is taken to compute the ID ? In the case of several pixels, is it the
mean value of all the pixels enclosed in the unitary area ? If so, it would
explain the variation in ID, but I think it should sum the pixels inside the
unitary area, not averaging them.

>
> I had also a look at an old Optimas manual, and found that the grey value
> can
> also be specified in engineering units.  So I checked this in IJ and
> indeed
> if one does greyscale calibration, then the ID will have a different value
> as
> well.
>
> Cheers
>
> G.
>

[Gabriel Landini]

On Tuesday 01 April 2008 08:24:04 Christophe Leterrier wrote:
> If the image is scaled, the scale unit (microns for exemple) can have an
> area of several pixels (10x10 in my first exemple), or even worst an area
> of a fraction of a pixel (if for exemple 1pixel=10microns). So what "pixel
> value" is taken to compute the ID ? In the case of several pixels, is it
> the mean value of all the pixels enclosed in the unitary area ? If so, it
> would explain the variation in ID, but I think it should sum the pixels
> inside the unitary area, not averaging them.

I think ID is calculated like this (please correct if I am wrong):
Sum all the pixels grey values in the blob (applying the greyscale
calibration, if set).
If the spatial calibration is set, then multiply this value by the area
conversion factor (this is from the Image>Properties: pixel height * pixel
depth).

So the ID value is still sample-related (i.e. how many pixels your blobs are
made of) but scaled by those calibration factors... there is no new
information, really.

Yes, it can be confusing to have blobs IDs expressed in calibrated units. I
guess that using calibration units it may give a false sense of resolution
independence (it is still not the same resolution of information to have a
blob made of 1 pixel than made of 1000 even if both are reported in terms of
micrometres squared). However, comparisons using the same setup and same
calibration should still be valid.

I hope it helps.

G.