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How is the line plot profile generated?

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Avital Steinberg

How is the line plot profile generated?

Hi,
When I use ImageJ's graphical user interface and draw a line and then
select Analyze, plot profile (with the default settings), I get a plot of
intensities vs. the distance from the beginning of the line. I was
wondering how the plot is generated, in terms of which pixels in the
neighborhood are taken into the weighted average, and how the weights are
determined.

Herbie helped me in the other ImageJ forum by suggesting that I plot a ramp
image. Now I can sometimes predict the values that will appear in the
profile plot. (but only in some simple cases) After experimenting with an
image, I noticed that the plot's x-axis scale changes abruptly from 1.5 to
2.0 (for example) and I was wondering if the distance between 2 adjacent
points changes when the scale suddenly changes.

Thank you,
Avital

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ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Emmanuel Levy

Re: How is the line plot profile generated?

Dear All,

I'd like to add to Avital's question with one more point as I've also been
wondering how plot profile works.

I created a 16x16 black image and added a white pixel at the centre. I
then drew a line either horizontally or vertically **only on black pixels**
next to the white one. This showed interpolation, but strangely it is not
symmetric. When the line is left or above the white pixel the profile is
not flat (i.e., the white pixel is used in calculating the profile), but
when the line is drawn below or on the right of the white pixel the profile
is flat.

I would have expected that, by default, only the pixels onto which the line
is drawn are used and interpolated when calculating the profile. Is this
non-symmetric behaviour of the interpolation an intended behaviour?

Note: when using 2px width, symmetry is restored actually.

Thanks for your comments,

All the best,

Emmanuel

On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
wrote:

> Hi,
> When I use ImageJ's graphical user interface and draw a line and then
> select Analyze, plot profile (with the default settings), I get a plot of
> intensities vs. the distance from the beginning of the line. I was
> wondering how the plot is generated, in terms of which pixels in the
> neighborhood are taken into the weighted average, and how the weights are
> determined.
>
> Herbie helped me in the other ImageJ forum by suggesting that I plot a ramp
> image. Now I can sometimes predict the values that will appear in the
> profile plot. (but only in some simple cases) After experimenting with an
> image, I noticed that the plot's x-axis scale changes abruptly from 1.5 to
> 2.0 (for example) and I was wondering if the distance between 2 adjacent
> points changes when the scale suddenly changes.
>
> Thank you,
> Avital
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Jan Eglinger

Re: How is the line plot profile generated?

Dear Avital and Emmanuel,

> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
> wrote:
>> Herbie helped me in the other ImageJ forum

Let's be nice and link to this discussion, so others can follow:
http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070

On 10.03.2016 07:26, Emmanuel Levy wrote:
> I would have expected that, by default, only the pixels onto which the line
> is drawn are used and interpolated when calculating the profile. Is this
> non-symmetric behaviour of the interpolation an intended behaviour?

I agree that there are inconsistencies between how lines and segmented
line selection are displayed on the image and the measurements of those
lines. Please see also my following related post on the forum:

http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan

I remember previous discussions about rectangular selections and the
behavior of the Fill and Draw commands that by now have been fixed. It
would be great to have a consistent ROI behavior through all types of
selections in ImageJ.

Cheers,
Jan

>
>
> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
> wrote:
>
>> Hi,
>> When I use ImageJ's graphical user interface and draw a line and then
>> select Analyze, plot profile (with the default settings), I get a plot of
>> intensities vs. the distance from the beginning of the line. I was
>> wondering how the plot is generated, in terms of which pixels in the
>> neighborhood are taken into the weighted average, and how the weights are
>> determined.
>>
>> Herbie helped me in the other ImageJ forum by suggesting that I plot a ramp
>> image. Now I can sometimes predict the values that will appear in the
>> profile plot. (but only in some simple cases) After experimenting with an
>> image, I noticed that the plot's x-axis scale changes abruptly from 1.5 to
>> 2.0 (for example) and I was wondering if the distance between 2 adjacent
>> points changes when the scale suddenly changes.
>>
>> Thank you,
>> Avital

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Emmanuel Levy

Re: How is the line plot profile generated?

Dear All,

I wished to add a piece of macro to illustrate the behaviour I observed and
was describing (see below).

Discussing offline with Avital made it clear what happens: pixel values are
represented by the image-coordinate system and this introduces asymmetry -
let's consider 3 pixels:
- x=0,y=0 (black)
- x=0,y=1 (white)
-x=0,y=2 (black)

If I draw two horizontal lines at y=0.5 and y=2.5. They are both
equidistant from the white pixel on the image (i.e., it looks symmetric)
but they are not equidistant in the coordinate system, the line at y=0.5 is
only 0.5 pixels far from the while pixel's origin (at x=0,y=1), while the
line at y=2.5 is 1.5 pixels away. This introduces asymmetry when plot
profile calculates values.

Would anyone know of a way of producing a symmetric behaviour for plot
profile?

Thanks for your help,
All the best,

Emmanuel

===========

The macro below creates a whitish region at the centre of a 17 by 17px
image, and adds a white pixel at the top of the image as well. It then
draws two pairs of lines. I would expect the profile for the two pairs to
be identical because the pixel environment is identical. However, the two
profiles within each pair are different. e.g., if the line is 0.5 pixel
above or below a white pixel will yield a very different outcome.

newImage("Untitled", "8-bit Black", 17, 17, 1);
makeRectangle(8, 8, 1, 1);
run("Clear", "slice");
run("Select All");
run("Gaussian Blur...", "sigma=2");
makeRectangle(7, 1, 1, 1);
run("Clear", "slice");
run("Enhance Contrast", "saturated=0.35");

///// FIRST PAIR OF PROFILES (left and right to the whitish spot)
selectWindow("Untitled");
makeLine(4.5, 5.5, 4.5, 11.5);
run("Plot Profile");

selectWindow("Untitled");
makeLine(12.5, 5.5, 12.5, 11.5);
run("Plot Profile");

///// SECOND PAIR OF PROFILES (top and bottom to the white pixel)
selectWindow("Untitled");
makeLine(5.5, 0.5, 9.5, 0.5);
run("Plot Profile");

selectWindow("Untitled");
makeLine(5.5, 2.5, 9.5, 2.5);
run("Plot Profile");

On 10 March 2016 at 10:06, Jan Eglinger <[hidden email]> wrote:

> Dear Avital and Emmanuel,
>
> > On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
> > wrote:
> >> Herbie helped me in the other ImageJ forum
>
> Let's be nice and link to this discussion, so others can follow:
> http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070
>
>
> On 10.03.2016 07:26, Emmanuel Levy wrote:
>
>> I would have expected that, by default, only the pixels onto which the
>> line
>> is drawn are used and interpolated when calculating the profile. Is this
>> non-symmetric behaviour of the interpolation an intended behaviour?
>>
>
> I agree that there are inconsistencies between how lines and segmented
> line selection are displayed on the image and the measurements of those
> lines. Please see also my following related post on the forum:
>
>
> http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan
>
>
> I remember previous discussions about rectangular selections and the
> behavior of the Fill and Draw commands that by now have been fixed. It
> would be great to have a consistent ROI behavior through all types of
> selections in ImageJ.
>
> Cheers,
> Jan
>
>
>
>
>>
>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>> wrote:
>>
>> Hi,
>>> When I use ImageJ's graphical user interface and draw a line and then
>>> select Analyze, plot profile (with the default settings), I get a plot of
>>> intensities vs. the distance from the beginning of the line. I was
>>> wondering how the plot is generated, in terms of which pixels in the
>>> neighborhood are taken into the weighted average, and how the weights are
>>> determined.
>>>
>>> Herbie helped me in the other ImageJ forum by suggesting that I plot a
>>> ramp
>>> image. Now I can sometimes predict the values that will appear in the
>>> profile plot. (but only in some simple cases) After experimenting with an
>>> image, I noticed that the plot's x-axis scale changes abruptly from 1.5
>>> to
>>> 2.0 (for example) and I was wondering if the distance between 2 adjacent
>>> points changes when the scale suddenly changes.
>>>
>>> Thank you,
>>> Avital
>>>
>>

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Herbie

Re: How is the line plot profile generated?

Emmanuel,

as Avital might have told you, the line profile uses nearest
neighborhood interpolation and I assume that coordinates having xy.5
values will be rounded up.

Please note that pixel values are mathematical points and the squares
that are commonly mistaken as pixels are for visualization only.

HTH

Herbie

:::::::::::::::::::::::::::::::::::::::::::
Am 13.03.16 um 20:50 schrieb Emmanuel Levy:

> Dear All,
>
> I wished to add a piece of macro to illustrate the behaviour I observed and
> was describing (see below).
>
> Discussing offline with Avital made it clear what happens: pixel values are
> represented by the image-coordinate system and this introduces asymmetry -
> let's consider 3 pixels:
> - x=0,y=0 (black)
> - x=0,y=1 (white)
> -x=0,y=2 (black)
>
> If I draw two horizontal lines at y=0.5 and y=2.5. They are both
> equidistant from the white pixel on the image (i.e., it looks symmetric)
> but they are not equidistant in the coordinate system, the line at y=0.5 is
> only 0.5 pixels far from the while pixel's origin (at x=0,y=1), while the
> line at y=2.5 is 1.5 pixels away. This introduces asymmetry when plot
> profile calculates values.
>
> Would anyone know of a way of producing a symmetric behaviour for plot
> profile?
>
> Thanks for your help,
> All the best,
>
> Emmanuel
>
>
> ===========
>
> The macro below creates a whitish region at the centre of a 17 by 17px
> image, and adds a white pixel at the top of the image as well. It then
> draws two pairs of lines. I would expect the profile for the two pairs to
> be identical because the pixel environment is identical. However, the two
> profiles within each pair are different. e.g., if the line is 0.5 pixel
> above or below a white pixel will yield a very different outcome.
>
> newImage("Untitled", "8-bit Black", 17, 17, 1);
> makeRectangle(8, 8, 1, 1);
> run("Clear", "slice");
> run("Select All");
> run("Gaussian Blur...", "sigma=2");
> makeRectangle(7, 1, 1, 1);
> run("Clear", "slice");
> run("Enhance Contrast", "saturated=0.35");
>
> ///// FIRST PAIR OF PROFILES (left and right to the whitish spot)
> selectWindow("Untitled");
> makeLine(4.5, 5.5, 4.5, 11.5);
> run("Plot Profile");
>
> selectWindow("Untitled");
> makeLine(12.5, 5.5, 12.5, 11.5);
> run("Plot Profile");
>
>
> ///// SECOND PAIR OF PROFILES (top and bottom to the white pixel)
> selectWindow("Untitled");
> makeLine(5.5, 0.5, 9.5, 0.5);
> run("Plot Profile");
>
> selectWindow("Untitled");
> makeLine(5.5, 2.5, 9.5, 2.5);
> run("Plot Profile");
>
> On 10 March 2016 at 10:06, Jan Eglinger <[hidden email]> wrote:
>
>> Dear Avital and Emmanuel,
>>
>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>> wrote:
>>>> Herbie helped me in the other ImageJ forum
>>
>> Let's be nice and link to this discussion, so others can follow:
>> http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070
>>
>>
>> On 10.03.2016 07:26, Emmanuel Levy wrote:
>>
>>> I would have expected that, by default, only the pixels onto which the
>>> line
>>> is drawn are used and interpolated when calculating the profile. Is this
>>> non-symmetric behaviour of the interpolation an intended behaviour?
>>>
>>
>> I agree that there are inconsistencies between how lines and segmented
>> line selection are displayed on the image and the measurements of those
>> lines. Please see also my following related post on the forum:
>>
>>
>> http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan
>>
>>
>> I remember previous discussions about rectangular selections and the
>> behavior of the Fill and Draw commands that by now have been fixed. It
>> would be great to have a consistent ROI behavior through all types of
>> selections in ImageJ.
>>
>> Cheers,
>> Jan
>>
>>
>>
>>
>>>
>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>> wrote:
>>>
>>> Hi,
>>>> When I use ImageJ's graphical user interface and draw a line and then
>>>> select Analyze, plot profile (with the default settings), I get a plot of
>>>> intensities vs. the distance from the beginning of the line. I was
>>>> wondering how the plot is generated, in terms of which pixels in the
>>>> neighborhood are taken into the weighted average, and how the weights are
>>>> determined.
>>>>
>>>> Herbie helped me in the other ImageJ forum by suggesting that I plot a
>>>> ramp
>>>> image. Now I can sometimes predict the values that will appear in the
>>>> profile plot. (but only in some simple cases) After experimenting with an
>>>> image, I noticed that the plot's x-axis scale changes abruptly from 1.5
>>>> to
>>>> 2.0 (for example) and I was wondering if the distance between 2 adjacent
>>>> points changes when the scale suddenly changes.
>>>>
>>>> Thank you,
>>>> Avital
>>>>
>>>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Michael Schmid

Re: How is the line plot profile generated?

In reply to this post by Emmanuel Levy

Hi Emmanuel,

at high magnification, the line profiles are very accurate if you enable
'Sub-Pixel Resolution' in the (Profile) Plot options. You may also want to
have 'Interploate Line Profiles' checked.

Without subpixel resolution, you should not expect an accurate result for
lines that have non-integer coordinates.

To ensure these settings don't get deactivated, I have them in the AutoRun
section of my StartupMacros file:

macro "AutoRun" {
run("Profile Plot Options...", "draw interpolate sub-pixel");
//and anything else you want to happen at startup, e.g. Binary options, ...
}

Michael
______________________________________________________________

On Sun, March 13, 2016 20:50, Emmanuel Levy wrote:

> Dear All,
>
> I wished to add a piece of macro to illustrate the behaviour I observed
> and
> was describing (see below).
>
> Discussing offline with Avital made it clear what happens: pixel values
> are
> represented by the image-coordinate system and this introduces asymmetry -
> let's consider 3 pixels:
> - x=0,y=0 (black)
> - x=0,y=1 (white)
> -x=0,y=2 (black)
>
> If I draw two horizontal lines at y=0.5 and y=2.5. They are both
> equidistant from the white pixel on the image (i.e., it looks symmetric)
> but they are not equidistant in the coordinate system, the line at y=0.5
> is
> only 0.5 pixels far from the while pixel's origin (at x=0,y=1), while the
> line at y=2.5 is 1.5 pixels away. This introduces asymmetry when plot
> profile calculates values.
>
> Would anyone know of a way of producing a symmetric behaviour for plot
> profile?
>
> Thanks for your help,
> All the best,
>
> Emmanuel
>
>
> ===========
>
> The macro below creates a whitish region at the centre of a 17 by 17px
> image, and adds a white pixel at the top of the image as well. It then
> draws two pairs of lines. I would expect the profile for the two pairs to
> be identical because the pixel environment is identical. However, the two
> profiles within each pair are different. e.g., if the line is 0.5 pixel
> above or below a white pixel will yield a very different outcome.
>
> newImage("Untitled", "8-bit Black", 17, 17, 1);
> makeRectangle(8, 8, 1, 1);
> run("Clear", "slice");
> run("Select All");
> run("Gaussian Blur...", "sigma=2");
> makeRectangle(7, 1, 1, 1);
> run("Clear", "slice");
> run("Enhance Contrast", "saturated=0.35");
>
> ///// FIRST PAIR OF PROFILES (left and right to the whitish spot)
> selectWindow("Untitled");
> makeLine(4.5, 5.5, 4.5, 11.5);
> run("Plot Profile");
>
> selectWindow("Untitled");
> makeLine(12.5, 5.5, 12.5, 11.5);
> run("Plot Profile");
>
>
> ///// SECOND PAIR OF PROFILES (top and bottom to the white pixel)
> selectWindow("Untitled");
> makeLine(5.5, 0.5, 9.5, 0.5);
> run("Plot Profile");
>
> selectWindow("Untitled");
> makeLine(5.5, 2.5, 9.5, 2.5);
> run("Plot Profile");
>
> On 10 March 2016 at 10:06, Jan Eglinger <[hidden email]> wrote:
>
>> Dear Avital and Emmanuel,
>>
>> > On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>> > wrote:
>> >> Herbie helped me in the other ImageJ forum
>>
>> Let's be nice and link to this discussion, so others can follow:
>> http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070
>>
>>
>> On 10.03.2016 07:26, Emmanuel Levy wrote:
>>
>>> I would have expected that, by default, only the pixels onto which the
>>> line
>>> is drawn are used and interpolated when calculating the profile. Is
>>> this
>>> non-symmetric behaviour of the interpolation an intended behaviour?
>>>
>>
>> I agree that there are inconsistencies between how lines and segmented
>> line selection are displayed on the image and the measurements of those
>> lines. Please see also my following related post on the forum:
>>
>>
>> http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan
>>
>>
>> I remember previous discussions about rectangular selections and the
>> behavior of the Fill and Draw commands that by now have been fixed. It
>> would be great to have a consistent ROI behavior through all types of
>> selections in ImageJ.
>>
>> Cheers,
>> Jan
>>
>>
>>
>>
>>>
>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>> wrote:
>>>
>>> Hi,
>>>> When I use ImageJ's graphical user interface and draw a line and then
>>>> select Analyze, plot profile (with the default settings), I get a plot
>>>> of
>>>> intensities vs. the distance from the beginning of the line. I was
>>>> wondering how the plot is generated, in terms of which pixels in the
>>>> neighborhood are taken into the weighted average, and how the weights
>>>> are
>>>> determined.
>>>>
>>>> Herbie helped me in the other ImageJ forum by suggesting that I plot a
>>>> ramp
>>>> image. Now I can sometimes predict the values that will appear in the
>>>> profile plot. (but only in some simple cases) After experimenting with
>>>> an
>>>> image, I noticed that the plot's x-axis scale changes abruptly from
>>>> 1.5
>>>> to
>>>> 2.0 (for example) and I was wondering if the distance between 2
>>>> adjacent
>>>> points changes when the scale suddenly changes.
>>>>
>>>> Thank you,
>>>> Avital
>>>>
>>>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Emmanuel Levy

Re: How is the line plot profile generated?

In reply to this post by Herbie

Hi Herbie,

Thanks for your reply.

as Avital might have told you, the line profile uses nearest neighborhood
> interpolation and I assume that coordinates having xy.5 values will be
> rounded up.
>
>
The line profile uses continuous coordinates and there is no rounding as
far as I can see. That's perhaps clearer if you use the "live" mode of the
profile plot and move a line around.

> Please note that pixel values are mathematical points and the squares that
> are commonly mistaken as pixels are for visualization only.
>

I see what you mean but I don't fully agree because (i) camera sensors are
not dimensionless, they take up space and I find pixels a convenient
physical representation of sensors, beyond just being a "data structure".
And (ii) light captured by cameras is not discreet but continuous, and one
can try to estimate continuous parameters from pixel data. i.e., sub-pixel
information can be inferred from the data.

All the best,

Emmanuel

> HTH
>
> Herbie
>
> :::::::::::::::::::::::::::::::::::::::::::
> Am 13.03.16 um 20:50 schrieb Emmanuel Levy:
>
>> Dear All,
>>
>> I wished to add a piece of macro to illustrate the behaviour I observed
>> and
>> was describing (see below).
>>
>> Discussing offline with Avital made it clear what happens: pixel values
>> are
>> represented by the image-coordinate system and this introduces asymmetry -
>> let's consider 3 pixels:
>> - x=0,y=0 (black)
>> - x=0,y=1 (white)
>> -x=0,y=2 (black)
>>
>> If I draw two horizontal lines at y=0.5 and y=2.5. They are both
>> equidistant from the white pixel on the image (i.e., it looks symmetric)
>> but they are not equidistant in the coordinate system, the line at y=0.5
>> is
>> only 0.5 pixels far from the while pixel's origin (at x=0,y=1), while the
>> line at y=2.5 is 1.5 pixels away. This introduces asymmetry when plot
>> profile calculates values.
>>
>> Would anyone know of a way of producing a symmetric behaviour for plot
>> profile?
>>
>> Thanks for your help,
>> All the best,
>>
>> Emmanuel
>>
>>
>> ===========
>>
>> The macro below creates a whitish region at the centre of a 17 by 17px
>> image, and adds a white pixel at the top of the image as well. It then
>> draws two pairs of lines. I would expect the profile for the two pairs to
>> be identical because the pixel environment is identical. However, the two
>> profiles within each pair are different. e.g., if the line is 0.5 pixel
>> above or below a white pixel will yield a very different outcome.
>>
>> newImage("Untitled", "8-bit Black", 17, 17, 1);
>> makeRectangle(8, 8, 1, 1);
>> run("Clear", "slice");
>> run("Select All");
>> run("Gaussian Blur...", "sigma=2");
>> makeRectangle(7, 1, 1, 1);
>> run("Clear", "slice");
>> run("Enhance Contrast", "saturated=0.35");
>>
>> ///// FIRST PAIR OF PROFILES (left and right to the whitish spot)
>> selectWindow("Untitled");
>> makeLine(4.5, 5.5, 4.5, 11.5);
>> run("Plot Profile");
>>
>> selectWindow("Untitled");
>> makeLine(12.5, 5.5, 12.5, 11.5);
>> run("Plot Profile");
>>
>>
>> ///// SECOND PAIR OF PROFILES (top and bottom to the white pixel)
>> selectWindow("Untitled");
>> makeLine(5.5, 0.5, 9.5, 0.5);
>> run("Plot Profile");
>>
>> selectWindow("Untitled");
>> makeLine(5.5, 2.5, 9.5, 2.5);
>> run("Plot Profile");
>>
>> On 10 March 2016 at 10:06, Jan Eglinger <[hidden email]> wrote:
>>
>> Dear Avital and Emmanuel,
>>>
>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>>> wrote:
>>>>
>>>>> Herbie helped me in the other ImageJ forum
>>>>>
>>>>
>>> Let's be nice and link to this discussion, so others can follow:
>>> http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070
>>>
>>>
>>> On 10.03.2016 07:26, Emmanuel Levy wrote:
>>>
>>> I would have expected that, by default, only the pixels onto which the
>>>> line
>>>> is drawn are used and interpolated when calculating the profile. Is this
>>>> non-symmetric behaviour of the interpolation an intended behaviour?
>>>>
>>>>
>>> I agree that there are inconsistencies between how lines and segmented
>>> line selection are displayed on the image and the measurements of those
>>> lines. Please see also my following related post on the forum:
>>>
>>>
>>>
>>> http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan
>>>
>>>
>>> I remember previous discussions about rectangular selections and the
>>> behavior of the Fill and Draw commands that by now have been fixed. It
>>> would be great to have a consistent ROI behavior through all types of
>>> selections in ImageJ.
>>>
>>> Cheers,
>>> Jan
>>>
>>>
>>>
>>>
>>>
>>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>>> wrote:
>>>>
>>>> Hi,
>>>>
>>>>> When I use ImageJ's graphical user interface and draw a line and then
>>>>> select Analyze, plot profile (with the default settings), I get a plot
>>>>> of
>>>>> intensities vs. the distance from the beginning of the line. I was
>>>>> wondering how the plot is generated, in terms of which pixels in the
>>>>> neighborhood are taken into the weighted average, and how the weights
>>>>> are
>>>>> determined.
>>>>>
>>>>> Herbie helped me in the other ImageJ forum by suggesting that I plot a
>>>>> ramp
>>>>> image. Now I can sometimes predict the values that will appear in the
>>>>> profile plot. (but only in some simple cases) After experimenting with
>>>>> an
>>>>> image, I noticed that the plot's x-axis scale changes abruptly from 1.5
>>>>> to
>>>>> 2.0 (for example) and I was wondering if the distance between 2
>>>>> adjacent
>>>>> points changes when the scale suddenly changes.
>>>>>
>>>>> Thank you,
>>>>> Avital
>>>>>
>>>>>
>>>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Emmanuel Levy

Re: How is the line plot profile generated?

In reply to this post by Michael Schmid

Hi Michael,

Thanks a lot, that's exactly what we needed!

Best wishes,

Emmanuel

>
>
> On 13 March 2016 at 23:02, Michael Schmid <[hidden email]> wrote:
>
>> Hi Emmanuel,
>>
>> at high magnification, the line profiles are very accurate if you enable
>> 'Sub-Pixel Resolution' in the (Profile) Plot options. You may also want to
>> have 'Interploate Line Profiles' checked.
>>
>> Without subpixel resolution, you should not expect an accurate result for
>> lines that have non-integer coordinates.
>>
>> To ensure these settings don't get deactivated, I have them in the AutoRun
>> section of my StartupMacros file:
>>
>> macro "AutoRun" {
>> run("Profile Plot Options...", "draw interpolate sub-pixel");
>> //and anything else you want to happen at startup, e.g. Binary options,
>> ...
>> }
>>
>> Michael
>> ______________________________________________________________
>>
>> On Sun, March 13, 2016 20:50, Emmanuel Levy wrote:
>> > Dear All,
>> >
>> > I wished to add a piece of macro to illustrate the behaviour I observed
>> > and
>> > was describing (see below).
>> >
>> > Discussing offline with Avital made it clear what happens: pixel values
>> > are
>> > represented by the image-coordinate system and this introduces
>> asymmetry -
>> > let's consider 3 pixels:
>> > - x=0,y=0 (black)
>> > - x=0,y=1 (white)
>> > -x=0,y=2 (black)
>> >
>> > If I draw two horizontal lines at y=0.5 and y=2.5. They are both
>> > equidistant from the white pixel on the image (i.e., it looks symmetric)
>> > but they are not equidistant in the coordinate system, the line at y=0.5
>> > is
>> > only 0.5 pixels far from the while pixel's origin (at x=0,y=1), while
>> the
>> > line at y=2.5 is 1.5 pixels away. This introduces asymmetry when plot
>> > profile calculates values.
>> >
>> > Would anyone know of a way of producing a symmetric behaviour for plot
>> > profile?
>> >
>> > Thanks for your help,
>> > All the best,
>> >
>> > Emmanuel
>> >
>> >
>> > ===========
>> >
>> > The macro below creates a whitish region at the centre of a 17 by 17px
>> > image, and adds a white pixel at the top of the image as well. It then
>> > draws two pairs of lines. I would expect the profile for the two pairs
>> to
>> > be identical because the pixel environment is identical. However, the
>> two
>> > profiles within each pair are different. e.g., if the line is 0.5 pixel
>> > above or below a white pixel will yield a very different outcome.
>> >
>> > newImage("Untitled", "8-bit Black", 17, 17, 1);
>> > makeRectangle(8, 8, 1, 1);
>> > run("Clear", "slice");
>> > run("Select All");
>> > run("Gaussian Blur...", "sigma=2");
>> > makeRectangle(7, 1, 1, 1);
>> > run("Clear", "slice");
>> > run("Enhance Contrast", "saturated=0.35");
>> >
>> > ///// FIRST PAIR OF PROFILES (left and right to the whitish spot)
>> > selectWindow("Untitled");
>> > makeLine(4.5, 5.5, 4.5, 11.5);
>> > run("Plot Profile");
>> >
>> > selectWindow("Untitled");
>> > makeLine(12.5, 5.5, 12.5, 11.5);
>> > run("Plot Profile");
>> >
>> >
>> > ///// SECOND PAIR OF PROFILES (top and bottom to the white pixel)
>> > selectWindow("Untitled");
>> > makeLine(5.5, 0.5, 9.5, 0.5);
>> > run("Plot Profile");
>> >
>> > selectWindow("Untitled");
>> > makeLine(5.5, 2.5, 9.5, 2.5);
>> > run("Plot Profile");
>> >
>> > On 10 March 2016 at 10:06, Jan Eglinger <[hidden email]> wrote:
>> >
>> >> Dear Avital and Emmanuel,
>> >>
>> >> > On 9 March 2016 at 21:28, Avital Steinberg <
>> [hidden email]>
>> >> > wrote:
>> >> >> Herbie helped me in the other ImageJ forum
>> >>
>> >> Let's be nice and link to this discussion, so others can follow:
>> >> http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070
>> >>
>> >>
>> >> On 10.03.2016 07:26, Emmanuel Levy wrote:
>> >>
>> >>> I would have expected that, by default, only the pixels onto which the
>> >>> line
>> >>> is drawn are used and interpolated when calculating the profile. Is
>> >>> this
>> >>> non-symmetric behaviour of the interpolation an intended behaviour?
>> >>>
>> >>
>> >> I agree that there are inconsistencies between how lines and segmented
>> >> line selection are displayed on the image and the measurements of those
>> >> lines. Please see also my following related post on the forum:
>> >>
>> >>
>> >>
>> http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan
>> >>
>> >>
>> >> I remember previous discussions about rectangular selections and the
>> >> behavior of the Fill and Draw commands that by now have been fixed. It
>> >> would be great to have a consistent ROI behavior through all types of
>> >> selections in ImageJ.
>> >>
>> >> Cheers,
>> >> Jan
>> >>
>> >>
>> >>
>> >>
>> >>>
>> >>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]
>> >
>> >>> wrote:
>> >>>
>> >>> Hi,
>> >>>> When I use ImageJ's graphical user interface and draw a line and then
>> >>>> select Analyze, plot profile (with the default settings), I get a
>> plot
>> >>>> of
>> >>>> intensities vs. the distance from the beginning of the line. I was
>> >>>> wondering how the plot is generated, in terms of which pixels in the
>> >>>> neighborhood are taken into the weighted average, and how the weights
>> >>>> are
>> >>>> determined.
>> >>>>
>> >>>> Herbie helped me in the other ImageJ forum by suggesting that I plot
>> a
>> >>>> ramp
>> >>>> image. Now I can sometimes predict the values that will appear in the
>> >>>> profile plot. (but only in some simple cases) After experimenting
>> with
>> >>>> an
>> >>>> image, I noticed that the plot's x-axis scale changes abruptly from
>> >>>> 1.5
>> >>>> to
>> >>>> 2.0 (for example) and I was wondering if the distance between 2
>> >>>> adjacent
>> >>>> points changes when the scale suddenly changes.
>> >>>>
>> >>>> Thank you,
>> >>>> Avital
>> >>>>
>> >>>
>> >
>> > --
>> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>> >
>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>
>

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Herbie

Re: How is the line plot profile generated?

In reply to this post by Emmanuel Levy

Emmanuel,

sensor elements deliver numbers not squares.
(What happens in camera sensors is integrative sampling which causes a
small lowpass effect on the recorded light distribution.)

Subpixel resolution is obtained by spatial interpolation (and this is
perfectly ok if the camera sensor samples according to the sampling
theorem) of an array of discrete numbers.

There are many interpolation schemes but only one is correct but costly
and not used for lcd/oled-displays.

Best

Herbie

:::::::::::::::::::::::::::::::::::::::::::
Am 13.03.16 um 22:04 schrieb Emmanuel Levy:

> Hi Herbie,
>
> Thanks for your reply.
>
> as Avital might have told you, the line profile uses nearest neighborhood
>> interpolation and I assume that coordinates having xy.5 values will be
>> rounded up.
>>
>>
> The line profile uses continuous coordinates and there is no rounding as
> far as I can see. That's perhaps clearer if you use the "live" mode of the
> profile plot and move a line around.
>
>
>> Please note that pixel values are mathematical points and the squares that
>> are commonly mistaken as pixels are for visualization only.
>>
>
> I see what you mean but I don't fully agree because (i) camera sensors are
> not dimensionless, they take up space and I find pixels a convenient
> physical representation of sensors, beyond just being a "data structure".
> And (ii) light captured by cameras is not discreet but continuous, and one
> can try to estimate continuous parameters from pixel data. i.e., sub-pixel
> information can be inferred from the data.
>
> All the best,
>
> Emmanuel
>
>
>
>
>> HTH
>>
>> Herbie
>>
>> :::::::::::::::::::::::::::::::::::::::::::
>> Am 13.03.16 um 20:50 schrieb Emmanuel Levy:
>>
>>> Dear All,
>>>
>>> I wished to add a piece of macro to illustrate the behaviour I observed
>>> and
>>> was describing (see below).
>>>
>>> Discussing offline with Avital made it clear what happens: pixel values
>>> are
>>> represented by the image-coordinate system and this introduces asymmetry -
>>> let's consider 3 pixels:
>>> - x=0,y=0 (black)
>>> - x=0,y=1 (white)
>>> -x=0,y=2 (black)
>>>
>>> If I draw two horizontal lines at y=0.5 and y=2.5. They are both
>>> equidistant from the white pixel on the image (i.e., it looks symmetric)
>>> but they are not equidistant in the coordinate system, the line at y=0.5
>>> is
>>> only 0.5 pixels far from the while pixel's origin (at x=0,y=1), while the
>>> line at y=2.5 is 1.5 pixels away. This introduces asymmetry when plot
>>> profile calculates values.
>>>
>>> Would anyone know of a way of producing a symmetric behaviour for plot
>>> profile?
>>>
>>> Thanks for your help,
>>> All the best,
>>>
>>> Emmanuel
>>>
>>>
>>> ===========
>>>
>>> The macro below creates a whitish region at the centre of a 17 by 17px
>>> image, and adds a white pixel at the top of the image as well. It then
>>> draws two pairs of lines. I would expect the profile for the two pairs to
>>> be identical because the pixel environment is identical. However, the two
>>> profiles within each pair are different. e.g., if the line is 0.5 pixel
>>> above or below a white pixel will yield a very different outcome.
>>>
>>> newImage("Untitled", "8-bit Black", 17, 17, 1);
>>> makeRectangle(8, 8, 1, 1);
>>> run("Clear", "slice");
>>> run("Select All");
>>> run("Gaussian Blur...", "sigma=2");
>>> makeRectangle(7, 1, 1, 1);
>>> run("Clear", "slice");
>>> run("Enhance Contrast", "saturated=0.35");
>>>
>>> ///// FIRST PAIR OF PROFILES (left and right to the whitish spot)
>>> selectWindow("Untitled");
>>> makeLine(4.5, 5.5, 4.5, 11.5);
>>> run("Plot Profile");
>>>
>>> selectWindow("Untitled");
>>> makeLine(12.5, 5.5, 12.5, 11.5);
>>> run("Plot Profile");
>>>
>>>
>>> ///// SECOND PAIR OF PROFILES (top and bottom to the white pixel)
>>> selectWindow("Untitled");
>>> makeLine(5.5, 0.5, 9.5, 0.5);
>>> run("Plot Profile");
>>>
>>> selectWindow("Untitled");
>>> makeLine(5.5, 2.5, 9.5, 2.5);
>>> run("Plot Profile");
>>>
>>> On 10 March 2016 at 10:06, Jan Eglinger <[hidden email]> wrote:
>>>
>>> Dear Avital and Emmanuel,
>>>>
>>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>>>> wrote:
>>>>>
>>>>>> Herbie helped me in the other ImageJ forum
>>>>>>
>>>>>
>>>> Let's be nice and link to this discussion, so others can follow:
>>>> http://forum.imagej.net/t/how-is-the-plot-profile-calculated/1070
>>>>
>>>>
>>>> On 10.03.2016 07:26, Emmanuel Levy wrote:
>>>>
>>>> I would have expected that, by default, only the pixels onto which the
>>>>> line
>>>>> is drawn are used and interpolated when calculating the profile. Is this
>>>>> non-symmetric behaviour of the interpolation an intended behaviour?
>>>>>
>>>>>
>>>> I agree that there are inconsistencies between how lines and segmented
>>>> line selection are displayed on the image and the measurements of those
>>>> lines. Please see also my following related post on the forum:
>>>>
>>>>
>>>>
>>>> http://forum.imagej.net/t/change-in-pixels-using-reslice-function/999/2?u=imagejan
>>>>
>>>>
>>>> I remember previous discussions about rectangular selections and the
>>>> behavior of the Fill and Draw commands that by now have been fixed. It
>>>> would be great to have a consistent ROI behavior through all types of
>>>> selections in ImageJ.
>>>>
>>>> Cheers,
>>>> Jan
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>> On 9 March 2016 at 21:28, Avital Steinberg <[hidden email]>
>>>>> wrote:
>>>>>
>>>>> Hi,
>>>>>
>>>>>> When I use ImageJ's graphical user interface and draw a line and then
>>>>>> select Analyze, plot profile (with the default settings), I get a plot
>>>>>> of
>>>>>> intensities vs. the distance from the beginning of the line. I was
>>>>>> wondering how the plot is generated, in terms of which pixels in the
>>>>>> neighborhood are taken into the weighted average, and how the weights
>>>>>> are
>>>>>> determined.
>>>>>>
>>>>>> Herbie helped me in the other ImageJ forum by suggesting that I plot a
>>>>>> ramp
>>>>>> image. Now I can sometimes predict the values that will appear in the
>>>>>> profile plot. (but only in some simple cases) After experimenting with
>>>>>> an
>>>>>> image, I noticed that the plot's x-axis scale changes abruptly from 1.5
>>>>>> to
>>>>>> 2.0 (for example) and I was wondering if the distance between 2
>>>>>> adjacent
>>>>>> points changes when the scale suddenly changes.
>>>>>>
>>>>>> Thank you,
>>>>>> Avital
>>>>>>
>>>>>>
>>>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>
>>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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ImageJ mailing list: http://imagej.nih.gov/ij/list.html

Herbie

Re: How is the line plot profile generated?

In reply to this post by Emmanuel Levy

Emmanuel,

with your test image you get the symmetric result for:
//
selectWindow("Untitled");
makeLine(4.5, 5.5, 4.5, 11.5);
run("Plot Profile");
selectWindow("Untitled");
makeLine(10.5, 5.5, 10.5, 11.5);
run("Plot Profile");
//
As I've mentioned before, xy.5 is rounded up.

Of course you can escape to different interpolation schemes as Michael
proposed. (However, checking subpixel alone doesn't help with the above
example.)

Best

Herbie

:::::::::::::::::::::::::::::::::::::::::::
Am 13.03.16 um 22:04 schrieb Emmanuel Levy:

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