Science and Technology news... :: View topic

Guest · Posted: Thu Jul 17, 2008 5:54 pm Post subject: Accurate edge detection?

I originally posted the following on the sci.optics newsgroup because
it>s more of an optical query. Nevertheless, the folks here may be
more familiar with the available references and research that>s been
done. Please forgive my statement of some things that will no doubt be
obvious to many here. (BTW: I also have a description of the
experiments we>ve performed for anyone interested.)

===================================================
In the image processing community, there are discussions of edge
detection techniques. For a simple case, imagine an opaque knife
edge
with a uniform back light behind it. Further imagine there is a lens
that images the knife edge onto a pixel detector of a camera.

In general, the transition from dark to light at the detector is some
smoothly varying function, not a sharp jump. Diffraction, of course,
limits the ultimate sharpness of the edge image -- diffraction at the
edge itself, and diffraction at the aperture of the lens.
Aberrations
of the lens will also contribute to this edge smoothing.

The digital image as presented *by* the camera may take only a pixel
or two to transition from dark to light, or it might take many more.
Regardless, digitization and pixel size and other factors such as MTF
of the electronics themselves serve to mask the true edge function

A very common starting point in the discussions and papers about edge
detection techniques is the assumption that the point at which the
slope of the edge is maximum represents the "true" edge position.
From then on, the various edge detection algorithms usually present
different methods of more accurately calculating this maximum slope,
especially in the face of optical and electronic noise, etc.

Nevertheless, it seems to me that the assumption that the maximum
slope represents the true edge is at least unmotivated (no matter how
"common sense" it feels) if not wrong. I have in mind the pictures
of
edge diffraction as produced by using Cornu>s spiral. The location
of
the true edge, relative to the average intensity of the light area
(smoothing out the diffraction oscillations), looks to be at a
position of increasing slope as you go from dark to light, but NOT
maximum. Furthermore, the edge is less than the 50% point of peak
light intensity. (Another assumption sometimes made in image
processing is that the 50% point of the dark to light transistion
represents the edge.)

Does anyone have references they can point to (or their own pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function? We have done a couple of bench
tests to suggest under the experimental conditions that the best edge
location is about 41% to 46% of the range of the dark to light
transition. We haven>t yet completed our analysis regarding how this
compares to the peak slope.

This problem has to have been tackled successfully before, but so far
I>ve not found any good sources that address the optical issue, only
software techniques.

Thanks!

Spencer

Science.Medical.Imaging L · Guest

On Jul 17, 10:54 am, slus...@lw4u.com wrote:
[quote]I originally posted the following on the sci.optics newsgroup because
it>s more of an optical query. Nevertheless, the folks here may be
more familiar with the available references and research that>s been
done. Please forgive my statement of some things that will no doubt be
obvious to many here. (BTW: I also have a description of the
experiments we>ve performed for anyone interested.)

==================================================> In the image processing community, there are discussions of edge
detection techniques. For a simple case, imagine an opaque knife
edge
with a uniform back light behind it. Further imagine there is a lens
that images the knife edge onto a pixel detector of a camera.

In general, the transition from dark to light at the detector is some
smoothly varying function, not a sharp jump. Diffraction, of course,
limits the ultimate sharpness of the edge image -- diffraction at the
edge itself, and diffraction at the aperture of the lens.
Aberrations
of the lens will also contribute to this edge smoothing.

The digital image as presented *by* the camera may take only a pixel
or two to transition from dark to light, or it might take many more.
Regardless, digitization and pixel size and other factors such as MTF
of the electronics themselves serve to mask the true edge function

A very common starting point in the discussions and papers about edge
detection techniques is the assumption that the point at which the
slope of the edge is maximum represents the "true" edge position.
From then on, the various edge detection algorithms usually present
different methods of more accurately calculating this maximum slope,
especially in the face of optical and electronic noise, etc.

Nevertheless, it seems to me that the assumption that the maximum
slope represents the true edge is at least unmotivated (no matter how
"common sense" it feels) if not wrong. I have in mind the pictures
of
edge diffraction as produced by using Cornu>s spiral. The location
of
the true edge, relative to the average intensity of the light area
(smoothing out the diffraction oscillations), looks to be at a
position of increasing slope as you go from dark to light, but NOT
maximum. Furthermore, the edge is less than the 50% point of peak
light intensity. (Another assumption sometimes made in image
processing is that the 50% point of the dark to light transistion
represents the edge.)

Does anyone have references they can point to (or their own pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function? We have done a couple of bench
tests to suggest under the experimental conditions that the best edge
location is about 41% to 46% of the range of the dark to light
transition. We haven>t yet completed our analysis regarding how this
compares to the peak slope.

This problem has to have been tackled successfully before, but so far
I>ve not found any good sources that address the optical issue, only
software techniques.

Thanks!

Spencer
[/quote]

Good post!

With edge detection techniques that focus only on algorithmic aspects
of it, without a concern for how the image was acquired, your post
raises an important point: an image analysis algorithm must know how
the image was acquired in the first place, and make use of that
information.

But again, if an image is provided with some representation of an
edge, along with all the givens of noise sources in hardware,
sampling, etc., but NOT given is its source or how it was acquired, a
computer program can at best (if ever) only mimic what human visual
system will do to mark the edge: 'it will only consider what is
*visible* in the image'.

So to me, it seems like there cannot be a general edge detection
method that will work on images acquired using all available methods
in all available conditions. Hence your pursuit to mark the 'correct'
or 'accurate' edge in a digital image, considering all the optical
phenomenon that may affect the process, may still depend on how the
image is acquired.

Or can it be generalized?

Good luck.

[http://groups.google.com/group/medicalimagingscience/web/smiviewer-
download-page]

aruzinsky · Guest

On Jul 17, 11:54 am, slus...@lw4u.com wrote:
[quote]I originally posted the following on the sci.optics newsgroup because
it>s more of an optical query. Nevertheless, the folks here may be
more familiar with the available references and research that>s been
done. Please forgive my statement of some things that will no doubt be
obvious to many here. (BTW: I also have a description of the
experiments we>ve performed for anyone interested.)

==================================================> In the image processing community, there are discussions of edge
detection techniques. For a simple case, imagine an opaque knife
edge
with a uniform back light behind it. Further imagine there is a lens
that images the knife edge onto a pixel detector of a camera.

In general, the transition from dark to light at the detector is some
smoothly varying function, not a sharp jump. Diffraction, of course,
limits the ultimate sharpness of the edge image -- diffraction at the
edge itself, and diffraction at the aperture of the lens.
Aberrations
of the lens will also contribute to this edge smoothing.

The digital image as presented *by* the camera may take only a pixel
or two to transition from dark to light, or it might take many more.
Regardless, digitization and pixel size and other factors such as MTF
of the electronics themselves serve to mask the true edge function

A very common starting point in the discussions and papers about edge
detection techniques is the assumption that the point at which the
slope of the edge is maximum represents the "true" edge position.
From then on, the various edge detection algorithms usually present
different methods of more accurately calculating this maximum slope,
especially in the face of optical and electronic noise, etc.

Nevertheless, it seems to me that the assumption that the maximum
slope represents the true edge is at least unmotivated (no matter how
"common sense" it feels) if not wrong. I have in mind the pictures
of
edge diffraction as produced by using Cornu>s spiral. The location
of
the true edge, relative to the average intensity of the light area
(smoothing out the diffraction oscillations), looks to be at a
position of increasing slope as you go from dark to light, but NOT
maximum. Furthermore, the edge is less than the 50% point of peak
light intensity. (Another assumption sometimes made in image
processing is that the 50% point of the dark to light transistion
represents the edge.)

Does anyone have references they can point to (or their own pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function? We have done a couple of bench
tests to suggest under the experimental conditions that the best edge
location is about 41% to 46% of the range of the dark to light
transition. We haven>t yet completed our analysis regarding how this
compares to the peak slope.

This problem has to have been tackled successfully before, but so far
I>ve not found any good sources that address the optical issue, only
software techniques.

Thanks!

Spencer
[/quote]
The information you seek mostly resides within the more general topic
of image interpolation/enlargement and not edge detection.

Google "edge interpolation" .

Also,

http://www.cs.huji.ac.il/~raananf/projects/upsampling/upsampling.html

http://www.general-cathexis.com/subpixel%20edge%20localization%20and%20interpolation.pdf

I uploaded the last for your benefit only and will delete it in 2
days.

Generally speaking, the influence of optics, sensor size and shape,
demosaicing, and size reduction can be represented by an undetermined
linear transformation Ax = y. You determine enlarged image x' (with
sharp edges) such that Ax' = y subject to regularity constraints which
incorporate a priori knowledge of natural images.

Guest · Posted: Fri Jul 18, 2008 8:45 pm Post subject: Re: Accurate edge detection?

On Jul 17, 4:14 pm, "Science.Medical.Imaging List"
<pixel.to.l...@gmail.com> wrote:
[quote]On Jul 17, 10:54 am, slus...@lw4u.com wrote:

I originally posted the following on the sci.optics newsgroup because
it>s more of an optical query. Nevertheless, the folks here may be
more familiar with the available references and research that>s been
done. Please forgive my statement of some things that will no doubt be
obvious to many here. (BTW: I also have a description of the
experiments we>ve performed for anyone interested.)

==================================================> > In the image processing community, there are discussions of edge
detection techniques. For a simple case, imagine an opaque knife
edge
with a uniform back light behind it. Further imagine there is a lens
that images the knife edge onto a pixel detector of a camera.

In general, the transition from dark to light at the detector is some
smoothly varying function, not a sharp jump. Diffraction, of course,
limits the ultimate sharpness of the edge image -- diffraction at the
edge itself, and diffraction at the aperture of the lens.
Aberrations
of the lens will also contribute to this edge smoothing.

The digital image as presented *by* the camera may take only a pixel
or two to transition from dark to light, or it might take many more.
Regardless, digitization and pixel size and other factors such as MTF
of the electronics themselves serve to mask the true edge function

A very common starting point in the discussions and papers about edge
detection techniques is the assumption that the point at which the
slope of the edge is maximum represents the "true" edge position.
From then on, the various edge detection algorithms usually present
different methods of more accurately calculating this maximum slope,
especially in the face of optical and electronic noise, etc.

Nevertheless, it seems to me that the assumption that the maximum
slope represents the true edge is at least unmotivated (no matter how
"common sense" it feels) if not wrong. I have in mind the pictures
of
edge diffraction as produced by using Cornu>s spiral. The location
of
the true edge, relative to the average intensity of the light area
(smoothing out the diffraction oscillations), looks to be at a
position of increasing slope as you go from dark to light, but NOT
maximum. Furthermore, the edge is less than the 50% point of peak
light intensity. (Another assumption sometimes made in image
processing is that the 50% point of the dark to light transistion
represents the edge.)

Does anyone have references they can point to (or their own pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function? We have done a couple of bench
tests to suggest under the experimental conditions that the best edge
location is about 41% to 46% of the range of the dark to light
transition. We haven>t yet completed our analysis regarding how this
compares to the peak slope.

This problem has to have been tackled successfully before, but so far
I>ve not found any good sources that address the optical issue, only
software techniques.

Thanks!

Spencer

Good post!

With edge detection techniques that focus only on algorithmic aspects
of it, without a concern for how the image was acquired, your post
raises an important point: an image analysis algorithm must know how
the image was acquired in the first place, and make use of that
information.

But again, if an image is provided with some representation of an
edge, along with all the givens of noise sources in hardware,
sampling, etc., but NOT given is its source or how it was acquired, a
computer program can at best (if ever) only mimic what human visual
system will do to mark the edge: 'it will only consider what is
*visible* in the image'.

So to me, it seems like there cannot be a general edge detection
method that will work on images acquired using all available methods
in all available conditions. Hence your pursuit to mark the 'correct'
or 'accurate' edge in a digital image, considering all the optical
phenomenon that may affect the process, may still depend on how the
image is acquired.

Or can it be generalized?

Good luck.

[http://groups.google.com/group/medicalimagingscience/web/smiviewer-
download-page]- Hide quoted text -

- Show quoted text -
[/quote]
My guess is that generalizing the optical edge function for the real
world would be an infinite project. Let>s start with Fresnel
diffraction for just a perfect knife edge and screen using
monochromatic, coherent, nearly perfectly collimated light. This can
be solved to show that the the intensity pattern at the screen looks
something like this, with intensity vertical and x-position of the
knife edge and screen being horizontal.

-
- -
-
- - - -
- -
- - - -
- - -
-- -
--
--
----
===> true knife edge

Here we see that the maximum slop does not necessarily correspond to
the true knife edge position, nor to the 50% point of the peak average
light level. But this is for one case at one wavelength, with no
imaging lens involved.

For non-monocrhomatic, non-spatially coherent, non-collimated sources
it gets *much* more complex. Then you add a real lens, with it>s own
aberrations, and diffraction effects due to the aperture (possibly
convolve the point spread function with the edge diffraction
function?) at different f-numbers!

Admittedly some of the effects may be small, and mostly ignorable.
But, when one is trying to do robust and very accurate sub-pixel
interpolation...

Spencer

Guest · Posted: Sat Jul 19, 2008 2:14 am Post subject: Re: Accurate edge detection?

On Jul 18, 4:45 pm, slus...@lw4u.com wrote:
[quote]On Jul 17, 4:14 pm, "Science.Medical.Imaging List"

pixel.to.l...@gmail.com> wrote:
On Jul 17, 10:54 am, slus...@lw4u.com wrote:

I originally posted the following on the sci.optics newsgroup because
it>s more of an optical query. Nevertheless, the folks here may be
more familiar with the available references and research that>s been
done. Please forgive my statement of some things that will no doubt be
obvious to many here. (BTW: I also have a description of the
experiments we>ve performed for anyone interested.)

==================================================> > > In the image processing community, there are discussions of edge
detection techniques. For a simple case, imagine an opaque knife
edge
with a uniform back light behind it. Further imagine there is a lens
that images the knife edge onto a pixel detector of a camera.

In general, the transition from dark to light at the detector is some
smoothly varying function, not a sharp jump. Diffraction, of course,
limits the ultimate sharpness of the edge image -- diffraction at the
edge itself, and diffraction at the aperture of the lens.
Aberrations
of the lens will also contribute to this edge smoothing.

The digital image as presented *by* the camera may take only a pixel
or two to transition from dark to light, or it might take many more.
Regardless, digitization and pixel size and other factors such as MTF
of the electronics themselves serve to mask the true edge function

A very common starting point in the discussions and papers about edge
detection techniques is the assumption that the point at which the
slope of the edge is maximum represents the "true" edge position.
From then on, the various edge detection algorithms usually present
different methods of more accurately calculating this maximum slope,
especially in the face of optical and electronic noise, etc.

Nevertheless, it seems to me that the assumption that the maximum
slope represents the true edge is at least unmotivated (no matter how
"common sense" it feels) if not wrong. I have in mind the pictures
of
edge diffraction as produced by using Cornu>s spiral. The location
of
the true edge, relative to the average intensity of the light area
(smoothing out the diffraction oscillations), looks to be at a
position of increasing slope as you go from dark to light, but NOT
maximum. Furthermore, the edge is less than the 50% point of peak
light intensity. (Another assumption sometimes made in image
processing is that the 50% point of the dark to light transistion
represents the edge.)

Does anyone have references they can point to (or their own pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function? We have done a couple of bench
tests to suggest under the experimental conditions that the best edge
location is about 41% to 46% of the range of the dark to light
transition. We haven>t yet completed our analysis regarding how this
compares to the peak slope.

This problem has to have been tackled successfully before, but so far
I>ve not found any good sources that address the optical issue, only
software techniques.

Thanks!

Spencer

Good post!

With edge detection techniques that focus only on algorithmic aspects
of it, without a concern for how the image was acquired, your post
raises an important point: an image analysis algorithm must know how
the image was acquired in the first place, and make use of that
information.

But again, if an image is provided with some representation of an
edge, along with all the givens of noise sources in hardware,
sampling, etc., but NOT given is its source or how it was acquired, a
computer program can at best (if ever) only mimic what human visual
system will do to mark the edge: 'it will only consider what is
*visible* in the image'.

So to me, it seems like there cannot be a general edge detection
method that will work on images acquired using all available methods
in all available conditions. Hence your pursuit to mark the 'correct'
or 'accurate' edge in a digital image, considering all the optical
phenomenon that may affect the process, may still depend on how the
image is acquired.

Or can it be generalized?

Good luck.

[http://groups.google.com/group/medicalimagingscience/web/smiviewer-
download-page]- Hide quoted text -

- Show quoted text -

My guess is that generalizing the optical edge function for the real
world would be an infinite project. Let>s start with Fresnel
diffraction for just a perfect knife edge and screen using
monochromatic, coherent, nearly perfectly collimated light. This can
be solved to show that the the intensity pattern at the screen looks
something like this, with intensity vertical and x-position of the
knife edge and screen being horizontal.

-
- -
-
- - - -
- -
- - - -
- - -
-- -
--
--
----
===> true knife edge

Here we see that the maximum slop does not necessarily correspond to
the true knife edge position, nor to the 50% point of the peak average
light level. But this is for one case at one wavelength, with no
imaging lens involved.

For non-monocrhomatic, non-spatially coherent, non-collimated sources
it gets *much* more complex. Then you add a real lens, with it>s own
aberrations, and diffraction effects due to the aperture (possibly
convolve the point spread function with the edge diffraction
function?) at different f-numbers!

Admittedly some of the effects may be small, and mostly ignorable.
But, when one is trying to do robust and very accurate sub-pixel
interpolation...

Spencer- Hide quoted text -

- Show quoted text -
[/quote]
Oops. Sorry about the bad "graphic". Let>s see if fixed font works
better:
-
- - -
- - - - -
- - - -
-
-
--
====> True knife edge

Spencer

Science.Medical.Imaging L · Guest

On Jul 18, 9:19 am, aruzinsky <aruzin...@general-cathexis.com> wrote:
[quote]On Jul 17, 11:54 am, slus...@lw4u.com wrote:

I originally posted the following on the sci.optics newsgroup because
it>s more of an optical query. Nevertheless, the folks here may be
more familiar with the available references and research that>s been
done. Please forgive my statement of some things that will no doubt be
obvious to many here. (BTW: I also have a description of the
experiments we>ve performed for anyone interested.)

==================================================> > In the image processing community, there are discussions of edge
detection techniques. For a simple case, imagine an opaque knife
edge
with a uniform back light behind it. Further imagine there is a lens
that images the knife edge onto a pixel detector of a camera.

In general, the transition from dark to light at the detector is some
smoothly varying function, not a sharp jump. Diffraction, of course,
limits the ultimate sharpness of the edge image -- diffraction at the
edge itself, and diffraction at the aperture of the lens.
Aberrations
of the lens will also contribute to this edge smoothing.

The digital image as presented *by* the camera may take only a pixel
or two to transition from dark to light, or it might take many more.
Regardless, digitization and pixel size and other factors such as MTF
of the electronics themselves serve to mask the true edge function

A very common starting point in the discussions and papers about edge
detection techniques is the assumption that the point at which the
slope of the edge is maximum represents the "true" edge position.
From then on, the various edge detection algorithms usually present
different methods of more accurately calculating this maximum slope,
especially in the face of optical and electronic noise, etc.

Nevertheless, it seems to me that the assumption that the maximum
slope represents the true edge is at least unmotivated (no matter how
"common sense" it feels) if not wrong. I have in mind the pictures
of
edge diffraction as produced by using Cornu>s spiral. The location
of
the true edge, relative to the average intensity of the light area
(smoothing out the diffraction oscillations), looks to be at a
position of increasing slope as you go from dark to light, but NOT
maximum. Furthermore, the edge is less than the 50% point of peak
light intensity. (Another assumption sometimes made in image
processing is that the 50% point of the dark to light transistion
represents the edge.)

Does anyone have references they can point to (or their own pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function? We have done a couple of bench
tests to suggest under the experimental conditions that the best edge
location is about 41% to 46% of the range of the dark to light
transition. We haven>t yet completed our analysis regarding how this
compares to the peak slope.

This problem has to have been tackled successfully before, but so far
I>ve not found any good sources that address the optical issue, only
software techniques.

Thanks!

Spencer

The information you seek mostly resides within the more general topic
of image interpolation/enlargement and not edge detection.

Google "edge interpolation" .

Also,

http://www.cs.huji.ac.il/~raananf/projects/upsampling/upsampling.html

http://www.general-cathexis.com/subpixel%20edge%20localization%20and%...

I uploaded the last for your benefit only and will delete it in 2
days.

Generally speaking, the influence of optics, sensor size and shape,
demosaicing, and size reduction can be represented by an undetermined
linear transformation Ax = y. You determine enlarged image x' (with
sharp edges) such that Ax' = y subject to regularity constraints which
incorporate a priori knowledge of natural images.- Hide quoted text -

- Show quoted text -
[/quote]
About the last part: are you sure most of the influence of 'optics,
sensor size and shape,
demosaicing, and size reduction' can be represented by a linear
transformation on acquired values?

I would think you meant not 'represented' but 'estimated'.

I would be really interested in knowing about any existing (published)
proofs in support of your response.

aruzinsky · Guest

For some reason, my Google Usenet portal is not automatically producing
quotes on my reply to your post therefore I have done it manually.

"About the last part: are you sure most of the influence of 'optics,
sensor size and shape,
demosaicing, and size reduction' can be represented by a linear
transformation on acquired values?

I would think you meant not 'represented' but 'estimated'.

I would be really interested in knowing about any existing (published)
proofs in support of your response."

It is not a linear transformation on "acquired values," y, but on x which
represents
a higher resolution discrete image that approximates the continuous
(infinite resolution) image falling on the sensors. x' is an estimate of
x. Depending on the estimation method, x' may or may not be a linear
function of observations, y.

The matrix A represents convolution and decimation and is not invertible.
It is well known that most, if not all, optical effects are convolutions, a
linear transformation. Possibly the convolution kernel is a function of
spatial coordinate (as in the case of the bad Hubble telescope lens) but
it still can be represented by a linear transformation, A. The effect of
pixel sensor size and shape is represented by continuous convolution
followed by decimation which again can be incorporated into A. Some, but
not all cases of demosaicing are also linear transformations.

--
Message posted using http://www.talkaboutgraphics.com/group/sci.image.processing/
More information at http://www.talkaboutgraphics.com/faq.html

Science.Medical.Imaging L · Guest

On Jul 19, 7:44 am, "aruzinsky" <aruzin...@nospam.general-
cathexis.com> wrote:
[quote]For some reason, my Google Usenet portal is not automatically producing
quotes on my reply to your post therefore I have done it manually.

"About the last part: are you sure most of the influence of 'optics,
sensor size and shape,
demosaicing, and size reduction' can be represented by a linear
transformation on acquired values?

I would think you meant not 'represented' but 'estimated'.

I would be really interested in knowing about any existing (published)
proofs in support of your response."

It is not a linear transformation on "acquired values," y, but on x which
represents
a higher resolution discrete image that approximates the continuous
(infinite resolution) image falling on the sensors. x' is an estimate of
x. Depending on the estimation method, x' may or may not be a linear
function of observations, y.

The matrix A represents convolution and decimation and is not invertible.
It is well known that most, if not all, optical effects are convolutions, a
linear transformation. Possibly the convolution kernel is a function of
spatial coordinate (as in the case of the bad Hubble telescope lens) but
it still can be represented by a linear transformation, A. The effect of
pixel sensor size and shape is represented by continuous convolution
followed by decimation which again can be incorporated into A. Some, but
not all cases of demosaicing are also linear transformations.

--
Message posted usinghttp://www.talkaboutgraphics.com/group/sci.image.processing/
More information athttp://www.talkaboutgraphics.com/faq.html
[/quote]
This makes more sense now. Your earlier post suggested (perhaps it was
the words) that all optical effects can be represented by a
combination of linear transformations. That was hard to understand. It
is more reasonable to say that 'some' of the optical effects can be
represented as linear transformations.

aruzinsky · Guest

On Jul 20, 2:24 pm, "Science.Medical.Imaging List"
<pixel.to.l...@gmail.com> wrote:
[quote]On Jul 19, 7:44 am, "aruzinsky" <aruzin...@nospam.general-

cathexis.com> wrote:
For some reason, my Google Usenet portal is not automatically producing
quotes on my reply to your post therefore I have done it manually.

"About the last part: are you sure most of the influence of 'optics,
sensor size and shape,
demosaicing, and size reduction' can be represented by a linear
transformation on acquired values?

I would think you meant not 'represented' but 'estimated'.

I would be really interested in knowing about any existing (published)
proofs in support of your response."

It is not a linear transformation on "acquired values," y, but on x which
represents
a higher resolution discrete image that approximates the continuous
(infinite resolution) image falling on the sensors. x' is an estimate of
x. Depending on the estimation method, x' may or may not be a linear
function of observations, y.

The matrix A represents convolution and decimation and is not invertible.
It is well known that most, if not all, optical effects are convolutions, a
linear transformation. Possibly the convolution kernel is a function of
spatial coordinate (as in the case of the bad Hubble telescope lens) but
it still can be represented by a linear transformation, A. The effect of
pixel sensor size and shape is represented by continuous convolution
followed by decimation which again can be incorporated into A. Some, but
not all cases of demosaicing are also linear transformations.

--
Message posted usinghttp://www.talkaboutgraphics.com/group/sci.image.processing/
More information athttp://www.talkaboutgraphics.com/faq.html

This makes more sense now. Your earlier post suggested (perhaps it was
the words) that all optical effects can be represented by a
combination of linear transformations. That was hard to understand. It
is more reasonable to say that 'some' of the optical effects can be
represented as linear transformations.- Hide quoted text -

- Show quoted text -
[/quote]
I was suggesting that, but I am not knowledgeable of every possible
optical effect. Name one optical effect that can>t be represented by
a linear transformation.

Science.Medical.Imaging L · Guest

On Jul 20, 4:24 pm, aruzinsky <aruzin...@general-cathexis.com> wrote:
[quote]On Jul 20, 2:24 pm, "Science.Medical.Imaging List"

pixel.to.l...@gmail.com> wrote:
On Jul 19, 7:44 am, "aruzinsky" <aruzin...@nospam.general-

cathexis.com> wrote:
For some reason, my Google Usenet portal is not automatically producing
quotes on my reply to your post therefore I have done it manually.

"About the last part: are you sure most of the influence of 'optics,
sensor size and shape,
demosaicing, and size reduction' can be represented by a linear
transformation on acquired values?

I would think you meant not 'represented' but 'estimated'.

I would be really interested in knowing about any existing (published)
proofs in support of your response."

It is not a linear transformation on "acquired values," y, but on x which
represents
a higher resolution discrete image that approximates the continuous
(infinite resolution) image falling on the sensors. x' is an estimate of
x. Depending on the estimation method, x' may or may not be a linear
function of observations, y.

The matrix A represents convolution and decimation and is not invertible.
It is well known that most, if not all, optical effects are convolutions, a
linear transformation. Possibly the convolution kernel is a function of
spatial coordinate (as in the case of the bad Hubble telescope lens) but
it still can be represented by a linear transformation, A. The effect of
pixel sensor size and shape is represented by continuous convolution
followed by decimation which again can be incorporated into A. Some, but
not all cases of demosaicing are also linear transformations.

--
Message posted usinghttp://www.talkaboutgraphics.com/group/sci.image.processing/
More information athttp://www.talkaboutgraphics.com/faq.html

This makes more sense now. Your earlier post suggested (perhaps it was
the words) that all optical effects can be represented by a
combination of linear transformations. That was hard to understand. It
is more reasonable to say that 'some' of the optical effects can be
represented as linear transformations.- Hide quoted text -

- Show quoted text -

I was suggesting that, but I am not knowledgeable of every possible
optical effect. Name one optical effect that can>t be represented by
a linear transformation.- Hide quoted text -

- Show quoted text -
[/quote]
Here are two optical effects that treat light non linearly:

Raman effect
Brillouin scattering

Here is one start:

http://en.wikipedia.org/wiki/Nonlinear_optics

Now an argument could be that these effects (or their kins) dont
usually affect many common image acquisition systems. But they do
affect some. And hence my statement: that some optical effects can
only be approximated with a linear transformation - they cannot be
truly represented using just linear transforms. Given above are the
examples.

Andrew_M · Guest

This is not a simple task, even if you have opaque flat object and a
uniform back light behind it. Do not try solve really complicated prob
using simple methods. Let>s try to imagine opague circle instead of
your knife. Lens and scanning system transforms this source object to
some grayscale image. Where the true edge should be placed, depends on
the source circle radius, savvy? It means, as a matter of fact, that
you shouldn>t think about it as about an "edge detection problem".
This is the problem of restoration of a transformed image, and,
unfortunately, this is an incorrect one. Lots of very different source
images may produce similar results after transforming, so some
regularization is a must. It is possible for example, if you have an
opaque object with more or less smooth edges. What kind of objects do
you actually have? If you really need some assistance, send me some
sample image (not very big- my Net is very slow).

Guest · Posted: Tue Jul 22, 2008 2:04 pm Post subject: Re: Accurate edge detection?

On Jul 22, 5:19 am, Andrew_M <m...@smartfills.com> wrote:
[quote]This is not a simple task, even if you have opaque flat object and a
uniform back light behind it. Do not try solve really complicated prob
using simple methods. Let>s try to imagine opague circle instead of
your knife. Lens and scanning system transforms this source object to
some grayscale image. Where the true edge should be placed, depends on
the source circle radius, savvy? It means, as a matter of fact, that
you shouldn>t think about it as about an "edge detection problem".
This is the problem of restoration of a transformed image, and,
unfortunately, this is an incorrect one. Lots of very different source
images may produce similar results after transforming, so some
regularization is a must. It is possible for example, if you have an
opaque object with more or less smooth edges. What kind of objects do
you actually have? If you really need some assistance, send me some
sample image (not very big- my Net is very slow).
[/quote]
Andrew,

Thank you for your interest and offer to review some sample images.
Unfortunately, our concern is not on the software or algorithmic side,
but on the optical side. As I mentioned in my original post:

"Does anyone have references they can point to (or their own
pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function?"

I also mentioned that I originally posted to sci.optics, then added
sci.image.processing because I thought the folks here might be more
aware of relavent references. The (apparently) commonly held belief
that the maximum slope of the edge image, or the midpoint between the
maximum and minimum grey level values of the edge image corresponds to
the true edge location seems unmotivated or unsupported to me, even
though it "feels" like common sense. We have also performed bench
experiments that suggest that neither the max. slope nor the grey
level midpoint corresponds to the true edge, with errors being in the
range of 0.2 to 0.45 pixels in the experimental set up we used. We
are continuing our own investigation, but I have to believe that
someone has already done this at some time and published their
results. I>d love to find out that our own efforts at inventing the
wheel are unecessary. :-)

Thanks again,

Spencer

aruzinsky · Guest

On Jul 22, 8:04 am, slus...@lw4u.com wrote:
[quote]
Thank you for your interest and offer to review some sample images.
Unfortunately, our concern is not on the software or algorithmic side,
but on the optical side. As I mentioned in my original post:

"Does anyone have references they can point to (or their own
pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function?"

[/quote]
I already did. What is wrong with you?

[quote]
I also mentioned that I originally posted to sci.optics, then added
sci.image.processing because I thought the folks here might be more
aware of relavent references. The (apparently) commonly held belief
that the maximum slope of the edge image, or the midpoint between the
maximum and minimum grey level values of the edge image corresponds to
the true edge location seems unmotivated or unsupported to me, even
though it "feels" like common sense.
[/quote]
That is an algorithm, albeit a really stupid one that is not common
sense, so don>t tell me that you are not interest in algorithms.
Furthermore, that is not a commonly held belief, e.g., it is common
knowledge that shock filters sharpen an edge around the inflection
point (the inflection point is preserved) and nobody, I know of,
pretends that shock filtering is deconvolution.

[quote]We have also performed bench
experiments that suggest that neither the max. slope nor the grey
level midpoint corresponds to the true edge, with errors being in the
range of 0.2 to 0.45 pixels in the experimental set up we used.
[/quote]
I hope my tax money didn>t fund that busy work.

[quote] We
are continuing our own investigation, but I have to believe that
someone has already done this at some time and published their
results. I>d love to find out that our own efforts at inventing the
wheel are unecessary. :-)

[/quote]
I already gave you a reference to a relatively simple algorithm that
might do better than 0.2 pixels. It would be foolish not to try it.

Andrew_M · Guest

[quote]Andrew,

Thank you for your interest and offer to review some sample images.
Unfortunately, our concern is not on the software or algorithmic side,
but on the optical side. As I mentioned in my original post:

"Does anyone have references they can point to (or their own
pesuasive
arguments) that describe where the true edge location should be
relative to the edge image function?"

[/quote]
I do not see, what do you mean. What cardinal enchancement with
optical side could be done? To change wave lenght, use larger lens or
increase exposure? As a result in any event you>ll get a scanned
digital image, what has to be processed by some soft. There are some
things, what cannot be done without proper algorithms. Have you ever
heard about superresolution (or overresolution- I>m not sure about
proper term- English isn>t my mother>s tongue). It is something like
what you want to get- obtain better resolution than your optical
system allows. I could only repeat- it is not a problem of where the
true edge is, it is a problem of restoration of a transformed image.
This problem requires specific methods. I twice made progs for science
image processing, and in any event I had to use much more complicated
methods than what my client thought.
Andrew

Martin Brown · Guest

aruzinsky wrote:
[quote]On Jul 20, 2:24 pm, "Science.Medical.Imaging List"
pixel.to.l...@gmail.com> wrote:
On Jul 19, 7:44 am, "aruzinsky" <aruzin...@nospam.general-

cathexis.com> wrote:
For some reason, my Google Usenet portal is not automatically producing
quotes on my reply to your post therefore I have done it manually.
"About the last part: are you sure most of the influence of 'optics,
sensor size and shape,
demosaicing, and size reduction' can be represented by a linear
transformation on acquired values?
I would think you meant not 'represented' but 'estimated'.
I would be really interested in knowing about any existing (published)
proofs in support of your response."
It is not a linear transformation on "acquired values," y, but on x which
represents
a higher resolution discrete image that approximates the continuous
(infinite resolution) image falling on the sensors. x' is an estimate of
x. Depending on the estimation method, x' may or may not be a linear
function of observations, y.
The matrix A represents convolution and decimation and is not invertible.
It is well known that most, if not all, optical effects are convolutions, a
linear transformation. Possibly the convolution kernel is a function of
spatial coordinate (as in the case of the bad Hubble telescope lens) but
it still can be represented by a linear transformation, A. The effect of
pixel sensor size and shape is represented by continuous convolution
followed by decimation which again can be incorporated into A. Some, but
not all cases of demosaicing are also linear transformations.
--
Message posted usinghttp://www.talkaboutgraphics.com/group/sci.image.processing/
More information athttp://www.talkaboutgraphics.com/faq.html
This makes more sense now. Your earlier post suggested (perhaps it was
the words) that all optical effects can be represented by a
combination of linear transformations. That was hard to understand. It
is more reasonable to say that 'some' of the optical effects can be
represented as linear transformations.- Hide quoted text -

- Show quoted text -

I was suggesting that, but I am not knowledgeable of every possible
optical effect. Name one optical effect that can>t be represented by
a linear transformation.
[/quote]
The most common ones that break modern deconvolution codes are a point
spread function that is not position invariant. The is the imaging
system has off axis abberations (most real diffraction limited optics
suffer some degradation as you go off axis).

And the real killer in the general photography situation is depth of
field. You can model the psf for a given subject distance, but when
different parts of the same image are all at different unknown distances
you have a pretty much intractable problem. Or one that is only
resolvable with binocular pairs of images and insane amounts of
computing power.

If the OP wants specifically to find sharp edges with the utmost
precision and doesn>t care about the computational cost then one of the
Bayesian methods using all available prior knowledge will probably give
the optimum result. This reference is a bit old but is a start:

http://adsabs.harvard.edu/abs/1980ITAC...25...36M

There seem to be few papers on this application which suggests to me
that it doesn>t work well enough to be worth the computational cost.

Regards,
Martin Brown
** Posted from http://www.teranews.com **


www.GetXFactor.com Leading Technology, Science, Agriculture News and information	Part of the Identityscape.com network... getxfactor.com jmoodmusic.com smartbusinesschoices.com mintdepot.com lowfaresalways.com evangelicalview.com shoppingpodder.com soproudlywehail.com webnews.ws currenthumor.com

Science and Technology news... Forum Index -> Image Processing Forum	Goto page 1, 2, 3 Next
Page 1 of 3