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Adam Chapman
Posted: Sun Apr 06, 2008 2:40 am
Guest
I remember that it is very easy to find the neutral axis of a
symmetric beam cross-section, just locating the centroid and
intersecting a line of symmetry.

However, I want to find the neutral axis of an area which is non-
symmetrical. Does anybody know off-hand what to do?

I am tryingto use the principle in image processing- if i see an
object which can be rotated through any angle 0-360 degrees, i want to
find the neutral axis of the object and rotate the image to attenuate
inaccuracy in my recognition algorithm.

If anyone has a link that would be great, all i can find on google is
symemetric examples- doh!

Thanks for any help, it is greatly appreciated.
Adam
Adam Chapman
Posted: Sun Apr 06, 2008 9:43 am
Guest
On Apr 6, 6:15 pm, Adam <n...@spam.net> wrote:
Quote:
On Sun, 6 Apr 2008 05:40:13 -0700 (PDT), Adam Chapman wrote:
I remember that it is very easy to find the neutral axis of a
symmetric beam cross-section, just locating the centroid and
intersecting a line of symmetry.

However, I want to find the neutral axis of an area which is non-
symmetrical. Does anybody know off-hand what to do?

I am tryingto use the principle in image processing- if i see an
object which can be rotated through any angle 0-360 degrees, i want to
find the neutral axis of the object and rotate the image to attenuate
inaccuracy in my recognition algorithm.

If anyone has a link that would be great, all i can find on google is
symemetric examples- doh!

Thanks for any help, it is greatly appreciated.
Adam

http://www.google.com/search?hl=en&q=%22neutral+axis%22+bending+centroid

http://physics.uwstout.edu/StatStr/statics/Beams/bdsn47.htm

        the neutral axis (an axis running
        through the centroid of beam cross section).

just locating the centroid and
intersecting a line of symmetry

Why locate an "intersecting a line of symmetry"?

The moment of inertia with respect to a line parallel to the axis of
bending will change as you rotate the shape.  Does that matter in your
application?  Are you searching for an orientation to minimize (or
maximize) that moment of inertia?

How does beam flexure theory relate to image processing?

Adam

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Im making a character recognition algorithm, and my camera could see
alphabetic characters rotated about any angle.
My inputs to the recognition algorithm are effectively the moments of
inertia of the black pixels that make up the image of the character.
The problem I have is that, like you said, the moments of inertia
change with rotation of the shape. I think recognition accuracy could
be improved by finding a neutral axis and rotating the black pixel are
to line up that axis will improve accuracy.

Sorry the only examples of neutral axes that i have studied in
mechanics about 3 years ago were all for symmetrical beam sections.
Adam
Posted: Sun Apr 06, 2008 12:15 pm
Guest
On Sun, 6 Apr 2008 05:40:13 -0700 (PDT), Adam Chapman wrote:

Quote:
I remember that it is very easy to find the neutral axis of a
symmetric beam cross-section, just locating the centroid and
intersecting a line of symmetry.

However, I want to find the neutral axis of an area which is non-
symmetrical. Does anybody know off-hand what to do?

I am tryingto use the principle in image processing- if i see an
object which can be rotated through any angle 0-360 degrees, i want to
find the neutral axis of the object and rotate the image to attenuate
inaccuracy in my recognition algorithm.

If anyone has a link that would be great, all i can find on google is
symemetric examples- doh!

Thanks for any help, it is greatly appreciated.
Adam

http://www.google.com/search?hl=en&q=%22neutral+axis%22+bending+centroid

http://physics.uwstout.edu/StatStr/statics/Beams/bdsn47.htm

the neutral axis (an axis running
through the centroid of beam cross section).

Quote:
just locating the centroid and
intersecting a line of symmetry

Why locate an "intersecting a line of symmetry"?

The moment of inertia with respect to a line parallel to the axis of
bending will change as you rotate the shape. Does that matter in your
application? Are you searching for an orientation to minimize (or
maximize) that moment of inertia?

How does beam flexure theory relate to image processing?

Adam

--
Posted via a free Usenet account from http://www.teranews.com
Adam
Posted: Sun Apr 06, 2008 6:56 pm
Guest
On Sun, 6 Apr 2008 12:43:49 -0700 (PDT), Adam Chapman wrote:

Quote:
On Apr 6, 6:15 pm, Adam <n...@spam.net> wrote:
On Sun, 6 Apr 2008 05:40:13 -0700 (PDT), Adam Chapman wrote:
I remember that it is very easy to find the neutral axis of a
symmetric beam cross-section, just locating the centroid and
intersecting a line of symmetry.

However, I want to find the neutral axis of an area which is non-
symmetrical. Does anybody know off-hand what to do?

I am tryingto use the principle in image processing- if i see an
object which can be rotated through any angle 0-360 degrees, i want to
find the neutral axis of the object and rotate the image to attenuate
inaccuracy in my recognition algorithm.

If anyone has a link that would be great, all i can find on google is
symemetric examples- doh!

Thanks for any help, it is greatly appreciated.
Adam

http://www.google.com/search?hl=en&q=%22neutral+axis%22+bending+centroid

http://physics.uwstout.edu/StatStr/statics/Beams/bdsn47.htm

        the neutral axis (an axis running
        through the centroid of beam cross section).

just locating the centroid and
intersecting a line of symmetry

Why locate an "intersecting a line of symmetry"?

The moment of inertia with respect to a line parallel to the axis of
bending will change as you rotate the shape.  Does that matter in your
application?  Are you searching for an orientation to minimize (or
maximize) that moment of inertia?

How does beam flexure theory relate to image processing?

Adam

--
Posted via a free Usenet account fromhttp://www.teranews.com- Hide quoted text -

- Show quoted text -


Im making a character recognition algorithm, and my camera could see
alphabetic characters rotated about any angle.
My inputs to the recognition algorithm are effectively the moments of
inertia of the black pixels that make up the image of the character.
The problem I have is that, like you said, the moments of inertia
change with rotation of the shape. I think recognition accuracy could
be improved by finding a neutral axis and rotating the black pixel are
to line up that axis will improve accuracy.

Sorry the only examples of neutral axes that i have studied in
mechanics about 3 years ago were all for symmetrical beam sections.

Interesting stuff. Thanks for elaborating.

In doing more reading, the statement quoted in my previous post seems
incomplete.

It appears that a particular kind of symmetry is needed for the
neutral axis to coincide with the centroid of a homogeneous and
isotropic shape: "the plane of loading contains an axis of symmetry of
the cross section", according to Cernica's book, _Strength of
Materials_.

A teardrop-shaped beam is symmetrical about only one plane. It seems
that the neutral axis will be through the centroid of the teardrop
only if the vectors for all bending forces are in the plane of
symmetry.

Further, the neutral axis coincides with the centroid of straight
beams -- not curved beams, as shown here:
http://www.roymech.co.uk/Useful_Tables/Beams/Curved_beams.html

Good stuff on unsymmetrical beams here:
http://courses.washington.edu/mengr354/jenkins/notes/chap4.pdf

From what I understand of your description, I still think that the
centroid is the point that you want in dealing with 2-dimensional
shapes.

These might be useful:
http://en.wikipedia.org/wiki/Second_moment_of_area#Parallel_axis_theorem
http://en.wikipedia.org/wiki/Second_moment_of_area#Axes_rotation


Adam

--
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