how to make a oval to a circle in a 2d wave
Dahair
I have a 2D binary value wave (eg, 256*256 pixels wave storing only 0 and 1). The middle area pixels are 1 and the rest are 0. If we view the wave as an image, there should have a circle shape in the center of the image (eg, center is (128, 128) and radius = 50). However, a wave which has a oval in the middle area (a little off circle shape). My question is that is there a function in Igor that I can "fit" the oval in to a circle shape?
Thanks!
A sample experiment (creation, waves and the image) would be amazingly useful to help you.
HJ
March 25, 2015 at 06:55 am - Permalink
Hey HJ,
Thanks for your reply.
The problems I met is that I have 2 sets of 2D waves. One set is a stack of simulation 2D waves. The first wave of the stack is a binary value wave in which the middle area is 1 and surrounding area is 0. So the image looks like a bright circle sitting in the dark background. The rest of the first stack images have the same bright area(the size and position), but have some patterns inside the circle area. The second set is the same as the first one, but it's from experiment. Because of some non-ideal condition in the experiment, the bright area has a little deformation and is a oval.
Because I want to compare the patterns in the 2 sets of waves layer by layer (the first layer in set A compare the first layer in set B) and pixel by pixel, I need to "fit" the oval to a circle shape.
March 25, 2015 at 09:43 am - Permalink
If that is the case, then if you use NewImage to display the image, it will by default make the graph window be square. But to keep it square when you resize the window, you need to set one of the special axis modes in the Modify Graph dialog. If you set the Height mode to Aspect and enter 1 in the box the graph should remain square when resized. Plan mode will also do what you want, but it's a bit more complicated.
John Weeks
WaveMetrics, Inc.
support@wavemetrics.com
March 25, 2015 at 09:44 am - Permalink
Hey John,
No, the image in both sets, simulation and experiment, are square. Each image in both sets looks like a image of moon or sun. What I want to do is compare the detail patterns of the moon (like the craters) in simulation image with it in experiment image using chi-square calculation.
In simulation, we set it to a circle, but in the experiment, the actual "moon or sun" is not a exact circle (it's a oval now). If the "moon" in the experiment image is a oval, the edge area will have large difference compared to simulation which would dominate the chi-square calculation. Only when we make the moon in experiment image the same shape and size as it is in the simulation image, the small detail patterns on the moon dominate chi-square calculation.
So what I want to do is just use some mathematical method make the oval moon in experiment to a circle.
Thanks
March 25, 2015 at 10:02 am - Permalink
Also because there is a stack of experiment images, once I find how to "fit" the first image's moon to a circle, I want to perform the same operation (the same parameters settings, so in other experiment images, each corresponding pixel has the same movement vector as the first experiment image) to the rest of images in experiment set.
March 25, 2015 at 10:09 am - Permalink
I don't fully understand your experiment but I am attaching a simple pxp illustrating a "best" fit of a circle to a 2D ellipse. It is shown for an upright 2D test ellipse wave, but ought to work for an arbitrary orientation.
March 25, 2015 at 10:37 am - Permalink
For different orientations you might have to perform a transformation according to the principal axis theorem. (I only did this on paper so far, so my knowledge in Igor of this issue is limited.)
A small sample experiment illustrating your problem would be really helpful.
HJ
March 25, 2015 at 10:58 am - Permalink
Hi Chinn,
Thank you for your example. I attached an example to help you understand my problem. In the example, there are 4 2D waves. e0 and e1 are from experiment, s0 and s1 are from simulation. These images are from diffraction in transmission electron microscopy. e0 and s0 are the condition with out sample so there is no patterns in the middle bright area and the edge is not blurred. e1 and s1 has sample so the edge is not clear to decide.
What I want to do is compare the patterns in the bright area in e1 and s1 by calculating chi-square.
In all 4 images, center bright area should be a circle, but in experiment (e0 and e1) it is not a circle because of aperture's shape. This prevent me from chi-square comparison. So I want to applied a kind of transform to make the bright area in e0 to a circle shape. Also I want to applied the same transform on e1 (I mean use the transform parameter got from e0's transform) so that it can imitate the circle aperture condition. In this way, I can compare patterns in the middle bright area in e1 and s1 pixel by pixel and calculate the chi-square between e1 and s1.
Thanks.
March 25, 2015 at 11:50 am - Permalink
Hi HJ,
I have post an example and explanation above. Please have a look and thanks for your help!
March 25, 2015 at 11:52 am - Permalink
Hi John,
I have post an example and some explanation above. Please have a look and thanks for your help!
March 25, 2015 at 11:53 am - Permalink
A.G.
WaveMetrics, Inc.
March 25, 2015 at 12:00 pm - Permalink
As Igor mentioned ImageAnalyzeParticles is the way to go. Internally it probably does the transformation with the principal axis theorem (since the result is called M_rawMoments).
HJ
March 25, 2015 at 02:25 pm - Permalink