User:TheLarry/Notebook/Larrys Notebook/2009/11/16

Generating Data

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Making the Microtubule Now that i have the Airy Disc i have to place them on the microtubule. From yesterday Koch suggested that i randomly try to put one every 8/13ths of a nanometer along the microtubule which is just a line for right now which makes sense since it is so much smaller than a pixel width. Anyway that was easy. I just roll a dice and if the dice comes out lower than the concentration percentage then i place the dot there if not then there is no dot. The part i have a question with now is that koch said this yesterday, "A kind of first thing to do would be to give each emitter a PSF that you defined above ... with a random amplitude, but no randomness in terms of pixel intensity within the PSF." I am not 100% following him. There is an [math]\displaystyle{ I_0 }[/math] in the Airy disc which (I thought would be chosen randomly by a Gaussian or Poisson distribution. I thought Poisson since the intensity is actually the collection of photons by camera so that is a counting thing.). I just don't know what Koch meant by no randomness in terms of pixel intensity. That I_0 relates to the pixel intensity so i don't know how you can have a random amplitude but not random pixel intensity. Unless he means that it follows the Airy Disc. But for right now i'll go with choosing a random amplitude, [math]\displaystyle{ I_0 }[/math], by either a Gaussian or Poisson. I don't think it matters because at high number of collected photons the Poisson will look like a Gaussian, but I think I understand why it will look like Poisson for lower numbers so i feel comfortable with it. Koch answered my question. I'll roll the dice on the intensity, I_0, and it will follow a Gaussian shape. I don't know what kind of standard deviation to use for it yet, and I am not sure where that information will come from but i'll get it working and figure that out afterwards. This .vi goes very slow. I can make this considerably faster if i limit the array size. Right now i am calculating the Airy Disc over the entire image which is a waste of time since 99% of it is black. I wanna see this work then i'll make it faster. This all sets up the first image. But i think the I_0 should change from frame to frame since it depends on the photon capture. So that can be random. This could possibly be the Poisson Distribution. The Gaussian will set the I_0 but how bright it actually is in each frame could be Poisson. I gotta ask Koch about this, and if i can't i can try it out if i get that far and then take it out of the program if it is wrong. Here is my first simulated microtubule. It has an I_0 mean of 1000 and a standard deviation of 100. It should be about 50 pixels long Above is my first simulated microtubule. My I_0 Gaussian is a bit off. Too bright, but it look pretty good other than that. I have some things to play around with still. But once I get this first image right it should be fun making the movie. Improvements Make it faster by not calculating every pixel for the entire image Get better I_0 Gaussian information I gotta figure out if I do these intensities to very from frame to frame. I think i do since that'll make it flicker a bit. It will have a different standard deviation than what i am doing here since this is like finding the maximum intensity that each dot can have. and then i'll find the intensity of each dot in each frame. shouldn't be that bad and it sounds right. OK I made it faster. It's a lot better now. You can select how big of a rectangle to put around each dot so you don't have to calculate every pixel for every dot. a 10 pixel radius is more than enough. OK so let me reiterate: what i think i am calculating is the highest intensity each one of these dots can take. From here i can run through each frame of my "movie" and adjust the intensity of each pixel based on a Gaussian (or Poisson). I think this will make the flickering more apparent. OK I added the Poisson part now--so i'll show you what i mean SJK 19:18, 16 November 2009 (EST) 19:18, 16 November 2009 (EST) That looks pretty cool! And interesting that it's splotchier than I thought it would be, but probably not as splotchy as the real data? Very cool. I don't get the difference between Gaussian and Poisson image, wouldn't they look essentially the same? Not a big deal, you can explain to me later. So the guy on the left is from the Gaussian. It found a random intensity for each dot placed on the microtubule. the guy on the right took those intensities and found a random Poisson distributed intensity for each one of those dots. It looks a bit different and if i take this for the first frame and do this for each frame after this i should have some flickering like i do in the movies. /Quantitative Comparison of Algorithms for Tracking Single Fluorescent Particles