Random points from an image using a BernoulliDistribution

Question

I am a Mathematica newbie. I need to sample random points from an image which I have stored in a variable img as:

image=Import["ExampleData/ocelot.jpg"]    
img = ImageData[image]

Can you guys suggest how I can use a BernoulliDistribution to sample points from the image using Flatten, Map, RandomVariate, Partition and Image functions?

I know a similar problem was discussed here but the solutions there are very convoluted and I am not able to follow them. Thanks a lot for the help and very sorry if this seems like a duplicate post but I have spent the whole evening banging my head over the link to the post above but am not able to reproduce the same with the above functions. Thanks again!

Answer 1

I'm assuming you want to vary the Bernoulli parameter p depending on the pixel grayscale value. Darker areas of the image are more likely to generate a black pixel and lighter areas more likely to be white.

img = Import["ExampleData/ocelot.jpg"];
dat = ImageData[img];
result = Image[
  Map[RandomVariate[BernoulliDistribution[#]] &, dat, {2}]]

The positions where a 1 appears are given by:

PixelValuePositions[result, 1]

The sum of many images averaged over time converges to the grayscale image in the limit.

img = Import["ExampleData/ocelot.jpg"];
dat = ImageData[img];
ListAnimate[
 ImageAdjust[Image[#]] & /@ 
  Accumulate[
   ParallelTable[
    Map[RandomVariate[BernoulliDistribution[#]] &, dat, {2}], {30}]]
 ]