Thursday, April 08, 2010


oh man. i haven't learned anything today, except that there's only so far you can take a visual simulation before it breaks. so, i've been measuring thresholds for a simulated observer at different spatial frequencies, for content within photographs which has been thresholded depending on a trial-to-trial staircase. it works pretty well for the images themselves. the original image gets compared with the image containing a thresholded band, and the observer is able to converge at a measure of the threshold over several hundred trials, similar to a human observer.

what i do is this: the original image gets filtered at the frequency in question, and the filtered image (the output of the filter) is thresholded and added back into the original image minus the filtered image. so, we actually have the original image minus the subthreshold content within the filter. if the threshold is zero, these two images are identical, i.e. they are whole, unfiltered photographs. this is the experiment as i originally ran it on myself, trying to find the just-detectable threshold (the threshold-threshold). to do the experiment simulation, the thresholded image then gets filtered again, meaning that the filter picks up the thresholded content along with residual off-frequency content. this is the only reasonable way to get the test content, since 1) that off-frequency content is there in the image and would be seen by the filter, and thus can't be ignored, and 2) the filtered band contains harmonics which wouldn't be seen by the filter.

naturally, i eventually decided to do the same experiment without the complete image; i.e., just measure threshold-thresholds for the content within the filter. i thought this would be straightforward - i just use the filtered image as the 'original', and the thresholded filtered image as the 'test'. but then, i thought, ah, almost screwed up there: the thresholded filtered image should be filtered again, just like in the original experiment. so, you can see the problem. the original content is lifted straight out of the source image, while the thresholded content gets lifted out of the source image and again out of the thresholded image, which means it will be multiplied twice by the filter. so, even if the threshold is zero, the test and original images will be different.

this is a problem. in fact, it must also be a problem in the original experiment. but, the test and original images in the original experiment are the same when the threshold is zero - i assume this is because the off-frequency content amounts to the difference between the filtered and double-filtered content, and adding the filtered content back into the image basically restores the lost content.

i need to think about this.

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