Spoiler
my definition of what qualified as a 'line' turned out to be pretty loose for rule A! i went by the 'sight test' which was: "anything which seems to my eye like a contiguous border", which allowed things like checkerboards or the borders between two images, but i also allowed lines that were several pixels thick. i'm not sure whether this wound up causing major problems or not, but it did create ambiguity in cases like https://i.imgur.com/ikanw9R.png and https://i.imgur.com/W9iUlHX.png , where one border seemed contiguous, but the other didn't.

rule U turned out to be really difficult for me. it became subjective really quick what lines qualified as straight enough to be part of a polygon, whether partially obscured polygons qualified, how rounded a corner had to be before it ceased being a corner, and how to judge very small shapes. in some images, i found very small triangles that made me wonder if i'd missed similar things in other images. if i were to do this again, i would omit this rule or try to tighten the conditions. i apologize if my ambiguity on this rule confused you and i hope that you enjoyed the contest anyway!

honorable mention:

"wait shit i judged this wrong. those polygons don't count because there's the image border."
"wait, isn't there a triangle in there?"
"oh yeah."