Some authors solved this problem with very good time and very small memory. But if we store input data without compressing it is necessary near 1Mb. Maybe there exist solution without storing input at all?
Who can help me to understand how it is possible?

You just calculate frequencies of appearing black cells for every row and column. This requires only ~10Kb of memory, and at the same time allows to recognize the figure

Thank you for your answer. But I still don't know how to use frequencies for recognition figures...

Just think how density functions of projection of every of these figures look like. Circle recognition is easy even by one projection. For some bad cases of squares and triangles you need both projections.

wow! beautifull idea :)
My solution use symmetric of figures.

In fact, better solution than Sergei said is possible. I think if done in assembly under MS-DOS, solution could use less than half of kilobyte of memory.

I save only 8 points which enough for solution

Moment of inertia ;)