How to balance doing a literature review and just solving the problem yourself
Before trying to solve the problem yourself, it is always a good idea to search the literature, to see if somebody else has already solved it, or at least has worked on something similar.  This is especially true in computer vision.  A good strategy is to allocate some reasonable amount of time to read papers. If you find nothing useful in that time, then you give up and try to come up with your own solution.

Yes the number of computer vision papers published every year is staggering. So a good strategy is to try to keep up with a few top conferences, such as CVPR, ICCV, ECCV, and BMVC, and a few top journals, such as PAMI and IJCV.

Also, it is good to find researchers and research groups who are working in your particular area of computer vision, and follow their progress, and the papers which cite them.