The aspect of Computer Vision I find the most interesting is recognition of articulated objects, such as animals and humans. This is arguably the most essential part of vision for animals and humans, who are quite good in recognizing other animals, either moving or still. In Computer Vision, however, this problem remains largely unsolved.
Many problems thus arise.
For example, we can observe a horse's head from different view points, so it looks different but we can still recognize it. The cues we use to identify segments include color and texture constancy, spatial consistence and proximity and many others, but if the cues lead to contradicting conclusions, a human is usually able to determine the correct one. To do this, a computer, like a human, would have to use global information. For example, the fact that the surrounding of a segment look like a horse and the position of the segment may lead us to conclude that the segment is a leg. It would be hard, however, to find just a horse leg in an image where the rest of the horse is not present.