There has been an artist named Giuseppe Arcimboldo from the 16th century who drew portraits of people made out of fruits, vegetables or books. If you look at that picture, you will always recognize both, the face and the vegetables. However, the split brain patient will only recognize that there is a face if he covers his right eye. This is due to ability of processing emotional data from the right side of the brain. An individual is able to express feelings with its face and the observer is able to determine the feeling based on the mimic expression. For that reason facial expressions are processed by the right hemisphere, the emotional part of the brain. In the case of the split brain patient, you can keep asking the patient whether he recognized the vegetables and he will always deny. But let’s assume the opposite is the case. The patient covers his left eye and has a look at the drawing with his right eye. The information received by the right eye is now processed in the left brain hemisphere (the analytical part). Accordingly the patient won’t recognize the face anymore but the vegetables instead. So now he is more focused on the details of the picture and the overall meaning gets lost. You can even ask the patient to look closer in order to see the face; he just won’t recognize it since the received information by the right eye is only processed by the left brain.
But usually the brain hemispheres are connected to each other which makes it on the one hand hard to understand how these patient aren’t able to recognize those things and on the other hand we now see that due to the connection of the two brain hemispheres, we always recognize the whole picture and not just one single aspect of it.