Randy Williams, an artist and professor, suggests trying "aesthetic meditation"—looking at objects with a concentrated focus. Experience your own visceral response to the object and at the same time, refrain from naming, categorizing, or describing it. In other words, stay out of your left brain for a few minutes! By not comparing the object to something else in your internal dialogue, you maximize direct experience. Just let the thoughts come in and go right out again, while "feeling into" the object.
Another technique Williams uses is to write for a maximum of 10 minutes about a recent event. Then distill the writing into 12 essential words, then six, then 3, and finally, one. This final word is the true essence of the experience. I suspect that a similar sort of exercise could be done with abstract drawings that distill the essence of feelings.