Discussion
When looking at our visual environment, we are not only aware of the rich details of the 3-D visual scene, but we also summarize the details into a simple description of “what is where,” which provides the crucial information of a visual scene. Therefore, we can formulate the problem of vision in terms of the following three variables. (1) Image: a 2-D matrix (or a pair of matrix sequences). (2) Details: a representation of the 3-D scene in full detail. (3) Summary: the abstract description of “what is where.” Of course, summary and details are relative concepts, and the two variables Details and Summary should be understood as the bottom and the top of a pyramid of increasingly abstract layers of visual concepts. We call this pyramid the “scene description.” For instance, for a scenery image, the Summary may consist of abstract concepts such as river, trees, and their overall shapes, and Details may consist of concepts like water ripples and waves, tree leaves, and branches, and their shapes and locations. The meaning of the Summary can be de ned in terms of how the details look and how they are composed together. Mathematically, this amounts to a generative model P (Details j Summary), which decomposes the complexity in Details into deterministic redundancy