Think of the different retinal images formed by an object. Although the retinal images are different, the underlying cause of all those images are the same - the object itself. All that we need to do to identify an object is to associate an image with its cause.
An object is composed of several parts. And those parts are tied to the object in a particular way. When the object moves, it produces a particular motion pattern of the parts. The parts themselves causally influence sub-parts. For example a contour which moves to the left causes a line-segment that is part of it to move in a particular way. A particular sequence of movement of a line segment can be caused by a contour or a corner. A particular sequence of movement of a corner could be due to a table or a chair. The same lower level sequences are reused as part of different high level contexts. Thus the world seems to be naturally organized into a hierarchy of sequences. We believe that the cortex is capturingthis causal hierarchical structure of the world using its own hierarchical cortical structure to solve the invariance problem.
Suppose that a region of cortex which can see only a small patch of any image learns all possible ways a line segment can move when it is part of a corner. Now,whenever one of those sequences of movement of that line seqment occurs, the region would be able to say that although the inputs are changing they all belong to the same corner. It seems plausible that by learning the sequences in the context of their causal influences, the invariance problem can be tackled. By doing that in a hierarchy, the same lower level representations can be shared among multiple higher level objects. Therefore, invariances learned for one set of objects will automatically apply to others.
I will use this chapter to elaborate the above ideas. Towards the end of this section you will find MATLAB source code for the simulations that I did. You can also download a Windows executable version to try out the simulation. You are welcome to try out all the simulations and make your own modifications.