  The puzzle of computer vision might find new challenging solutions when we
realize that most successful methods are working at image level, which is
remarkably more difficult than processing directly visual streams, just as
happens in nature. In this paper, we claim that their processing naturally
leads to formulate the motion invariance principle, which enables the
construction of a new theory of visual learning based on convolutional
features. The theory addresses a number of intriguing questions that arise in
natural vision, and offers a well-posed computational scheme for the discovery
of convolutional filters over the retina. They are driven by the Euler-Lagrange
differential equations derived from the principle of least cognitive action,
that parallels laws of mechanics. Unlike traditional convolutional networks,
which need massive supervision, the proposed theory offers a truly new scenario
in which feature learning takes place by unsupervised processing of video
signals. An experimental report of the theory is presented where we show that
features extracted under motion invariance yield an improvement that can be
assessed by measuring information-based indexes.
