TABLE OF CONTENTS We propose to describe and comment on a small part of David Marr's work. We limit our discussion to Marr's analysis of the "low-level" processing of luminous information by the retinal cells. Marr suggested that the coding of this luminous information was based on the zero-crossings of an operator that is now called a wavelet transform. This hypothesis leads us to state the famous "Marr conjecture" and then to state its precise form as conjectured by Mallat. This precise form yields a remarkably effective algorithm. We will see, however, that Mallat's conjecture is not generally correct, and this poses some fascinating new problems.
Marr's book, Vision, A Computational Investigation into the Human Representation and Processing of Visual Information [198], appeared in 1982. Stylistically it is reminiscent of Descartes's Discours de la m thode. Exactly as Descartes did, Marr takes us into his confidence and speaks to us as if we were a friend or colleague from his laboratory. Marr confides in us his intellectual progress and tells us about his doubts, his hopes, and his enthusiasms. He gives a lively description of the theories he has struggled with and rejected, and he explains his own research with an infectious enthusiasm.
We recall that the goal of Marvin Minsky's group at the Massachusetts Institute of Technology (MIT) artificial intelligence laboratory was to solve the problem of artificial vision for robots. The challenge was to construct a robot endowed with a perception of its environment that enabled it...
