  We present a heuristic derivation of Born's rule and unitary transforms in
Quantum Mechanics, from a simple set of axioms built upon a physical
phenomenology of quantization. This approach naturally leads to the usual
quantum formalism, within a new realistic conceptual framework that is
discussed in details. Physically, the structure of Quantum Mechanics appears as
a result of the interplay between the quantized number of "modalities"
accessible to a quantum system, and the continuum of "contexts" that are
required to define these modalities. Mathematically, the Hilbert space
structure appears as a consequence of a specific "extra-contextuality" of
modalities, closely related to the hypothesis of Gleason's theorem, and
consistent with its conclusions.
