  The paper is devoted to integral quantization, a procedure based on
operator-valued measure and resolution of the identity. We insist on covariance
properties in the important case where group representation theory is involved.
We also insist on the inherent probabilistic aspects of this classical-quantum
map. The approach includes and generalizes coherent state quantization. Two
applications based on group representation are carried out. The first one
concerns the Weyl-Heisenberg group and the euclidean plane viewed as the
corresponding phase space. We show that there exists a world of quantizations
which yield the canonical commutation rule and the usual quantum spectrum of
the harmonic oscillator. The second one concerns the affine group of the real
line and gives rise to an interesting regularization of the dilation origin in
the half-plane viewed as the corresponding phase space.
