Let B be a twisted Poisson manifold with a fixed tropical affine structure. In this talk, we will discuss the classification of almost symplectically complete isotropic realizations (ASCIRs) over B in the spirit of Dazord-Delzant. We will construct a product among ASCIRs in analogy with tensor product of line bundles, thereby introducing the notion of the Picard group of B. We will give descriptions of the Picard group and the corresponding 'Neron-Severi group' using certain sheaf cohomology groups.