A new model for the spatial singularities component of the texture field and parameter estimation and synthesis procedures are presented. The spatial singularities field includes the local-structural components of the texture. The field is modeled by a 2-D compound Poisson-cliques model, after testing the fitness of the proposed model to the detected singularities field. According to this model the spatial singularities field is a 2-D point process where each of the events is a clique. The test of fit is based on a discrete version of the Kolmogorov-Smirnov test. In the analysis procedure the intensity of the 2-D point process is estimated, as well as the empirical distribution function of the clique occurrences. These parameters are then used to synthesize the singularities field.