We propose the joint value-driven mathematical morphology framework, which extends conventional morphological operators [5,6]. This framework incorporates joint functions to establish relationships between input functions. A key feature of this model is the regulation of particle adhesion probability, implemented using Alias sampling [7] to optimize computational efficiency. While existing morphological simulation algorithm [1] provides control over the overall compactness of the final aggregation, it does not account for the specific relationships between individual particles. Additionally, its performance can be slower when handling arbitrarily shaped objects, necessitating the use of spherical particle representations for more efficient calculations. Our new model facilitates highly customizable simulations by enabling precise control over the bonding probabilities between particles, accommodating particles of arbitrary shape and size. This innovative methodology enhances the ability to replicate real-world scenarios in colloidal systems accurately. One targeted application is heterogeneous catalyst [2,3,4], more specifically the impregnation process of MoS₂ sheets onto a gamma-alumina support. By carefully adjusting the bonding probabilities between sheets and between sheets and the support, this research offers valuable insights into the precise control and optimization of the porous network in heterogeneous catalysts. These digital twins of microstructure guide the design of materials with tailored transport properties and performance characteristics.