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Deep implicit functions (DIFs) have emerged as a potent and articulate meansof representing 3D shapes. However, methods modeling object categories ornon-rigid entities have mainly focused on single-object scenarios. In thiswork, we propose MODIF, a multi-object deep implicit function that jointlylearns the deformation fields and instance-specific latent codes for multipleobjects at once. Our emphasis is on non-rigid, non-interpenetrating entitiessuch as organs. To effectively capture the interrelation between these entitiesand ensure precise, collision-free representations, our approach facilitatessignaling between category-specific fields to adequately rectify shapes. Wealso introduce novel inter-object supervision: an attraction-repulsion loss isformulated to refine contact regions between objects. Our approach isdemonstrated on various medical benchmarks, involving modeling different groupsof intricate anatomical entities. Experimental results illustrate that ourmodel can proficiently learn the shape representation of each organ and theirrelations to others, to the point that shapes missing from unseen instances canbe consistently recovered by our method. Finally, MODIF can also propagatesemantic information throughout the population via accurate pointcorrespondences

Implicit Modeling of Non-rigid Objects with Cross-Category Signals