Deep implicit functions (DIFs) have emerged as a potent and articulate means of representing 3D shapes. However, methods modeling object categories or non-rigid entities have mainly focused on single-object scenarios. In this work, we propose MODIF, a multi-object deep implicit function that jointly learns the deformation fields and instance-specific latent codes for multiple objects at once. Our emphasis is on non-rigid, non-interpenetrating entities such as organs. To effectively capture the interrelation between these entities and ensure precise, collision-free representations, our approach facilitates signaling between category-specific fields to adequately rectify shapes. We also introduce novel inter-object supervision: an attraction-repulsion loss is formulated to refine contact regions between objects. Our approach is demonstrated on various medical benchmarks, involving modeling different groups of intricate anatomical entities. Experimental results illustrate that our model can proficiently learn the shape representation of each organ and their relations to others, to the point that shapes missing from unseen instances can be consistently recovered by our method. Finally, MODIF can also propagate semantic information throughout the population via accurate point correspondences
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