Raw image intensities are a poor surrogate for similarity across images in correspondence problems. Further, while auxiliary segmentation labels can provide semantic identification and improve matching, they can assign only coarse identities to fine-grained anatomy and often cover only a subset of structures, particularly in whole-body settings. We present an approach that instead establishes correspondence using complementary representations of anatomy and demonstrate its utility for longitudinal whole-body PET/CT registration in the Learn2Reg 2026 PSMAReg Challenge. Our 3D foundation model, anatomix, is used to derive fine-grained, per-voxel semantic representations that are consistent across volumes, and we further employ off-the-shelf segmentation models to obtain coarse anatomical identities. Together, these representations drive a GPU-accelerated iterative registration solver (FireANTs) in a hybrid multistage framework: the first stage estimates alignment from dense multi-channel features, after which a second refines the deformation using both anatomix- and segmentation-based losses. Lastly, because registration should not introduce non-biological tumor volume changes across time, we develop lesion-specific component-wise volume preservation schemes. Without any task-specific training, our system won first place in the PSMAReg Challenge leaderboard. Code and interactive visualizations are available at http://www.neeldey.com/reps-for-reg.

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