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Accurate 3D models of the human heart require not only correct outer surfacesbut also realistic inner structures, such as the ventricles, atria, andmyocardial layers. Approaches relying on implicit surfaces, such as signeddistance functions (SDFs), are primarily designed for single watertightsurfaces, making them ill-suited for multi-layered anatomical structures. Theyoften produce gaps or overlaps in shared boundaries. Unsigned distancefunctions (UDFs) can model non-watertight geometries but are harder tooptimize, while voxel-based methods are limited in resolution and struggle toproduce smooth, anatomically realistic surfaces. We introduce apairwise-constrained SDF approach that models the heart as a set ofinterdependent SDFs, each representing a distinct anatomical component. Byenforcing proper contact between adjacent SDFs, we ensure that they formanatomically correct shared walls, preserving the internal structure of theheart and preventing overlaps, or unwanted gaps. Our method significantlyimproves inner structure accuracy over single-SDF, UDF-based, voxel-based, andsegmentation-based reconstructions. We further demonstrate its generalizabilityby applying it to a vertebrae dataset, preventing unwanted contact betweenstructures.

Pairwise-Constrained Implicit Functions for 3D Human Heart Modelling