The geometry of an object is inferred from values of the signed distance sampled on a uniform grid to efficiently model objects based on data derived from imaging technology that is now ubiquitous in medical diagnostics. Techniques for automated segmentation convert imaging intensity to a signed distance function (SDF), and a voxel structure imposes a uniform sampling grid. Essential properties of the SDF are used to construct upper and lower bounds on the allowed variation in signed distance in 1, 2, and 3 (or more) dimensions. The bounds are combined to produce interval-valued extensions of the SDF, including a tight global extension and more computationally efficient local bounds that provide useful criteria for root exclusion/isolation, enabling modeling of the objects and other applications.