Quantifying dynamic strain fields from time-resolved volumetric medical imaging and microscopy stacks is a pressing need for radiology and mechanobiology. A critical limitation of all existing techniques is regularization: because these volumetric images are inherently noisy, the current strain mapping techniques must impose either displacement regularization and smoothing that sacrifices spatial resolution, or material property assumptions that presuppose a material model, as in hyperelastic warping. Here, we present, validate, and apply the first three-dimensional (3D) method for estimating mechanical strain directly from raw 3D image stacks without either regularization or assumptions about material behavior. We apply the method to high-frequency ultrasound images of mouse hearts to diagnose myocardial infarction. We also apply the method to present the first ever in vivo quantification of elevated strain fields in the heart wall associated with the insertion of the chordae tendinae. The method shows promise for broad application to dynamic medical imaging modalities, including high-frequency ultrasound, tagged magnetic resonance imaging, and confocal fluorescence microscopy.