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To reduce noise within a tag line, unsharpen tag edges in the spatial domain, and amplify the tag-to-background contrast, a 3D energy minimization framework for the enhancement of tagged Cardiac Magnetic Resonance (CMR) images, that is based on first- and second-order learned visual appearance models, is proposed. The first-order appearance modeling uses an adaptive Linear Combination of Discrete Gaussians (LCDG) to accurately approximate the empirical marginal probability distribution of CMR signals for a given sequence, and to separate the tag and background submodels. It is also used to classify the tag lines and the background. The second-order model considers image sequences as samples of a translation- and rotation-invariant 3D Markov-Gibbs Random Field (MGRF), with multiple pairwise voxel interactions. A 3D energy function for this model is built by using the analytical estimation of the spatiotemporal geometry and the Gibbs potentials of interaction. To improve the strain estimation, through enhancement of the tag and background homogeneity and contrast, the given sequence is adjusted using comparisons to the energy minimizer. Special 3D geometric phantoms, motivated by the statistical analysis of the tagged CMR data, have been designed to validate the accuracy of our approach. Experiments with the phantoms and eight in-vivo data sets have confirmed the high accuracy of functional parameter estimation for the enhanced CMR images when using popular spectral techniques, such as spectral Harmonic Phase (HARP).