Structured regularization allows machine learning models to consider spatial relationships among parameters, leading to results that generalize better and are more interpretable compared to norm penalties. In this study, we evaluated a novel structured regularization method that incorporates approximate morphology operators defined using harmonic mean-based fW-filters. We extended this method to multiclass classification and conducted experiments aimed at classifying magnetic resonance images (MRI) of subjects into four stages of Alzheimer’s disease progression. The experimental results demonstrate that the novel structured regularization method not only performs better than standard sparse and structured regularization methods in terms of prediction accuracy (ACC), F1 scores, and the area under the receiver operating characteristic curve (AUC), but also produces interpretable coefficient maps.