Myocardial infarction (MI) is among the leading causes of death in the United States. It is imperative to identify and characterize MIs for timely delivery of life-saving medical interventions. Cardiac electrical activity propagates in space and evolves over time. Traditional works focus on the analysis of time-domain ECG (e.g., 12-lead ECG) on the body surface for the detection of MIs, but tend to overlook spatiotemporal dynamics in the heart. Body surface potential mappings (BSPMs) provide high-resolution distribution of electric potentials over the entire torso, and therefore provide richer information than 12-lead ECG. However, BSPM are available on the body surface. Clinicians are in need of a closer look of the electric potentials in the heart to investigate cardiac pathology and optimize treatment strategies. In this paper, we applied the method of spatiotemporal inverse ECG (ST-iECG) modeling to map electrical potentials from the body surface to the heart, and then characterize the location and extent of MIs by investigating the reconstructed heart-surface electrograms. First, we investigate the impact of mesh resolution on the inverse ECG modeling. Second, we solve the inverse ECG problem and reconstruct heart-surface electrograms using the ST-iECG model. Finally, we propose a wavelet-clustering method to investigate the pathological behaviors of heart-surface electrograms, and thereby characterize the extent and location of MIs. The proposed methodology is evaluated and validated with real data of MIs from human subjects. Experimental results show that negative QRS waves in heart-surface electrograms indicate potential regions of MI, and the proposed ST-iECG model yields superior characterization results of MIs on the heart surface over existing methods.