Left ventricular ejection fraction (LVEF) is the most important clinical parameter of cardiovascular function. The accuracy in estimating this parameter is highly dependent upon the precise segmentation of the left ventricle (LV) structure at the end diastole and systole phases. Therefore, it is crucial to develop robust algorithms for the precise segmentation of the heart structure during different phases. Methodology: In this work, an improved 3D UNet model is introduced to segment the myocardium and LV, while excluding papillary muscles, as per the recommendation of the Society for Cardiovascular Magnetic Resonance. For the practical testing of the proposed framework, a total of 8,400 cardiac MRI images were collected and analysed from the military hospital in Tunis (HMPIT), as well as the popular ACDC public dataset. As performance metrics, we used the Dice coefficient and the F1 score for validation/testing of the LV and the myocardium segmentation. Results: The data was split into 70%, 10%, and 20% for training, validation, and testing, respectively. It is worth noting that the proposed segmentation model was tested across three axis views: basal, medio basal and apical at two different cardiac phases: end diastole and end systole instances. The experimental results showed a Dice index of 0.965 and 0.945, and an F1 score of 0.801 and 0.799, at the end diastolic and systolic phases, respectively. Additionally, clinical evaluation outcomes revealed a significant difference in the LVEF and other clinical parameters when the papillary muscles were included or excluded.

Segmentation has emerged as a fundamental field of computer vision and natural language processing, which assigns a label to every pixel/feature to extract regions of interest from an image/text. To evaluate the performance of segmentation, the Dice and IoU metrics are used to measure the degree of overlap between the ground truth and the predicted segmentation. In this paper, we establish a theoretical foundation of segmentation with respect to the Dice/IoU metrics, including the Bayes rule and Dice-/IoU-calibration, analogous to classification-calibration or Fisher consistency in classification. We prove that the existing thresholding-based framework with most operating losses are not consistent with respect to the Dice/IoU metrics, and thus may lead to a suboptimal solution. To address this pitfall, we propose a novel consistent ranking-based framework, namely RankDice/RankIoU, inspired by plug-in rules of the Bayes segmentation rule. Three numerical algorithms with GPU parallel execution are developed to implement the proposed framework in large-scale and high-dimensional segmentation. We study statistical properties of the proposed framework. We show it is Dice-/IoU-calibrated, and its excess risk bounds and the rate of convergence are also provided. The numerical effectiveness of RankDice/mRankDice is demonstrated in various simulated examples and Fine-annotated CityScapes, Pascal VOC and Kvasir-SEG datasets with state-of-the-art deep learning architectures.