Recent advances in deep learning have greatly improved the ability to generate analysis models from medical images. In particular, great attention is focused on quickly generating models of the left ventricle from cardiac magnetic resonance imaging (cMRI) to improve the diagnosis and prognosis of millions of patients. However, even state-of-the-art frameworks present challenges, such as discontinuities of the cardiac tissue and excessive jaggedness along the myocardial walls. These geometrical features are often anatomically incorrect and may lead to unrealistic results once the geometrical models are employed in computational analyses. In this research, we propose an end-to-end pipeline for a subject-specific model of the heart's left ventricle from Cine cMRI. Our novel pipeline incorporates the uncertainty originating from the segmentation methods in the estimation of cardiac indices, such as ejection fraction, myocardial volume changes, and global radial and longitudinal strain, during the cardiac cycle. First, we propose an anatomically-guided deep learning model to overcome the common segmentation challenges while preserving the advantages of state-of-the-art frameworks, such as computational efficiency, robustness, and abstraction capabilities. Our anatomically-guided neural networks include a B-spline head, which acts as a regularization layer during training. In addition, the introduction of the B-spline head contributes to achieving a robust uncertainty quantification of the left ventricle inner and outer walls. We validate our approach using human short-axis (SA) cMRI slices and later apply transfer learning to verify its generalization capabilities in swine long-axis (LA) cMRI slices. Finally, we use the SA and LA contours to build a Gaussian Process (GP) model to create inner and outer walls 3D surfaces, which are then used to compute global indices of cardiac functions. Our results show that the proposed pipeline generates anatomically consistent geometries while also providing a robust tool for quantifying uncertainty in the geometry and the derived cardiac indices.