During the last two decades, MRI has been increasingly used for providing valuable quantitative information about spinal cord morphometry, such as quantification of the spinal cord atrophy in various diseases. However, despite the significant improvement of MR sequences adapted to the spinal cord, automatic image processing tools for spinal cord MRI data are not yet as developed as for the brain. There is nonetheless great interest in fully automatic and fast processing methods to be able to propose quantitative analysis pipelines on large datasets without user bias. The first step of most of these analysis pipelines is to detect the spinal cord, which is challenging to achieve automatically across the broad range of MRI contrasts, field of view, resolutions and pathologies. In this paper, a fully automated, robust and fast method for detecting the spinal cord centerline on MRI volumes is introduced. The algorithm uses a global optimization scheme that attempts to strike a balance between a probabilistic localization map of the spinal cord center point and the overall spatial consistency of the spinal cord centerline (i.e. the rostro-caudal continuity of the spinal cord). Additionally, a new post-processing feature, which aims to automatically split brain and spine regions is introduced, to be able to detect a consistent spinal cord centerline, independently from the field of view. We present data on the validation of the proposed algorithm, known as "OptiC", from a large dataset involving 20 centers, 4 contrasts (T-weighted n = 287, T-weighted n = 120, T-weighted n = 307, diffusion-weighted n = 90), 501 subjects including 173 patients with a variety of neurologic diseases. Validation involved the gold-standard centerline coverage, the mean square error between the true and predicted centerlines and the ability to accurately separate brain and spine regions. Overall, OptiC was able to cover 98.77% of the gold-standard centerline, with a mean square error of 1.02 mm. OptiC achieved superior results compared to a state-of-the-art spinal cord localization technique based on the Hough transform, especially on pathological cases with an averaged mean square error of 1.08 mm vs. 13.16 mm (Wilcoxon signed-rank test p-value < .01). Images containing brain regions were identified with a 99% precision, on which brain and spine regions were separated with a distance error of 9.37 mm compared to ground-truth. Validation results on a challenging dataset suggest that OptiC could reliably be used for subsequent quantitative analyses tasks, opening the door to more robust analysis on pathological cases.