Accurate segmentation of thalamic nuclei, crucial for understanding their role in healthy cognition and in pathologies, is challenging to achieve on standard T1-weighted (T1w) magnetic resonance imaging (MRI) due to poor image contrast. White-matter-nulled (WMn) MRI sequences improve intrathalamic contrast but are not part of clinical protocols or extant databases. Here, we introduce Histogram-based polynomial synthesis (HIPS), a fast preprocessing step that synthesizes WMn-like image contrast from standard T1w MRI using a polynomial approximation. HIPS was incorporated into our Thalamus Optimized Multi-Atlas Segmentation (THOMAS) pipeline, developed and optimized for WMn MRI. HIPS-THOMAS was compared to a convolutional neural network (CNN)-based segmentation method and THOMAS modified for T1w images (T1w-THOMAS). The robustness and accuracy of the three methods were tested across different image contrasts, scanner manufacturers, and field strength. HIPS-synthesized images improved intra-thalamic contrast and thalamic boundaries, and their segmentations yielded significantly better mean Dice, lower percentage of volume error, and lower standard deviations compared to both the CNN method and T1w-THOMAS. Finally, using THOMAS, HIPS-synthesized images were as effective as WMn images for identifying thalamic nuclei atrophy in alcohol use disorders subjects relative to healthy controls, with a higher area under the ROC curve compared to T1w-THOMAS (0.79 vs 0.73).