In magnetic resonance imaging (MRI), accuracy and precision with which brain structures may be quantified are frequently affected by the partial volume (PV) effect. PV is due to the limited spatial resolution of MRI compared to the size of anatomical structures. Accurate classification of mixed voxels and correct estimation of the proportion of each pure tissue (fractional content) may help to increase the precision of cortical thickness estimation in regions where this measure is particularly difficult, such as deep sulci. The contribution of this work is twofold: on the one hand, we propose a new method to label voxels and compute tissue fractional content, integrating a mechanism for detecting sulci with topology preserving operators. On the other hand, we improve the computation of the fractional content of mixed voxels using local estimation of pure tissue intensity means. Accuracy and precision were assessed using simulated and real MR data and comparison with other existing approaches demonstrated the benefits of our method. Significant improvements in gray matter (GM) classification and cortical thickness estimation were brought by the topology correction. The fractional content root mean squared error diminished by 6.3% (p<0.01) on simulated data. The reproducibility error decreased by 8.8% (p<0.001) and the Jaccard similarity measure increased by 3.5% on real data. Furthermore, compared with manually guided expert segmentations, the similarity measure was improved by 12.0% (p<0.001). Thickness estimation with the proposed method showed a higher reproducibility compared with the measure performed after partial volume classification using other methods.