Accurate reconstruction of the inner and outer cortical surfaces of the human cerebrum is a critical objective for a wide variety of neuroimaging analysis purposes, including visualization, morphometry, and brain mapping. The Anatomic Segmentation using Proximity (ASP) algorithm, previously developed by our group, provides a topology-preserving cortical surface deformation method that has been extensively used for the aforementioned purposes. However, constraints in the algorithm to ensure topology preservation occasionally produce incorrect thickness measurements due to a restriction in the range of allowable distances between the gray and white matter surfaces. This problem is particularly prominent in pediatric brain images with tightly folded gyri. This paper presents a novel method for improving the conventional ASP algorithm by making use of partial volume information through probabilistic classification in order to allow for topology preservation across a less restricted range of cortical thickness values. The new algorithm also corrects the classification of the insular cortex by masking out subcortical tissues. For 70 pediatric brains, validation experiments for the modified algorithm, Constrained Laplacian ASP (CLASP), were performed by three methods: (i) volume matching between surface-masked gray matter (GM) and conventional tissue-classified GM, (ii) surface matching between simulated and CLASP-extracted surfaces, and (iii) repeatability of the surface reconstruction among 16 MRI scans of the same subject. In the volume-based evaluation, the volume enclosed by the CLASP WM and GM surfaces matched the classified GM volume 13% more accurately than using conventional ASP. In the surface-based evaluation, using synthesized thick cortex, the average difference between simulated and extracted surfaces was 4.6 +/- 1.4 mm for conventional ASP and 0.5 +/- 0.4 mm for CLASP. In a repeatability study, CLASP produced a 30% lower RMS error for the GM surface and a 8% lower RMS error for the WM surface compared with ASP.