In this paper, we present a volume-based mucosa-based polyp candidate determination scheme for automatic polyp detection in computed colonography. Different from most of the existing computer-aided detection (CAD) methods where mucosa layer is a one-layer surface, a thick mucosa of 3-5 voxels wide fully reflecting partial volume effect is intentionally extracted, which excludes the direct applications of the traditional geometrical features. In order to address this dilemma, fast marching-based adaptive gradient/curvature and weighted integral curvature along normal directions (WICND) are developed for volume-based mucosa. In doing so, polyp candidates are optimally determined by computing and clustering these fast marching-based adaptive geometrical features. By testing on 52 patients datasets in which 26 patients were found with polyps of size 4-22 mm, both the locations and number of polyp candidates detected by WICND and previously developed linear integral curvature (LIC) were compared. The results were promising that WICND outperformed LIC mainly in two aspects: (1) the number of detected false positives was reduced from 706 to 132 on average, which significantly released our burden of machine learning in the feature space, and (2) both the sensitivity and accuracy of polyp detection have been slightly improved, especially for those polyps smaller than 5mm.