Colonic polyps are growths on the inner wall of the colon. They appear like elliptical protrusions which can be detected by curvature-derived shape discriminators. For reasons of computation efficiency, much of the past work in computer-aided diagnostic CT colonography adopted kernel-based convolution methods in curvature estimation. However, kernel methods can yield erroneous results at thin structures where the gradient diminishes. In this paper, we investigate three surface patch fitting methods: Cubic B-spline, paraboloid, and quadratic polynomials. This "patch" approach is based on the fact that a surface can be re-oriented such that it can be approximated by a bivariate function locally. These patch methods are evaluated by synthesized data with various orientations and sampling sizes. We find that the cubic spline method performs best regardless of large orientation variances. Cubic spline and quadratic polynomial methods perform equally well for large samples while the latter performs better for small ones. Based on the performance evaluation, we propose a new, two-stage curvature estimation method. The cubic spline fitting is performed first for its insensitivity to orientation. If the spline fitting errs by more than a preset value (indicating high surface tortuosity), a small data sample is fitted by a quadratic function. The evaluation is performed on 29 patients (58 data sets). With 88.7% sensitivity, the average number of false positives per data set is reduced by 44.5% from 33.5 (kernel method) to 18.6 (new method).