  Anatomical structures such as the hippocampus, liver, and bones can be
analyzed as orientable, closed surfaces. This permits the computation of
volume, surface area, mean curvature, Gaussian curvature, and the
Euler-Poincar\'e characteristic as well as comparison of these morphometrics
between structures of different topology. The structures are commonly
represented implicitly in curve evolution problems as the zero level set of an
embedding. Practically, binary images of anatomical structures are embedded
using a signed distance transform. However, quantization prevents the accurate
computation of curvatures, leading to considerable errors in morphometry. This
paper presents a fast, simple embedding procedure for accurate local
morphometry as the zero crossing of the Gaussian blurred binary image. The
proposed method was validated based on the femur and fourth lumbar vertebrae of
50 clinical computed tomography datasets. The results show that the signed
distance transform leads to large quantization errors in the computed local
curvature. Global validation of morphometry using regression and Bland-Altman
analysis revealed that the coefficient of determination for the average mean
curvature is improved from 93.8% with the signed distance transform to 100%
with the proposed method. For the surface area, the proportional bias is
improved from -5.0% for the signed distance transform to +0.6% for the proposed
method. The Euler-Poincar\'e characteristic is improved from unusable in the
signed distance transform to 98% accuracy for the proposed method. The proposed
method enables an improved local and global evaluation of curvature for
purposes of morphometry on closed, implicit surfaces.
