User-Driven 3D Mesh Region Targeting

We present a method for the fast selection of a region on a 3D mesh using geometric information. This is done using a weighted arc length minimization with a conformal factor based on the mean curvature of the 3D surface. A careful analysis of the geometric estimation process enables our geometric curve shortening to use a reliable smooth estimate of curvature and its gradient. The result is a robust way for a user to easily interact with particular regions of a 3D mesh construced from medical imaging. We describe the applicability of the method for real-time clinician use. In this study, we focus on building a robust and semi-automatic method for extracting selected folds on the cortical surface, specifically for isolating gyri by drawing a curve along the surrounding sulci. It is desirable to make this process semi-automatic because manually drawing a curve through the complex 3D mesh is extremely tedious, while automatic methods cannot realistically be expected to select the exact closed contour a user desires for a given dataset. In the technique described here, a user places a handful of seed points surrounding the gyri of interest; an initial curve is made from these points which then evolves to capture the region. We refer to this user-driven procedure as targeting or selection interchangeably. 1 Description of Purpose Many techniques have been devised for the structural segmentation of various anatomical features in medical imagery using 3D geometric information. Generally these fall into two broad categories. The first are the automated methods, where an algorithm must operate on an entire dataset without user interaction [1, 2]. The second group is that of user-driven methods, where some interaction is required to define parameters or initialization [3]. Our region selection method falls into the latter category, while the curvature estimation step could be applied to fully automatic algorithms that rely on curvature. The existence of automatic feature extraction methods does not eliminate the need for user-driven algorithms. In automatic approaches, the problems are typically ill-posed and a reference truth doesn’t exist. User-free Sulci extraction seeks to find as many curves as possible with minimal false positives; there is no guarantee that a particular region of interest would be selected. In contrast, user-driven methods use a minor initialization to make the problem well-posed and have a unique correct solution. 1.1 Our Contribution: New Work to be Presented The contribution consists of two primary components. First, we make explicit the sources of difficulty in estimating surface curvature on a noisy mesh and present robust solutions to this problem. In particular, we make clear the necessity of proper neighborhood selection and regularized least squares for an accurate estimate of surface curvature gradient. Second, we introduce an energy formulation with a weighted arc-length minimization incorporating geometry of both the contour and the underlying surface. Unlike methods based on point-to-point minimal cost path computation [3, 4, 5], we do not need to constrain the initialization points to lie on the final path. The resulting selected region is consistent with respect to varying initialization points; accuracy is not degraded by suboptimally placed initial points. We will also show demonstrate the use of of the contour generation as a real-time feedback mechanism.