Hessian-constrained detail-preserving 3D implicit reconstruction from raw volumetric dataset

Massive routinely-acquired raw volumetric datasets are hard to be deeply exploited by downstream applications due to the challenges in accurate and efficient shape modeling. This paper systematically advocates an interactive 3D shape modeling framework for raw volumetric datasets by iteratively optimizing Hessian-constrained local implicit surfaces. The key idea is to incorporate contour based interactive segmentation into the generalized local implicit surface reconstruction. Our framework allows a user to flexibly define derivative constraints up to the second order via intuitively placing contours on the cross sections of volumetric images and fine-tuning the eigenvector frame of Hessian matrix. It enables detail-preserving local implicit representation while combating certain difficulties due to ambiguous image regions, low-quality irregular data, close sheets, and massive coefficients involved extra computing burden. To this end, we propose several novel technical elements, including data-specific importance sampling for adaptive spherical-cover generation, close sheet determination based on distinguishable local samples, and parallel acceleration for local least squares fitting. Moreover, we conduct extensive experiments on some volumetric images with blurry object boundaries, and make comprehensive, quantitative performance evaluation between our method and the state-of-the-art radial basis function based techniques. And we also apply our method to two practical applications. All the results demonstrate our method's advantages in the accuracy, detail-preserving, efficiency, and versatility of shape modeling.