The wrapper: A surface optimization algorithm that preserves highly curved areas

Abstract

Software to construct polygonal models of anatomical structures embedded as isosurfaces in 3-D medical images has been available since the mid 1970s. Such models are used for visualization, simulation, measurements (single and multi-modality image registration), and statistics. When working with standard MR- or CT-scans, the surface obtained can contain several million triangles. These models contain data an order of magnitude larger than that can be efficiently handled by current workstations or transmitted through networks. These algorithms generally ignore efficient combinations that would produce fewer, well shaped triangles. An efficient algorithm must not create a larger data structure than present in the raw data. Recently, much research has been done on the simplification and optimization of surfaces ([Moore and Warren, 1991]; [Schroeder et al., 1992]; [Turk, 1992]; [Hoppe et al., 1993]; [Kalvin and Taylor, 1994]). All of these algorithms satisfy two criteria, consistency and accuracy, to some degree. Consistent simplification occurs via predictable patterns. Accuracy is measured in terms of fidelity to the original surface, and is prerequisite for collecting reliable measurements from the simplified surface. We describe the "Wrapper" algorithm that simplifies triangulated surfaces while preserving the same topological characteristics. We employ the same simplification operation in all cases. However, simplification is restricted but not forbidden in high curvature areas. This hierarchy of operations results in homogeneous triangle aspect and size. Images undergoing compression ratios between 10 and 20:1 are visually identical to full resolution images. More importantly, we report experimental results on the metric accuracy of the simplified surfaces. Measurements based upon "ridge curves" extracted on polygonal models were recently introduced ([Cutting et al., 1993]; [Ayache et al., 1993].) We compared ridge curves digitized from full resolution, Wrapper, and volume subsampled CT- scan isosurfaces. [Dean, 1993] introduced a method for measuring morphometric distances between homologous space curves. In the best case this method demonstrated that ridge curves digitized from the Wrapper simplified images were two orders of magnitude closer to the full resolution image than those taken from the volume subsampled images.