A Framework for Level Set Segmentation of Volume Datasets Ross Whitaker School of Computing University of Utah David Breen, Ken Museth, and Neha Soni Computer Science Department California Institute of Technology Abstract This paper presents a framework for extracting surface models from a broad variety of volumetric datasets. These datasets are produced from standard 3D imaging devices, and are all noisy samplings of complex biological structures with boundaries that have low and often varying contrasts. The level set segmentation method, which is well documented in the literature, creates a new volume from the input data by solving an initial-value partial differential equa- tion (PDE) with user-defined feature-extracting terms. Given the local/global nature of these terms, proper initialization of the level set algorithm is extremely important. Thus, level set deforma- tions alone are not sufficient, they must be combined with powerful initialization techniques in order to produce successful segmenta- tions. Our level set segmentation approach consists of defining a set of suitable pre-processing techniques for initialization and se- lecting/tuning different feature-extracting terms in the level set al- gorithm. This collection of techniques forms a toolkit that can be applied, under the guidance of a user, to segment a variety of vol- umetric data. Users can combine these methods in different ways and thereby access a wide range of functionalities, several of which are described in this paper and demonstrated on noisy volume data. 1 Introduction As visualization tasks grow in size and complexity, the problem of presenting data effectively is accompanied by another, potentially more difficult problem—how to extract presentable data from the flood of raw information produced by large simulations and high resolution instruments. Thus, the field of data visualization is in- timately tied to more traditional studies of data analysis such as signal and image processing, pattern recognition, artificial intelli- gence, and computer vision. However, in contrast to more conven- tional areas of data analysis, the field of visualization explicitly in- cludes the user in the process of filtering, extracting, and rendering meaningful data. This paper deals with a specific visualization problem—that is, how to build meaningful 3D models of complex structures from noisy datasets generated from 3D imaging devices. In certain cir- cumstances such data can be visualized directly [1, 2, 3, 4]. While direct techniques can provide useful insights into volume data, they are insufficient for many problems. For instance, direct vol- ume rendering techniques typically do not remove occluding struc- tures, i.e., they do not allow one to “peel back” the various layers of the data to expose the inner structures that might be of inter- est. They also do not generate the models needed for quantitative study/analysis of the visualized structures. Furthermore, direct vi- sualization techniques typically do not perform well when applied directly to noisy data, unless one filters the data first. Techniques for filtering noisy data are abundant in the literature, but there is a fundamental limitation—filtering that reduces noise tends to dis- tort the shapes of the objects in the data. The challenge is to find methods which present the best tradeoff between fidelity and noise. Level set segmentation relies on a surface-fitting strategy, which is effective for dealing with both small-scale noise and smoother intensity fluctuations in volume data. The level set segmentation method, which is well documented in the literature [5, 6, 7, 8], creates a new volume from the input data by solving an initial- value partial differential equation (PDE) with user-defined feature- extracting terms. Given the local/global nature of these terms, proper initialization of the level set algorithm is extremely impor- tant. Thus, level set deformations alone are not sufficient, they must be combined with powerful initialization techniques in or- der to produce successful segmentations. Our level set segmen- tation approach consists of defining a set of suitable pre-processing techniques for initialization and selecting/tuning different feature- extracting terms in the level set algorithm. We demonstrate that combining several pre-processing steps with level set deformations produces a powerful toolkit that can be applied, under the guidance of a user, to segment a wide variety of volumetric data. There are more sophisticated strategies for isolating meaningful 3D structures in volume data. Indeed, the so called segmentation problem constitutes a significant fraction of the literature in image processing, computer vision, and medical image analysis. For in- stance, statistical approaches [9, 10, 11, 12] typically attempt to identify tissue types, voxel by voxel, using a collection of measure- ments at each voxel. Such strategies are best suited to problems where the data is inherently multi-valued or where there is sufficient prior knowledge [13] about the shape or intensity characteristics of the relevant anatomy. Alternatively, anatomical structures can be isolated by grouping voxels based on local image properties. Tra- ditionally, image processing has relied on collections of edges, i.e. high-contrast boundaries, to distinguish regions of different types [14, 15, 16]. Furthermore deformable models, incorporating differ- ent degrees of domain-specific knowledge, can be fitted to the 3D input data [17, 18]. The work of this paper demonstrates a mathe- matical and computational framework which effectively combines or unifies classification, filtering, and surface-fitting approaches to modeling and visualizing 3D data. 2 Example Datasets Our work is largely motivated by the desire to produce a semi- automatic segmentation approach which can partly or fully replace the tedious and extremely time-consuming process of manual data segmentation – a solution which to our initial surprise is widely used by colleagues in biology and medicine. Thus, to scientists working in these fields even an approximate scheme which can segment out approximately 90% of the model is immensely use- ful because it reduces the manual labor needed to produce a final result. We stress that there exists no fully automatic solution to the segmentation problem typically encounter in 3D imaging. For example, Figure 1(a) shows one of 270 slices of an electron tomog- raphy (ET) volume of a spiny dendrite provided by the National Center for Microscopy and Imaging Research, at UC San Diego. The complex structure of the dendrite and the noisy nature of the data make the rendering of such volume data difficult. Figure 1(b) shows the results of attempting to isolate the relevant structures in this dataset by extracting isosurfaces at greyscale value of 129. For this example we have blurred the data with a small Gaussian ker-