IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 54, NO. 1, FEBRUARY 2007 167 Connectivity Analysis in Very Large 3D Microtomographic Images Lian Apostol and Françoise Peyrin Abstract—Osteoporosis, a bone fragility disease leading to spon- taneous bone fractures, is becoming a major health problem in many countries. The characterization of trabecular bone architec- ture has been shown to be important to predict fracture risk. Tra- becular bone may be characterized in vitro using 3D microtomog- raphy. New acquisition systems enable to get very high-resolution images with sizes up to 8 Gbytes. Among the different quantifica- tions, connected component analysis is useful to characterize con- nectivity. Such an analysis requires loading the whole 3D image in memory, which limits the maximum size of the volume to be pro- cessed. In this paper, we present a method for analyzing the con- nectivity of very large 3D images. They are decomposed in two or more sub-volumes and processed according to the following steps: a) objects in each sub-volume are separately labeled by an itera- tive sequential algorithm, b) the common border of each pair of sub-volumes is analyzed in order to identify interconnections be- tween objects situated on both sides of the border, c) objects in each sub-volume are relabeled according to interconnections infor- mation. The implementation is thought so as to minimize memory load. The program was successfully applied to bone volume images acquired using synchrotron radiation microtomography and con- taining various numbers of objects. Index Terms—Biomedical imaging, image analysis, topology, X-ray tomography. I. INTRODUCTION O STEOPOROSIS, a bone fragility disease leading to spon- taneous bone fractures, is becoming a major problem of health in many countries. Thus important research activity is de- voted to understanding the mechanisms involved in bone loss. Bone Mineral Density is routinely measured in vivo to diagnose osteoporosis but it is recognized to be somehow limited to pre- dict individual fracture risk. Bone quality involving tissue prop- erties and bone micro-architecture also plays a role in the biome- chanical properties of bone. The investigation of bone micro-ar- chitecture requires high-resolution techniques to access the fine and complex trabeculae network. If two-dimensional histomor- phometric techniques have been for many years the gold stan- dard for analyzing bone micro-architecture, three-dimensional imaging techniques are nowadays more and more employed [1]. For this purpose, Magnetic Resonance Imaging (MRI) and X-ray microtomography are mainly used. MRI presents Manuscript received October 27, 2004; revised October 6, 2006. This work was completed in the context of the French “GdR Stic-Santé” common to CNRS and Inserm. The authors are with CREATIS–UMR CNRS 5515–INSERM U630, INSA Lyon-Bât Blaise Pascal, 69621 Villeurbanne Cedex, France (e-mail: lian.apostol@free.fr; peyrin@esrf.fr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNS.2006.888815 the advantage of not using ionizing radiation, but the best spa- tial resolution available in vivo as compared to the size of bone trabeculae is still limited. X-ray enables imaging at higher spatial resolution. In addition, when coupled to synchrotron sources, images with very high contrast and very high signal to noise ratio may be achieved at a spatial resolution up to the micrometer level [2], [3]. Although limited to in vitro examination of bone samples or bone biopsies, it is a technique of choice to analyze bone samples [4]. With the progress in de- tectors, it is possible to acquire very large volumes (for instance voxels, i.e. 8 Gbytes of data). However the final goal for biologists and physicians is not imaging, but quantifying bone micro-architecture. For this pur- pose, characteristic parameters are computed from the images after segmentation of bone structure. With this respect, high-res- olution 3D imaging opens up new possibilities for the quantifi- cation of bone micro-architecture. On one hand, it is possible to measure accurately morphome- tric parameters of the trabecular structure, such as bone volume to bone tissue, bone surface to bone volume, trabecular thick- ness, and trabecular separation. If conventional bone investiga- tion methods required assumption on the geometrical organiza- tion of the structure (i.e. parallel plate model) [5], 3D images enable to compute model independent parameters [6], [7]. On the other hand, the computation of topologic parameters giving information on connectivity is also of great interest [8]. It is straightforward that 3D images are required to get reliable con- nectivity information since information delivered from a 2D slice is biased. For instance it is not possible to know if a ter- minal point in a trabeculae observed in a single slice is really a terminal point in the core sample. The conventional way to quantify connectivity is to use the Euler number. However, since the Euler number is a function of other topologic characteristics, it is necessary to do a connected component analysis to get a cor- rect interpretation. Such an analysis generally requires loading the whole 3D image in memory, which limits the maximum size of the volume to be processed. In this paper, we present a method for analyzing the connec- tivity of very large 3D images. After recalling the background on topological analysis, we present a method for analyzing the connectivity by loading sub-blocks of the 3D image. We present the application of this method to very large images of bone cores acquired on calcaneus and femur neck bone pieces. II. BACKGROUND ON CONNECTIVITY ANALYSIS Connectivity is defined as the maximum number of connec- tions that one can remove without separating a part of the struc- ture in two connected sub-structures. 0018-9499/$25.00 © 2007 IEEE