Snake modeling and distance transform approach to vascular centerline extraction and quantification Mahnaz Maddah a,b , Hamid Soltanian-Zadeh a,b,c, * , Ali Afzali-Kusha a a Control and Intelligent Processing Group, Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran b Signal and Image Processing Group, School of Intelligent Systems, Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran c Image Analysis Laboratory, Department of Radiology, Henry Ford Health System, One Ford Place, 2F, Detroit, MI 48202, USA Received 4 October 2002; revised 14 April 2003; accepted 14 April 2003 Abstract A new method for fully automated centerline extraction and quantification of microvascular structures in confocal microscopy (CM) images is presented. Our method uses the idea of active contour models as well as path planning and distance transforms for the three- dimensional centerline extraction of elongated objects such as vessels. The proposed approach is especially efficient for centerline extraction of complex branching structures. The method performance is validated in several CM images of both normal and stroked rat brains as well as simulated objects. The results confirm the efficiency of the proposed method in extracting the medial curve of vessels, which is essential for the computation of quantitative parameters. q 2003 Elsevier Ltd. All rights reserved. Keywords: Active contour models; Centerline extraction; Vascular quantification; Confocal microscopy 1. Introduction Numerous three-dimensional (3D) visualization tools exist to process and visualize thin 3D structures such as vessels. The most common tool is maximum intensity projection (MIP), which is a very simple ray tracer [1]. It generates a 2D projection of 3D object along a single direction, leading to some drawbacks such as visual occultation of vessels and artificial crossings that can only be detected by matching on several other projections [1]. Also, quantitative parameters such as diameter, length and volume of vessels, which are beneficial for diagnosis, planning surgery and therapy, are not accurately estimated. So, an accurate processing of the 3D images is required for a reliable visualization and proper extraction of the vessel parameters. Obtaining the 3D main structure or the center- line of the objects has received a great attention in recent years for its applications in data compression, medical image analysis, path planning, etc. Moreover, centerline extraction is the first and the most important step for quantification of tubular objects such as vessels. A number of methods for 3D skeletonization or centerline extraction of objects have been introduced in recent years, which are mostly extensions of 2D methods. The most popular methods for skeletonization are distance transform (DT)-based techniques [2–7], which tend to determine medial points by locating voxels lying farthest with respect to the boundary of the object on its cross- section normal to the local major axis. The method was first introduced by Blum [2], in which the DT of object voxels with respect to boundary voxels was used to determine maximal balls (disks) within a 3D (2D) object. The maximal balls are sphere-like sets of connected voxels with maximum radius, which are completely contained in the object but not in any other ball in the object. It has been shown that any object can be fully represented by the set of its maximal balls [3], whose set of centers gives the skeletal voxels. Thinning methods are another category of skeletoniza- tion [8–12]. The idea is to apply morphological erosion operators to successively ‘peel off’ the outer layer of the object until it is reduced to its skeleton. To prevent 0895-6111/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0895-6111(03)00040-5 Computerized Medical Imaging and Graphics 27 (2003) 503–512 www.elsevier.com/locate/compmedimag * Corresponding author. Address: Image Analysis Laboratory, Department of Radiology, Henry Ford Health System, One Ford Place, 2F, Detroit, MI 48202, USA. Tel.: þ1-313-874-4482; fax: þ 1-313-874- 4494. E-mail address: hamids@rad.hfh.edu (H. Soltanian-Zadeh).