Our research team has been working on the virtual surgery system. The three-dimensional (3D) geometric modeling of the human tissue or organ is the core module of the virtual surgery system. The 3D geometric model can aid doctors in diagnosing illnesses accurately and efficiently, which helps in improving the success rate of surgery. In this work, the methods used to design the geometric modeling software in the virtual surgery system have been introduced. The 3D geometric modeling of the human tissue consists of the preprocessing and 3D reconstruction of medical images. Herein, the core operation in the image preprocessing is the segmentation of medical images. R. Kayalvizh et al. proposed a new intelligent algorithm referred to as particle swarm optimization [1]. I. Cruz-Aceves et al. proposed an automatic image segmentation method based on an active contour model theory and estimation of distribution algorithms [2]. N. R. Nayak et al. proposed an improved clustering algorithm, which is applicable to gray images, by evaluating three different kinds of clustering algorithms [3]. For general medical images, it is difficult to achieve the required accuracy using automatic segmentation methods. Therefore, an interactive operation is required in image segmentation to obtain results that are more accurate. M. Milanova et al. proposed an image segmentation method based on vision to determine location, which applied the Chan-Vess model to the image segmentation [4]. Z. T. Liu et al. proposed a novel method for complex medical image segmentation based on the hierarchical characteristics of human visual perception [5]. R. Delgado-Gonzalo et al. proposed an interactive image segmentation method based on the B-spline curve [6]. A. Chavez-Aragon et al. proposed a network platform that collected the MRI images of volunteers to form a knowledge-based image segmentation of the hip [7]. Although many methods of image segmentation have been proposed in recent years, it is difficult to obtain satisfactory results using any individual method of the computer image segmentation, whether automatic or interactive, because of the limitations and difficulties in segmentation method. In this study, we combined the region growing method, which is based on the gray level difference, and the interactive segmentation method, which is based on the edge fill algorithm, the combination of the region growing method and interactive segmentation satisfied the general requirements of medical image segmentation.

Many 3D reconstruction methods have been proposed in the past [8-11]. The MC (Marching Cubes) algorithm has been used in this study. Compared to other algorithms, the MC algorithm is easily programmable and generates 3D models at a fast speed. Besides, the method, which utilizes ordinary computer graphics hardware to implement rapid geometric transformation and mapping, occupies less memory and has high portability. Furthermore, the surface structure of the human tissue can be expressed accurately to meet the requirements of the virtual surgery system.

Based on the region growing module, the interactive segmentation module, and the 3D reconstruction module, the geometric modeling software was created for human tissues or organs, which included two-dimensional (2D) medical image browsing, preprocessing, and 3D geometric reconstruction. This software can be used both independently and as a part of the virtual surgery system. The features of the software are as follows: (1) Medical images can be imported and then panned and zoomed for convenient observation. (2) Different medical image segmentation methods can be used. Image enhancement, noise reduction, segmentation, erasing and patching vulnerabilities for medical images can be conducted using the software. (3) 3D reconstruction can be carried out after preprocessing the images. Then, the 3D geometrical model can be displayed on the interface. The model can be zoomed, rotated, moved, etc. (4) The Smooth handling of the surface of the 3D geometrical model can be conducted easily to make it closer to real human tissues and organs. (5) The cutting of an arbitrary cross-section can be performed in the 3D geometrical model for the users to observe. (6) Data files can be obtained in multiple formats and exported to other software.

C++ is employed to design the geometric modeling interface. The core modules of the software include the region growing module, the interactive segmentation module, and the 3D reconstruction module.

2.3. The 3D Reconstruction Module

The classic MC algorithm is employed as the surface reconstruction algorithm. Users can isolate the tissues between two thresholds by setting a high threshold and a low threshold to implement the surface reconstruction of medical images. This module makes use of the 3D reconstruction algorithm based on voxels to carry out the 3D reconstruction for a set of 2D medical CT images after segmentation. In addition, users can zoom, move, and rotate the 3D model to conveniently observe the tissue structure, the size of the focus, the location, and other information about the tissue. The flow diagram of the 3D reconstruction algorithm is shown in Fig. (1).

Fig. (1). 3D reconstruction program flow chart.

The medical image data is derived from the CT images of the hip of a healthy man, whose age is 26 years, height is 175 cm, and weight is 65 kg. He is in good condition and has no history of hip fracture, muscle damage, etc. Axial continuous tomography is used in this work. Seven hundred tomographic images are selected. The space between the images is 1 mm. Every image is a lattice of 512×512 pixels. In addition, Visual C++ is used in the geometric modeling program, which is run on the Windows platform.

Fig. (2). Gracilis muscle segmentation result (dv=cv=30).

The program results include the following: (1) The segmentation results of the object under different parameters and the same seed points, and under the same parameters and different seeds points obtained using the region growing algorithm. (2) The segmentation results of the femur and the semitendinosus obtained using the region growing algorithm and the interactive segmentation algorithm.

• (1) The points selected in the source gracilis image are taken as the seed points. The value of dv and cv is taken as 30. The segmentation result can be obtained using the region growing method as shown in Fig. (2).
• (2) The points selected in the source gracilis image are taken as the seed points. The value of dv and cv is taken as 90. The segmentation result can be obtained using the region growing method as shown in Fig. (3).
• (3) The points selected in the source semitendinosus image are taken as the seed points. The value of dv and cv is taken as 30. The segmentation result can be obtained using the region growing method as shown in Fig. (4).
• (4) A point selected in the source femur image is taken as the seed point. Owing to the larger gray value of the bone, the value of dv is 300 and that of cv is 900. The segmentation result is shown in Fig. (5).

Fig. (3). Gracilis segmentation result (dv=cv=90).

Fig. (4). Semitendinosus segmentation result (dv=cv=30).

Fig. (5). Femur segmentation result.

The segmentation result shows that for the case where the points selected in the source gracilis muscle image are taken as the seed points, and the value of dv and cv is 30, the whole gracilis muscle section can be obtained using the region growing algorithm. However, for the same seed points, when the value of dv and cv is 90, owing to this larger value, multiple connected muscles are obtained using the region growing method. If the value of dv and cv is 30, then users can select a point in the semitendinosus as the seed point for segmentation. The segmentation result shows multiple muscles including the semitendinosus because the boundaries of the semitendinosus are fuzzy. As observed from the segmentation result of the muscle and the bone, the region growing algorithm put forward greater demand in the control of parameters and the selection of seed points. In addition, for the tissues whose boundaries are fuzzy, it is easy to extract excess parts along with the segmentation object, which results in over-segmentation.

• (5) The sources of medical data are the same for the region growing module, i.e., users utilize the interactive segmentation algorithm to conduct the segmentation of the muscle and the bone. The segmentation results of the semitendinosus and the femur are shown in Figs. (6 and 7), respectively.

Fig. (6). Muscle segmentation result.

Fig. (7). Femur segmentation result.

As observed in the segmentation result for case (5), users can take advantage of the interactive segmentation method to segment any tissue and organ of interest. However, the method has a high operating time. Furthermore, it places greater demand on the operator’s skill. Therefore, the tissues whose boundaries are clear and the gray level difference is high, such as the femur, can be segmented immediately using the region growing method. Comparatively, the muscle tissues whose boundaries are fuzzy, such as the semitendinosus, the interactive segmentation method can be used. Users can also employ the interactive segmentation method first to obtain the parts of interest. That is, the tissues whose gray level difference is small are separated. Then, users can employ the region growing method to obtain the desired results. This not only avoids the over-segmentation that results from the region growing method, but also improves the efficiency of the segmentation.

Since the 3D reconstruction model is created using a computer, which gives an unnatural image, users have to set and adjust the relevant parameters as needed. As a result, it is difficult to assess the results of the reconstruction quantitatively. At present, the assessment of the quality of the 3D reconstruction is mainly subjective. Based on the experience in anatomy or comparison with real human organs, users compare key feature points of the 3D model to judge the merits of the reconstruction results. The comparison between the 3D model reconstructed by our software and the structure of the real muscle and bone is shown in Figs. (8 and 9).

Fig. (8). Comparison of human sartorius muscle and muscle geometry model.

Fig. (9). Comparison of human hip and hip geometry model.

The comparison for the sartorius muscle is shown in Fig. (8). The real structure of the human sartorius and the geometry model of the sartorius muscle obtained using the software are shown on the left and right, respectively.

The comparison for the hipbone is shown in Fig. (9, 9(a) shows the front structure of the real hipbone. Fig. 9(c) shows the back of the real hipbone. Fig. 9(b, d) show the model for the front and back of the hipbone, respectively, obtained using the software.

As observed from Figs. (8 and 9), the 3D geometry model obtained using this software joins basically with the physiological structure of real muscle and bone and can show up the detailed characteristics of corresponding muscle and bone. In future studies, the generation of a volume model and the implementation of the program will be considered for integration with the meshing module and the finite element analysis of the biomechanics module that our research group has designed.