Three-dimensional Reconstruction of Foot based on Marching Cubes

Wang Hongjian Chongqing Engineering

Technology Research Center for Information Management in

Development, Chongqing Technology & Business University,

Chongqing,400067,China. e-mail: whj_cqu@163.com

Tang Yuelin Chongqing Special Equipment

Quality Safe Inspection Center, Chongqing,401121,China e-mail: tonnyue@163.com

Luo Fen School of Computer Science &

Information Engineering, Chongqing Technology & Business University.

Chongqing 400067,China. e-mail: luofcn@163.com

AbstractThree-dimensional medical image reconstruction for both transmission and emission tomography has traditionally decomposed the problem into a set of two-dimensional reconstructions on parallel transverse sections. An approach for reconstructing tomographic images based on the idea of continuous dynamical methods is presented. The method consists of a continuous-time image reconstruction (CIR) system described by differential equations for solving linear inverse problems.In this paper, it is provided to reconstruct three-dimensional(3D) models of human body by using CT slices and digital images and precisely finding locations of pathological formations such as tumour. It is necessary to incise a 3D object to obtain detail structure information inside in the process of developing 3D medical visualization system. We design the program reconstruct 3D images utilizing the CT slice sequence in PAT format based on marching cubes by visual C++ 6.0 and Visualization Toolkit (VTK) toolbox,which are used to Cuboids that can be controlled to zoom, move or circumrotate by mouse and used for clipping the object of 3D object. The results supplied by the proposed algorithm are examined with the help of some relevant examples.

KeywordsComputed tomography (CT),Three-dimensional reconstruction; Marching Cubes; Visualization Toolkit.

I. INTRODUCTION

The rapidly changing field of medical imaging has led to substantial efforts for developing a wide variety of imaging techniques dedicated to body studies.The traditional approach to three-dimensional medical image reconstruction for both transmission and emission tomography decomposes the problem into a set of two-dimensional reconstructions on independent parallel sections. Each two-dimensional section is reconstructed from a set of one-dimensional projection data using a standard filtered backprojection algorithm[1-2]. However, while this approach is computationally efficient, photons which pass obliquely through the chosen set of sections cannot be included in the reconstruction. Medical Imaging techniques are used for diagnosing and treatment of many diseases as well as surgical operations. CT,MRI and ultrasound imaging techniques are the mostly used ones[3]. For a long time, 3D models have being used in medical applications in many countries, which are used just at some high quality hospitals and medical centers. These

equipments have been indispensably for doctors diagnosis assisted by information technology, which need strong computers with dedicated software. It in medical imaging remain marginal because of a number of technical and computational difficulties. At present, such high-tech equipments are unable to be manufactured with domestic technology, but feasible developing supporting accessories and software can enhance their utilization effectivity and reduce the dependence on foreign maintenance system with high cost. On the other hand, medical information system does not shape clearly; medical units in national health care system have not united yet in any standard process to operate image diagnostic equipments or to manage patient data. Therefore, a project making facilities for medical information system in general and for medical imaging in particular has been alternatively developed in order to master mentioned technology and to develop domestic products partially taken place of very expensive imported facilities and soft wares[3-4].

This paper introduces our building 3D image reconstruction software with Marching Cubes(MC) algorithms on PC, which are very necessary tools for medical image processing,such as foot. This method consists of two steps, edge detection and correction.Moreover, to develop and optimize a new imaging system, and to recognize the influence of the various adjustable parameters, simulation can be a helpful tool.

Figure 1. Block diagram of an energy-discriminating X-raycomputed tomography(CT) system utilizing a cadmium telluride(CdTe)detector.MCA and PC are multi-channel analyzer and personalcomputer,respectively.

2010 International Conference on Intelligent Computation Technology and Automation

978-0-7695-4077-1/10 $26.00 2010 IEEEDOI 10.1109/ICICTA.2010.703

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Figure 2. Patterns of polygons generated Marching Cubes Algorithm

II. FUNDAMENTAL THEORY

Figure 1 shows a block diagram of an X-ray CT system utilizing a CdTe detector. Segmentation is the process of classifying pixels in an image or volume. It is one of the most difficult task in the visualization processes. For reconstruction of medical 3D surface and volume, interest tissue boundaries should be distinguished from others on all the image slices. After the boundaries have been found, the pixels, which constitute the tissue, can be assigned to a constant grey level value. This constant value represents

only this tissue.

A. 3D reconstruction For investigating the influence of OSAHS on human

airways, two volunteers are selected to receive the CT head scanning. One volunteer is a 30-year-old healthy male with normal bodyweight but no medical history of chronic upper airway illness. The other volunteer is a 46-year-old male who has been diagnosed OSAHS by polysomnograph recently.

In this paper, strategy for 3D reconstruction of complex ancient architecture is split into its component reconstruction problem[5]. All recent medical 3D image reconstruction techniques create 3D images from sets of 2D slices, which can be recorded by various equipments such as CT, MRI, ultrasound etc. Each type of scanner has his own characteristics due to physical principles of image recording, e.g. images of CT scanner are often parallel slices with high contrast, images of ultrasound scanner are either parallel or divergent slices with low contrast etc. Thus there are different 3D reconstruction techniques for each type of data.

B. Marching Cubes Marching Cubes (MC) algorithm is a 3D reconstruction

method developed by W. Lorensen and Cline in 1987. This algorithm produces a triangle mesh by computing iso-surfaces from discrete data. By connecting the patches from all cubes on the iso-surface boundary, we get a surface representation. Because of its merits of simple, easy to achieve, it has been widely used, is considered as one of the most popular algorithms for display[6-10].

The basic principle of MC algorithm are shown as below: 1) construct iso-surface in the 3D data, 2) find the cubes passed through iso-surface, 3) obtain the iso-surface in cubes and calculating correlation parameters, 4) use common software tools or graphics hardware to protract iso-surface [11]. In medical applications, the MC algorithm can be used in the reconstruction of the body contour or the internal organs, so that doctors can directly observe space relationship between interest organs and surrounding tissue in 3D image. MC algorithm takes full advantage of the graphics display hardware acceleration function and produces better reconstruction image quality[11-12].

In a 3D space we enumerate 256 different situations for the marching cubes representation. All these cases can be generalized in 15 families by rotations and symetries (seen Figure 2).In order to be able to determine each real case, a notation has been adopted. It aims at refering each case by an index created from a binary interpretation of the corner weights. In this way, vertexes from 1 to 8 are weighted from 1 to 128 (v1 = 1, v2 = 2, v3 = 4, etc.); for example, the family case 3 example you can see in the picture above, corresponds to the number 5 (v1 and v3 are positive, 1 + 4 = 5).

Figure 3. Marching cubes ambiguous cases

To all this cubes we can attribute a complementary one. Building a complementary cube consists in reversing normals of the original cube. In the next picture you can see some instances of cubes with their normals.

The creation of these complementary cubes allows to give an orientation to the surface.

C. The marching cubes ambiguous cases As for the marching squares we meet some ambiguous

marching cubes cases : for the family 4 and 10. But in 3D space a solution has to be found because of the topology

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problems these situations create. However not only real ambiguous cases can create topology disfunctions, some classical families are incompatible. See for instance the next picture[12].

To cope with these topology errors (as holes in the 3D model), 6 families have been added to the marching cubes cases. These families have to be used as complementary cases[13]. For instance, in the previous picture, you have to use the case 6c instead of the standard complementary of the case 6(seen Fig.3).

III. PROGRAMMING

Software for reconstructing 3D image from a set of CT images was built on Visual C++ 6.0. VTK has been chosen because of its open source toolkit professionally designed for computer graphics purposes, showed as fig.4.

A. Visualization Toolkit VTK is an open source, objectoriented software system

for computer graphics, visualization, and image processing, and visualization used by thousands of researchers and developers around the world,which contains installer for the Windows platform.VTK consists of a C++ class library, and several interpreted interface layers including Tcl/Tk, Java, and Python.In addition, dozens of imaging algorithms have been directly integrated to allow the user to mix 2D imaging or 3D graphics algorithms and data. The design and implementation of the library has been strongly influenced by object-oriented principles[14]. It usually has important limitations such as low efficient code execution, poor computing capacity [15].

B. Reconstruction of examples 1). Interface design. The main user interface of the

software is functionally similar to some commercial medical image software. It contains a screen on the right to display original and processing images. This screen can be displayed with different modes. General toolbar is placed on the top and control panel on the left. However, due to the main educational and training purpose of the software, it contains

some more control components which are not necessary in commercial software.

Fig.5 shows the reader of the CT images with sequences number of 1, and 50,75,100,150 and 200, respectively.

2).Example. Through this structure, a reconstructed triangle was stored in memory in the form of a bidirectional linked list, which could reconstruct a 3D shape. We use MC to reconstruction CT data of foot(556 309 223)

sequence, with gray CT images. The reconstruction of foot showed as fig.6. The source is PAT format image to reconstruct 3D image with techniques MPR, SR, VR with MC algorithm. Experimental data is 256 serial images which were transformed PAT(for Protein Analysis Toolkit) format.

The CT images are in the format of PAT, for Protein Analysis Toolkit, is an integrated biocomputing server. PAT is able to read and write data in many bioinformatics formats and to create any desired pipeline by seamlessly sending the output of a tool to the input of another tool. PAT can retrieve protein entries from identifier-based queries by using pre-computed database indexes[16-17].

PAT file is pattern image files which store a range of image data and will need to viewed using the applications that created them to be sure of viewing them correctly. The file often used for creating a textured background.

TABLE 1. RUN TIME OF FOOT RECONSTRUCTION

part Size(pixel) frame Process time Range of gray

foot 556309 223 17297 ms 51-255

foot 556309 223 17484 ms 72-255

We use the program run in PC,which is notebook about CPU 1.73G, Memory 1G. Harddisk 160G. the time of reconstructing is showed in tab.1. which shows the time-consuming of process is more than 17 seconds.

The timeGetTime() API function called by the program retrieves the system time, in milliseconds. The system time

Figure 4. Main screen of program included foot

No.1 No.50 No.75

No.100 No.150 No.200

Figure 5. Read part of CT images

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is the time elapsed since Windows was started. It must indicate that it need declare before use.

Note that the value returned by the timeGetTime() function is a DWORD value. The return value wraps around to 0 every 2^32 milliseconds, which is about 49.71 days. This can cause problems in code that directly uses the timeGetTime() return value in computations, particularly where the value is used to control code execution. You

should always use the difference between two timeGetTime() return values in computations.[18]

IV. CONCLUSION

We have presented a system for partial 3D reconstruction based on the marching cubes algorithm. The system allows manipulating easily all parameters involved in the process: threshold and range parameters. The system works very well and the 3D reconstruction is obtained in real-time.

VTK and visual c++ have powerful functions in the 3D visualization field. Its an important tool in development medical 3D visualization software system with marching cubes arithmetic. After the medical image 3D reconstruction, it is necessary to clipping 3D object to observe the inner structure. The cuboids interactive clipping provides an important solution. The experimental foot results shows cuboids clipping is a convenient and flexible approach and it can achieve real-time interactive clipping 3D objects.

ACKNOWLEDGMENT

This work was partially supported by fund of Chongqing Science & Technology Commission under Grant No.2006EA2011 and Chongqing Education Commission under Grant No.Kj070708 and KJ080711,China.

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Figure 6. Result of foot reconstruction

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