The KIPS Transactions:PartA (정보처리학회논문지A)

Korea Information Processing Society (한국정보처리학회)
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A Voxelization for Geometrically Defined Objects Using Cutting Surfaces of Cubes

큐브의 단면을 이용한 기하학적인 물체의 복셀화

  • 권오봉 (전북대학교 전자정보공학부)
  • Published : 2003.06.01
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Abstract

Volume graphics have received a lot of attention as a medical image analysis tool nowadays. In the visualization based on volume graphics, there is a process called voxelization which transforms the geometrically defined objects into the volumetric objects. It enables us to volume render the geometrically defined data with sampling data. This paper suggests a voxeliration method using the cutting surfaces of cubes, implements the method on a PC, and evaluates it with simple geometric modeling data to explore propriety of the method. This method features the ability of calculating the exact normal vector from a voxel, having no hole among voxels, having multi-resolution representation.

최근 볼륨 그래픽스가 의료 영상의 해석 도구로서 주목을 받아 오고 있다. 볼륨 그래픽스에서는 가시화를 위하여 복셀로 정의된 물체가 필요하다. 이 때문에 기하학적인 방법으로 정의한 다각형 및 곡면을 복셀 기반의 물체로 변환시키는데 이를 복셀화(voxelization)라고 한다. 기하학적인 물체를 복셀화하면 기하학적 물체 데이터를 샘플링 데이터와 함께 단일화된 방법으로 볼륨 렌더링할 수 있다. 본 논문에서는 큐브의 단면을 이용한 복셀화의 한 기법을 제안한다. 그리고 개인용 컴퓨터 환경에서 이 기법을 구현한 후에 단순한 기하학적인 데이터를 이용해서 평가하여 논리적인 타당성을 조사한다. 이 기법은 변환된 복셀로부터 정확한 법선 벡터를 계산할 수 있고 복셀간에 구멍(hole)이 발생하지 않고 다해상도(multi-resolution) 표현이 가능한 특성을 가지고 있다.

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References

  1. A. Kaufman, Efficient Algorithms for 3D Scan-Conversion of parametric Curves, Surfaces and Volumes, Computer Graphics, 21(4), pp.171-179, 1987 https://doi.org/10.1145/37402.37423
  2. A. Kaufman, D. Cohen and R. Yagel, Volume Graphics, IEEE Computer, 26(7), pp.51-64, 1993 https://doi.org/10.1109/MC.1993.274942
  3. A. Kaufman, R. Yagel and D. Cohen, Intermixing Surface and Volume Rendering, 3D Imaging in Medicine NATO ASI Series, Vol.F60, pp.217-227, 1990
  4. B.A. Payne and A.W. Toga, Distance Field Manipulation of Surface Models, IEEE Computer Graphics and Applications, 12(1), pp.65-71, 1992 https://doi.org/10.1109/38.135885
  5. D. Cohen-Or and A. Kaufman, Fundamentals of Surface Voxelization, Graphical Models and Image Processing, 57(6), pp.453-461, 1995 https://doi.org/10.1006/gmip.1995.1039
  6. D. Voorhies, Triangle-Cube Intersection, Graphics Gems III Edited by D. Kirk, Morgan Kaufman, 1992
  7. E-A. Karabassi, G.P. Papaioannou and T. Theharis, A Fast Depth-Buffer-Based Voxelization Algorithm, journal of graphics tools, 4(4), pp.5-10, 1999 https://doi.org/10.1080/10867651.1999.10487510
  8. F.D. IX and A. Kaufman, Incremental Triangle Voxelization, Graphics Interface 2000, pp.205-212, May, 2000
  9. J. Amanatides and A. Woo, A Fast Voxel Traversal Algorithm for Ray Tracing, EUROGRAPHICS87, Elsevier Science Publishers B.V., pp.3-9
  10. J. Arvo, A Simple Method for Box-Sphere Intersection Testing, Graphics Gems edited by A.S. Glassner, Morgan-kaman
  11. L.S. Chen, G.T. Herman, R.A. Reynolds and J.K. Udupa, Surface Shading in the Cuberille Environment, IEEE Computer Graphics and Applications, 5(12), pp.33-43, 1985 https://doi.org/10.1109/MCG.1985.276275
  12. M. Frhauf, Combining Volume Rendering with Line and Surface Rendering, EUROGRAPHICS 91, Elsevier Science Publishers B.V., pp.21-31, 1991
  13. M. Sramek and A.E. Kaufman, Alias-Free Voxelization of Geometric Objects, IEEE, Transactions on Visualization and Computer Graphics, 5(3), pp.251-267, 1999 https://doi.org/10.1109/2945.795216
  14. M.W. Jones, The Production of Vloume Data from Triangular Meshes Using Voxelisation, Computer Graphics Forum, 15(5), pp.311-318, 1996 https://doi.org/10.1111/1467-8659.1530311
  15. R.E. Webber, Shading Voxel Data via Local Curved-Surface Interpolation, Volume Visualization, IEEE Computer Society Press Tutorial, pp.229-239, 1991
  16. R. Yagel, D. Cohen and A. Kaufman, Discrete Ray Tracing, IEEE Computer Graphics and Application, 12(5), pp.19-28, 1992 https://doi.org/10.1109/38.156009
  17. R. Yagel, D. Cohen and A. Kaufman, Normal Estimation in 3D Discrete Space, The Visual Computer, 8(5-6), pp.278-291, 1992 https://doi.org/10.1007/BF01897115
  18. S. Fang and H. Chen, Hardware Accelerated Voxelization, Computers & Graphics, 24(3), pp.433-442, 2000 https://doi.org/10.1016/S0097-8493(00)00038-8
  19. S. Oomes, P. Snoeren and T. Dijkstra, 3D Shape Representation : Trasnforming Polygons into Voxels, Scale-Space Theory in Computer Vision, Springer Verlag, 1997
  20. S.W. Wang, A.E. Kaufman, Volume-Sampled 3D Modeling, IEEE Computer Graphics and Applications, 14(5), pp.26-32, 1994 https://doi.org/10.1109/38.310721
  21. T. Moller and Eric Hains, Real Time Rendering, A.K. Peters, 1999
  22. W.E. Loresen and H.E. Cline, Marching Cubes : A High Resolution 3D Surface Construcation Algorithm, SIGGRAPH87, pp.163-169, 1987 https://doi.org/10.1145/37401.37422
  23. Y.T. Lee, A.A.G. Requicha, Algorithms for Computing the Volume and Other Integral Properties of Solids. II. A Family of Algorithms Based on Representation Conversion and Cellular Approximation, Communications of the ACM, 25(9), pp.642-650, 1982 https://doi.org/10.1145/358628.358648