Mathematical Methods for 3D Reconstruction of Cell Structures

  • Dalibor Martišek Brno University of Technology
Keywords: Cell structure, 3D reconstruction, Scalar data, Direct volume rendering, Illuminant model, Line segment rasterization


The study of the complicated architecture of cell space structures is an important problem in biology and medical research. Optical cuts of cells produced by confocal microscopes contain a lot of information, however, most of this is unsubstantial for human vision. Therefore, it is necessary to use mathematical algorithms for the visualization of such images. Present software tools such as OpenGL or DirectX run quickly in a graphic station with special graphic cards, run very unsatisfactory on PC without these cards and outputs are usually poor for real data. These tools are black boxes for a common user and make it impossible to correct and improve them. With the method proposed, more parameters of the environment can be set. The quality of the output is incomparable to the earlier described methods and is worth increasing the computing time. We would like to offer mathematical methods of 3D scalar data visualization describing new algorithms that run on standard PCs very well.


Blinn, J. F. Light reflection functions for simulation of clouds and dusty surfaces. Acm Siggraph Computer Graphics 16, 3 (1982), 21–29.

Bresenham, J. E. Algorithm for computer control of a digital plotter. IBM Systems journal 4, 1 (1965), 25–30.

Cohen-Or, D., and Kaufman, A. 3d line voxelization and connectivity control. IEEE Computer Graphics and Applications 17, 6 (1997), 80–87.

Foley, J. D., Van, F. D., Van Dam, A., Feiner, S. K., and Hughes, J. F. Computer graphics: principles and practice, vol. 12110. Addison-Wesley Professional, 1996.

Glassner, A. S. Space subdivision for fast ray tracing. IEEE Computer Graphics and applications 4, 10 (1984), 15–24.

Kaufman, A. An Algorithm for 3D Scan-Conversion of Polygons. In EG 1987-Technical Papers (1987), Eurographics Association.

Kaufman, A., and Shimony, E. 3d scanconversion algorithms for voxel-based graphics. In Proceedings of the 1986 workshop on Interactive 3D graphics (1987), pp. 45–75.

Martisek, D. Methods of detection of equipotential surfaces in cell structures. Cells IV, Kopp Publ. Ceske Budejovice (2002), 47–54.

Martisek, D. Computer estimation of jrc index using function moments. MENDEL Journal 27, 2 (2021), 51–58.

Martisek, D., and Martisek, K. Direct volume rendering methods for cell structures. Scanning 34, 6 (2012), 367–377.

Martisek, K. Numerical methods of multispectral confocal microscopy. PhD thesis, Diploma Thesis, Brno University of Technology, Brno, Czech Republic. p 1–65, 2007.

Max, N. Optical models for direct volume rendering. IEEE Transactions on Visualization and Computer Graphics 1, 2 (1995), 99–108.

Mokrzycki, W. Algorithms of discretization of algebraic spatial curves on homogeneous cubical grids. Computers & Graphics 12, 3-4 (1988), 477–487.

Nielson, G. The volume rendering equations. tutorial for inclusion in the notes for CSE 573 (1993).

Phong, B. T. Illumination for computer generated pictures. Communications of the ACM 18, 6 (1975), 311–317.

How to Cite
Martišek, D. 2022. Mathematical Methods for 3D Reconstruction of Cell Structures. MENDEL. 28, 2 (Dec. 2022), 83-92. DOI:
Research articles