Three-dimensional visualization of two-dimensional data: the mathematical modeling

There are some method and tools which are use to get a vi- sualizations of one object from one media to the other media, especially in the world of computer design. But the problem is, can we get the result of visualization which is same like the object that we want to visu- alize. This paper presents the way to visualize three-dimensional object by using two-dimensional data structure in the form of a mathematical modeling. One of the important issues in this paper is how to guessing depth value by derive gradient estimates. In the other side, guessing depth value is equivalent in deriving z values of two-dimensional Carte- sian coordinated given x and y values. On this paper, we concentrated on the process of getting depth value given the two-dimensional geome- try information of the drawing. One method used in this paper is called skewed symmetry. The result were stored in the ones of data structure and were veri?ed by visualizing on the MATLAB graphic visualize kit.

[1]  Takeo Kanade,et al.  Recovery of the Three-Dimensional Shape of an Object from a Single View , 1981, Artif. Intell..

[2]  Hod Lipson,et al.  Optimization-based reconstruction of a 3D object from a single freehand line drawing , 1996, Comput. Aided Des..

[3]  Alan K. Mackworth Interpreting Pictures of Polyhedral Scenes , 1973, IJCAI.

[4]  Ralph R. Martin,et al.  Creating solid models from single 2D sketches , 1995, Symposium on Solid Modeling and Applications.

[5]  A. Macworth Interpreting pictures of polyhedral scenes , 1973 .

[6]  Takeo Kanade,et al.  A Theory of Origami World , 1979, Artif. Intell..

[7]  Irving Biederman,et al.  Human image understanding: Recent research and a theory , 1985, Comput. Vis. Graph. Image Process..

[8]  Ramakant Nevatia,et al.  Perception of 3-D Surfaces from 2-D Contours , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  W. Wen,et al.  Skewed symmetry detection of closed contours based on their geometric properties , 1995, Proceedings of Conference on Computer Architectures for Machine Perception.

[10]  Kazuhide Sugimoto,et al.  Detection of skewed-symmetrical shape , 1994, Proceedings of 1st International Conference on Image Processing.

[11]  Stuart A. Friedberg,et al.  Finding axes of skewed symmetry , 1986, Comput. Vis. Graph. Image Process..

[12]  Ivan E. Sutherland,et al.  Sketchpad a Man-Machine Graphical Communication System , 1899, Outstanding Dissertations in the Computer Sciences.

[13]  Stefan Posch,et al.  Detecting skewed symmetries , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol. III. Conference C: Image, Speech and Signal Analysis,.

[14]  Thomas Marill,et al.  Emulating the human interpretation of line-drawings as three-dimensional objects , 1991, International Journal of Computer Vision.

[15]  Adolfo Guzmán-Arenas,et al.  Decomposition of a visual scene into three-dimensional bodies , 1968, AFIPS Fall Joint Computing Conference.