Methods Conclusions References ResultsBackground The program using the enhanced algorithm produces an optimal surface when used with simple inputs. Here, “simple” inputs refer to contour sets having only a single contour line per section and the contour lines changing more or less smoothly from one section to the next section. Surfaces generated using the enhanced version seems to be closer to optimal surfaces than the ones generated using the VTK filter. The enhanced version is also capable of dealing with some non-trivial cases such as branching. However, this program is still sub-optimal and there are many complicated cases where the program would fail to produce a decent surface. Reconstructing Surface from Planar Contours Boyeong Woo Mentors: Professor Gabor Fichtinger, Andras Lasso, Csaba Pinter Laboratory for Percutaneous Surgery, School of Computing, Queen’s University, Kingston, ON In 3D computer graphics, a triangle mesh is often used to define the surface of an object. In order to generate a triangle mesh, the surface has to be decomposed into a set of triangles, and such process is called triangulation (or tessellation into triangles). Therefore, the problem of creating a closed surface model from a set of planar contour lines can be described more specifically as the problem of finding a set of triangles which can be used to generate an accurate surface of the original structure. To further simplify the problem, we can separately look for an optimal surface between each pair of consecutive contour lines and then combine all of the sub-solutions to create the whole. The Visualization Toolkit (VTK) is an open-source software toolkit developed for 3D computer graphics, and it comes with many supportive methods for visualization such as the Delaunay triangulation. Something that was of interest to us was the filter called vtkRuledSurfaceFilter, which generates a surface from a set of parallel lines. However, this filter fails to deal with non-trivial cases, such as multiple contour lines in a single section. Several enhancements were added to the algorithm from the filter in order to be able to deal with those cases. One major enhancement is the use of dynamic programming algorithm instead of greedy algorithm used by the filter. Put simply, the filter takes an optimal choice (shorter edge) at each iteration, but the enhanced algorithm evaluates as many viable choices as possible and then takes an overall optimal choice (minimum total edge length). Planning of medical procedures, such as radiation therapy or minimally invasive interventions, almost always requires delineation of organs and other important structures by closed curves. Most frequently this is performed manually, by drawing contours around the objects on several two-dimensional cross-sectional images. Typically these two-dimensional contours need to be converted to closed surface models, to be visualized in a 3D scene, or to serve as input for analysis and processing algorithms. This conversion is quite easy to do in two steps: converting the contours to volumetric data (labelmap), and then converting this labelmap to closed surface model. However, this two-step method is a lossy conversion, as its accuracy directly depends on the resolution of the intermediate labelmap volume. Figure 1: A directed graph representing the triangulation between two contour lines. This figure is taken from [1]. Figure 2: Example of a surface generated using the enhanced algorithm with a simple contour set. The enhanced program is certainly more versatile than vtkRuledSurfaceFilter, but the program still cannot be used for practical purposes. An example of “complicated” cases where this program fails to work is the “keyhole” case, where inner and outer contours are used to represent an excluded inner volume. Also, the program will be more useful if it could close the top and bottom surfaces of each object to produce a completely closed surface. It is suggested that further research be carried out to accomplish further optimization and be able to deal with more complicated cases. [1] Meyers, D., Skinner, S., & Sloan, K. (1992). Surfaces from contours. ACM Transactions on Graphics, 11(3), Figure 3: Examples of a surface generated using the enhanced algorithm with non-trivial contour sets. Objective The goal of this project was to develop a method to bypass this intermediate step and create the closed surface model from the contour directly, thus preserving the quality of the originally drawn contours, and saving time and memory.