针对伽玛刀立体定向放射治疗计划系统中靶点的数目、位置及准直器直径选择的优化问题，提出了一种改进的基于距离变换的几何优化方法，该方法类似于选用一定数目的球去填充任意形状的三维物体，通过对距离变换图中目标中轴的分析，得出了一种快速检测中轴端点及交叉点的方法，并将该方法用于放射治疗计划系统的几何优化，将靶点置于中轴的端点或交叉点，位于端点的靶点能保证覆盖目标较尖锐的部分，位于交叉点的靶点能保证覆盖目标较宽广平坦的区域，从而能够用较少的靶点覆盖较多的目标区域，对于每个靶点，取与该靶点距离值相邻的两种准直器直径作为该靶点的候选直径，由此对每个端点，可以得到一个用二叉树表示的计划方案集合，然后根据目标优化函数，从所有方案中选择最优方案，目标函数既考虑了肿瘤的覆盖率，又考虑了非肿瘤区域正常组织的覆盖程度，实验结果表明，与已有几何优化方法相比，该方法能实现自动靶点布置，并具有较快的计算速度。

A geometrically based method of treatment planning system for gamma knife stereosurgery optimization was developed to find the best number of shots, shot locations and collimator sizes for treatment planning. The problem is similar to the problem of filling an arbitrary 3D object with spheres--the goal is that small spheres fill the sharp corners and large spheres fill more open regions so that the total number of spheres is minimized while the target is fully filled. In our approach, firstly the distance map was generated, then the end points of medial axis of the object were detected directly from distance map. Choose one of the end points as the first shot position, the sphere centered at the shot was removed from the target volume. The distance map of the remainder of the target was generated, the location of one of the cross points whose distance to the up shot is shortest was chosen as the current shot, the sphere centered at the shot was removed from the target. The process is repeated until the maximum distance value of the remainder target was less than 80% of half of the minimum collimator size (4 mm). The above steps were repeated until all end points were processed, thus binary trees corresponding to each start shot can be got to denote all possible solutions, and one of the path of all binary trees which maximized the measure of our objective was chosen as the initial optimization solution consists of the start points, the measure considered both the coverage percentage of tumor and that of normal tissue, also the sensitive of the coved normal tissue of each shot. The experimental results showe that the approach is more effective and less time consumed than the existing methods.