直线网格B样条混合滤波GPU光线投射

摘要

To render rectilinear grid quickly to produce high quality image, this paper gives B-spline hybrid filtering and implementation speed grid that are applied to GPU-raycasting for rectilinear grid. Proposition about sign property of derivative of B-spline basics is proved. Furthermore, it is shown that there are significant errors in some cases when S&H method is used to compute derivative of B-spline. According to such a conclusion, in ray integration, S&H method is used if the condition is satisfied; otherwise B-spline basic equation is used. Moreover, proposition about range of derivatives of B-spline functions is proved, so that gradient magnitude modulation and speed grid are implemented in GPU; in ray integration, interfaces between materials are shown with gradient magnitude modulation and empty space is skipped with speed grid. As a result, GPU-raycasting with the hybrid method in this paper frees artifacts caused by generalized S&H algorithm; it is faster than stationary step GPU-raycasting based on B-spline basic equation; it can represent the true feature of things measured or simulated if they are smooth.%为了快速、高质量地绘制直线网格,提出B样条混合滤波方法,实现加速网格,并将其应用到直线网格GPU光线投射.证明了三次B样条基函数导数的符号性质,进而证明用快速三次滤波方法(S& H方法)计算非均匀B样条函数的导数会出现误差.据此,在光线积分计算中,如果条件允许,采用S & H方法；否则采用基于B样条基本公式的滤波方法.另外,证明三次B样条函数导数的范围,以实现梯度量调制和加速网格；在光线积分计算中,利用梯度量调制表现物质的分界面；利用加速网格,跳过无效积分步,加快绘制速度.实验结果表明,采用混合滤波的直线网格GPU光线投射方法能消除S&H方法导致的走样现象；与基于B样条基本公式的绘制方法相比,该方法更快；如果模拟或测量的物体本身是光滑的,该方法能快速反映其真实特征.