基于预计算的环境贴图实时O(1)滤波研究

环境贴图的O(1)滤波方法作为提高渲染图像质量的重要手段，被广泛应用于需要实时渲染速度的图形学应用中。与二维图像不同的是，环境贴图是对闭合球面的采样，其数据连续无边界。如何在保证滤波内容连续的基础上实现O(1)滤波是目前亟待解决的问题。本项目针对环境贴图中最常用的立方体图，在区域求和表的基础上，利用立方体图的特点，提出一种将立方体图上不规则区域的积分转化为辅助函数上规则长方体内积分的新思路，从而实现内容连续的实时O(1)均值滤波。在此基础上，本项目拟利用近似核函数的方法实现O(1)非均匀滤波，并进而利用分段线性近似的方法实现空间与值域核函数任意的O(1)双边滤波。此外，本项目也将利用积分直方图方法提出一种适用于立方体图的目标检测与跟踪框架。通过这些研究，本项目将产生一系列适合立方体图的新的O(1)滤波方法与目标检测、跟踪算法，这些成果可以为基于立方体图的计算机图形学与视觉应用提供重要工具。

As important tools to improve the quality of rendering images, O(1) filtering methods for environment maps have been widely used in computer graphics applications that require real-time rendering speed. However, different to 2D images, an environment map is the sampling of a closed sphere, whose data are defined in a closed surface without boundary. How to preserve the continuity of filtering content when O(1) filtering is performed is a still a problem. So far, there are few researches on this area. This project will focus on the most frequently used environment map format--cube map. Making use of the spatial distribution property of the cube map data, this project will propose a summed-area-table-based method to implement real-time O(1) average filter. The novel insight is to convert the integral of irregular regions on cube map to integral of a regular cuboid on an auxiliary 3D function. Based on the average filter, this project will design spatial non-uniform filter using the idea of kernel approximation. Thereafter, this project will design the bilateral filter with arbitrary spatial and range kernel functions by approximating the range function with piece-wise linear functions. Finally, this project will utilize integral histogram to design a framework for object detecting and tracking on cube maps. Through the researches in this project, a novel series of O(1) filtering methods, object extracting and tracking methods can be obtained. The outcomes of this project will provide important tools for not only computer graphics applications such as dynamic environment mapping, soft shadow rendering, but also computer vision applications such as panoramic image or video processing.