Hierarchical Methods in Graphics and Image Processing

层次多分辨率模型是计算机图形学和图像处理中强大而有效的计算工具，具有自适应和渐进的风格。我将集中在以下具体的主题：-应用混合层次建模方法开发的头发渲染的动态水模拟问题。例子包括瀑布的动态形状受到悬崖表面和风因素的影响，或者大浪溅到岩石上。在这项工作中，我们的目标是开发一个统一的框架，用于液体，液滴和薄雾之间的水状态转换。通过引入变化因子，扩展通过均值漂移算法实现的新兴区域分割方法的数学公式，并在尺度空间中探索该方法，从而在纹理分析和无参考图像度量领域中产生分层表示和两个新应用。研究了一种自适应分割的图像边缘检测算法。这项工作的扩展将导致一个新的稀疏矩阵表示的高维空间使用的霍夫变换在处理曲线。我的长期目标是：-推广我的混合层次建模方法到一个框架，可以处理各种复杂的自然现象的计算机图形学。-开发一个通用框架，用于从复杂图像中提取和组织对象边界，作为对象识别的通用目的的分段线和弧段。开发基于内容的无参考图像和视频质量度量。

Hierarchical multi-resolution models are powerful tools for robust and effective computation in computer graphics and image processing, in an adaptive and progressive style. I will focus on the following specific topics:- To apply the hybrid hierarchical modeling method developed for hair rendering to a dynamic water simulation problem. Examples include a waterfall's dynamic shape as influenced by the features of the cliff face and wind factors, or large waves splashing onto rocks. In this work, our goal is to develop a unified framework for water state transition between liquid, droplets, and mist.- To extend the mathematical formulation of an emerging region portioning method, achieved through the mean shift algorithm, by introducing a variation factor, and to explore this method in scale-space resulting in a hierarchical representation and two novel applications in the areas of texture analysis and no-reference image metrics.- To investigate an adaptive partitioning algorithm for edge detection in images that groups edge points hierarchically according to their natural spatial clustering. An extension of this work will result in a novel sparse matrix representation for the high-dimensional accumulators used by the Hough Transform in handling curves.My long-term goals are:- To generalize my hybrid hierarchical modeling method into a framework that can handle a variety of complex natural phenomena for computer graphics.- To develop a general framework for extracting and organizing object boundaries from complex images as piecewise lines and arc segments for the general purpose of object recognition.- To develop a content-based, no-reference image and video-quality metric.