ITR/AP: Variational-PDE Models Using Level Sets for Computer Vision

本项目将解决图像处理和计算机视觉中的几个重要问题。这项工作的应用包括对象检测和识别（例如，用于跟踪视频监控中的对象），医学图像的分割（例如，用于识别MRI大脑数据中的白色和灰质），缺失信息的遮挡和分析（例如，用于从2-D图像中找到深度）以及方向扩散（例如，用于分析指纹）。该项目将在计算和应用数学、计算机科学和工程以及医学图像之间的边界进行研究。该研究基于将水平集技术应用于从图像导出的变分模型和偏微分方程。这项工作使用了一个活动的轮廓模型，没有边缘的目标检测，基于Osher-Sethian水平集方法和Mumford-Shah分割技术。该模型具有许多优点，包括自动检测的内部轮廓和相对于噪声的鲁棒性。该项目将概括和扩展这个基本模型，并提供计算效率的实现。

This project will attack several important problems in image processing and computer vision. The applications for this work include object detection and recognition (e.g. for tracking objects in video surveillance), segmentation of medical images (e.g. for recognizing white and gray matter in MRI brain data), occlusion and analysis of missing information (e.g. for finding depth from 2-D images), and direction diffusion (e.g. for analyzing fingerprints). The project will work at the boundary between computational and applied mathematics, computer science and engineering, and medical imagery.The research is based on using level set techniques applied to variational models and partial differential equations derived from the images. The work uses an active contour model without edges for object detection, based on the Osher-Sethian level set method and Mumford-Shah segmentation techniques. This model has many advantages over classical ones, including automatic detection of interior contours and robustness with respect to noise. The project will generalize and extend this basic model and provide computationally efficient implementations.