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

本项目将研究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目标检测和识别（例如用于跟踪视频监控中的目标），医学图像的分割（例如用于识别MRI脑数据中的白质和灰质），缺失信息的遮挡和分析（例如用于从二维图像中寻找深度）以及方向扩散（例如用于分析指纹）。该项目将在计算与应用数学、计算机科学与工程以及医学图像之间进行研究。该研究是基于使用水平集技术应用于变分模型和从图像中导出的偏微分方程。该工作基于Osher-Sethian水平集方法和Mumford-Shah分割技术，使用无边缘的活动轮廓模型进行目标检测。与传统模型相比，该模型具有内部轮廓的自动检测和对噪声的鲁棒性等优点。该项目将推广和扩展这个基本模型，并提供计算效率高的实现。

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.