基于PDE的鲁棒视觉显著性目标感知先验的图像分割

Partial Differential Equations (PDEs) based image segmentation has been widely studying in the past decades while still remains interesting. These kinds of methods usually deal with image processing in a "continues setting", either by functional optimization or directly by evolving the corresponding PDEs. Related traditional models include active contour, Level Set methods, external force fields and so on. Within these methods, theories of PDEs, variational methods, curve evolution, and differential manifold are usually used. These kinds of methods tackle the problem of image processing in a systematic and robust way and can be extended more easily. However, there still exist some major issues of the local minimum problems to suppress their roustness, i.e., evolution's sensitiveness to the initial conditions, noises, occlusions, the "equilibrium issues" in dealing with complex concavities and etc. Thanks to the development of visual saliency research, further idea to overcome the above issues is inspired. The project will deeply study the visual saliency mechanism and make it as a prior information to redefine the Homogeneity to reveal the potential factor of local minima. With the perspective of studying the posedness for PDE to conqure the bottleneck of PDEs-based segmentation to improve their robustness.

基于偏微分方程的图像分割是现代图像、视频处理领域的重要方向，虽然发展了几十年但仍然具有很强的生命力。这类方法以“连续分析”的方式，建立刻画图像处理任务的目标泛函或直接以偏微分方程建模。经典分割模型有主动轮廓，水平集方法，外力场等；主要用到变分法、偏微分方程、曲线演化、微分流形等分析方法。他们使得图像分割过程更加系统化和自动化，拓展性更好。然而，其中依然存在以下局部极值等鲁棒性问题使其发展到了瓶颈：优化结果受初始值影响，演化过程受遮挡，受噪声影响，附加外力场方法存在“平衡点问题”等使得演化早熟，归根到底是微分方程的分岔。近年出现视觉显著性方法的研究给这些问题的解决带来了重要启示。本项目拟进一步研究视觉显著性机理并以此为先验，影响区域“同质性”定义，深度挖掘产生局部极值问题的各种因素，从PDE解适定性角度考虑，籍此提高这类图像分割方法的鲁棒性，使其有效突破发展瓶颈。

按项目任务书完成了对国际及国内解决基于PDEs图像分割领域的局部极值、选取初始值、噪声鲁棒性、实时性等问题的研究进展进行全面而细致的总结和分析。同时开展了以下工作：探讨了可变或依赖于初始值的向量场实现问题，结合动力系统的相关理论来解决目标函数的优化问题；研究解决如何结合正则性及其它整体性约束，定义目标函数；建立合适的度量，改变解空间的结构，以解决局部极值和噪声问题；结合多种因素，对显著性目标检测的发展情况做充分调研和跟进，研究基于视觉显著性检测的算法；利用显著性目标感知的先验，定义出图像空间像素的相对显著性；对同质性进行进一步的探索，以此来调整解空间的拓扑结构，同时开拓了显著性的方法在具体工程中的应用。

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