New Directions in Active Contours by Reformulating Geometric Gradients

活动轮廓（在图像中演化以捕获感兴趣对象的可变形曲线）是图像处理和计算机视觉中使用最广泛的工具之一。这项调查的重点是许多现有的活动轮廓模型的数学重新制定，以提高其鲁棒性和性能，以及制定全新的活动轮廓模型，是不可能在更传统的制定。由于活动轮廓线在医学成像、制造、监视、目标跟踪、视觉检测和视频压缩等领域的重要应用，这项研究的影响将是相当广泛的。二十多年来，活动轮廓线的梯度流算法在数学上建立在一个共同的、但经常被忽视的几何L2范数基础上。研究者将通过提出替代的范数类来研究改变这一基本的统一数学基础的好处，以大大改善主动轮廓梯度流格式的行为。大量的努力已经投入到设计越来越复杂的能量泛函中，而没有考虑“标准配方”背后的数学基础。梯度流计算。通过更改活动轮廓梯度下降计算背后的基本规范，研究人员将以数学上严格和有原则的方式引入新的活动轮廓流，这些活动轮廓流的行为可以被改进和定制，而不管相应的能量如何不降低

Active contours (deformable curves that evolve within an image in order to capture an object of interest) rank among the most widely used tools in image processing and computer vision. This investigation focuses on the mathematical reformulation of many existing active contour models to improve their robustness and performance as well as the formulation of brand new active contour models that are not possible under the more traditional formulation. The impact of the this investigation is therefore expected to be quite broad given the prominence of active contour applications in many fields ranging from medical imaging, manufacturing, survelliance, target tracking, visual inspection, and video compression.For over twenty years, gradient flow schemes for active contours have been mathematically founded upon a common, though often overlooked, geometric L2 norm. The investigator will study the benefits of changing this fundamental unifying mathematical foundation by proposing alternative classes of norms to greatly improve the behavior of gradient flow schemes for active contours.A tremendous amount of effort has gone into designing more and more sophisticated energy functionals yet not into considering the mathematical foundations behind the "standard recipe" gradient flow calculations.By changing the underlying norm behind gradient descent caluclations for active contours, the investigator will introduce in a mathematically rigorous and principled manner new active contour flows whose behaviors can be improved and tailored regardless of the corresponding energy functional.