Abstract
Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow as an inverse problem is ill-posed. Standard approaches to determine optical flow rely on formulating and solving an optimization problem that contains both a data fidelity term and a regularization term, the latter effectively resolves the otherwise ill-posedness of the inverse problem. In this work, we depart from the deterministic formalism, and instead treat optical flow as a statistical inverse problem. We discuss how a classical optical flow solution can be interpreted as a point estimate in this more general framework. The statistical approach, whose "solution" is a distribution of flow fields, which we refer to as Bayesian optical flow, allows not only "point" estimates (e.g., the computation of average flow field), but also statistical estimates (e.g., quantification of uncertainty) that are beyond any standard method for optical flow. As application, we benchmark Bayesian optical flow together with uncertainty quantification using several types of prescribed ground-truth flow fields and images.
Abstract (translated)
光流是指在两个连续图像之间观察到的视觉运动。由于自由度通常远大于图像观察所施加的约束，因此作为反问题的光流的直接公式是不适定的。确定光流的标准方法依赖于制定和求解包含数据保真度项和正则化项的优化问题，后者有效地解决了逆问题的其他不适定性。在这项工作中，我们偏离了确定性形式主义，而是将光流作为统计反问题。我们将讨论如何在这个更通用的框架中将经典光流解决方案解释为点估计。统计方法，其“解决方案”是流场的分布，我们称之为贝叶斯光流，不仅允许“点”估计（例如，平均流场的计算），而且还允许统计估计（例如，量化）不确定性）超出任何标准的光流方法。作为应用，我们使用几种类型的规定的地面实况流场和图像来对贝叶斯光流和不确定性量化进行基准测试。
URL
https://arxiv.org/abs/1611.01230
