RI: Small: Inferring Non-Rigid Geometry from Object Categories

该项目将组稀疏编码和运动非刚性结构（NRSFM）的新理论发展集成到基于模型的计算机视觉方法中。几何学是视觉感知的核心。人类毫不费力地将3D投影转化为2D投影，幸福地忽视了使这种转化成为可能所需的数学。在过去的几十年里，计算机视觉一直在努力解开这些数学秘密，认为要创造任何真正“看到”的机器，它必须能够执行从2D到3D的类似反演。从2D投影点的集合推断相机位置和场景/对象的3D结构在计算机视觉领域内被称为运动恢复结构（SFM）。 根据定义，静态3D结构是刚性的，然而，具有相同对象类别标签的3D结构的集合本质上是非刚性的;使得大规模NRSFM对于基于模型的类别分类和检测至关重要。用于对象类别分类和检测的基于模型的方法试图理解对象的投影光度外观与其底层几何之间的相互作用。然而，在过去的二十年里，这些方法在很大程度上被计算机视觉所抛弃，取而代之的是仅仅依赖于外观的方法（即基于视图的方法）。随着计算机视觉和机器人技术的不断融合，不仅要识别物体，还要了解如何抓住物体或与物体交互变得越来越重要-这是一项更适合基于模型的方法的任务。此外，随着增强现实的空间变得越来越复杂，很明显，对场景/对象的3D理解是至关重要的-基于模型的感知方法自然提供了这一点。最后，视觉机器要求越来越深入地了解视觉世界在学习过程中是如何变化的。基于模型的框架可以自然地适应学习框架内的这种类型的3D几何变化。

This project integrates new theoretical developments in group sparse coding and non-rigid structure from motion (NRSFM) within model-based methods for computer vision. Geometry is at the heart of visual perception. Humans invert the procedure of 3D to 2D projection effortlessly, blissfully ignorant of the mathematics required to make such inversion possible. Computer vision has been striving to unlock these mathematical secrets for the past few decades, with the view that to create any machine that truly "sees" it must be able to perform a similar inversion from 2D to 3D. Inferring the camera position and the 3D structure of a scene/object from an ensemble of 2D projected points is known within the field of computer vision as structure from motion (SFM). By definition a static 3D structure is rigid, however, the set of 3D structures with the same object category label is inherently non-rigid; making large-scale NRSFM crucial for model-based category classification and detection. Model-based methods for object category classification and detection attempt to understand the interplay between an object's projected photometric appearance and its underlying geometry. These methods, however, have largely been abandoned in computer vision over the last two decades in favor of methods that rely solely on appearance (i.e. view-based approaches). As the space of computer vision and robotics continues to merge it is becoming increasingly important to not only recognize an object, but also understand how to grasp or interact with it - a task much more suited to a model-based methodology. Further, as the space of augmented reality becomes more sophisticated it is clear that 3D understanding of a scene/object is crucial - something that model-based approaches to perception naturally provide. Finally, vision machines are demanding an increasingly deeper understanding of how the visual world is allowed to vary during learning. A model-based framework can naturally accommodate this type of 3D geometric variation within a learning framework.