Rolling shutter (RS) cameras dominate consumer and smartphone markets. Several methods for computing the absolute pose of RS cameras have appeared in the last 20 years, but the relative pose problem has not been fully solved yet. We provide a unified theory for the important class of order-one rolling shutter (RS$_1$) cameras. These cameras generalize the perspective projection to RS cameras, projecting a generic space point to exactly one image point via a rational map. We introduce a new back-projection RS camera model, characterize RS$_1$ cameras, construct explicit parameterizations of such cameras, and determine the image of a space line. We classify all minimal problems for solving the relative camera pose problem with linear RS$_1$ cameras and discover new practical cases. Finally, we show how the theory can be used to explain RS models previously used for absolute pose computation.

翻译：卷帘快门（RS）相机在消费级和智能手机市场中占据主导地位。过去20年间，虽已涌现多种计算RS相机绝对位姿的方法，但其相对位姿问题尚未完全解决。本文针对重要的一阶卷帘快门（RS$_1$）相机类别建立统一理论。该类相机将透视投影推广至RS相机，通过有理映射将空间一般点精确投影为单一像点。我们提出新型反投影RS相机模型，刻画RS$_1$相机的特性，构建其显式参数化方法，并确定空间直线的像。分类了线性RS$_1$相机相对位姿求解的所有最小问题，发现新实用情形。最后，展示该理论如何解释先前用于绝对位姿计算的RS模型。