In spatial augmented reality applications, incorrect projection mapping may occur when projecting images onto moving non-rigid surfaces. This may detract from the user experience, as the image may not be perceived as originally intended. This is especially apparent when using low-cost projectors and cameras or when surfaces are moving quickly. In this paper, an algorithm is developed which predicts the motion of a non-rigid surface, so that when an image is being projected onto the surface, the projection “matches” the surface shape, while using low-cost equipment. Using an interconnected mass–spring–damper system to model the surface, the surface position is predicted using a Kalman filter-based algorithm, which also compensates for the processing delays and fast-moving surfaces. To accurately model real-world materials, the mass–spring system parameters are found using a system identification approach. When the prediction algorithm is implemented experimentally, in real-time, the results show convergent results in the sense that the surface predictions converge to the measured position of a non-rigid surface. The error results show that the algorithm is both accurate and robust and can currently be applied in spatial augmented reality applications.

在空间增强现实应用中，将图像投影到移动的非刚性表面上时，可能会发生不正确的投影映射。这可能会损害用户体验，因为可能无法将图像视为最初的意图。当使用低成本的投影仪和照相机或表面快速移动时，这一点尤其明显。在本文中，开发了一种算法，该算法可预测非刚性表面的运动，以便在将图像投影到表面上时，投影“匹配”表面形状，同时使用低成本的设备。使用互连的质量－弹簧－阻尼器系统对表面进行建模，可以使用基于卡尔曼滤波器的算法预测表面位置，该算法还可以补偿加工延迟和快速移动的表面。为了准确地模拟现实世界的材料，使用系统识别方法找到质量弹簧系统参数。当通过实验实现预测算法时，在表面预测收敛到非刚性表面的测量位置的意义上，结果显示收敛的结果。错误结果表明该算法既准确又健壮，目前可以应用于空间增强现实应用中。