The Kinematic Theory of rapid movements and its associated Sigma-Lognormal model have been extensively used in a large variety of applications. While the physical and biological meaning of the model have been widely tested and validated for rapid movements, some shortcomings have been detected when it is used with continuous long and complex movements. To alleviate such drawbacks, and inspired by the motor equivalence theory and a conceivable visual feedback, this paper proposes a novel framework to extract the Sigma-Lognormal parameters, namely iDeLog. Specifically, iDeLog consists of two steps. The first one, influenced by the motor equivalence model, separately derives an initial action plan defined by a set of virtual points and angles from the trajectory and a sequence of lognormals from the velocity. In the second step, based on a hypothetical visual feedback compatible with an open-loop motor control, the virtual target points of the action plan are iteratively moved to improve the matching between the observed and reconstructed trajectory and velocity. During experiments conducted with handwritten signatures, iDeLog obtained promising results as compared to the previous development of the Sigma-Lognormal.

翻译：快速运动的运动学理论及其关联的西格玛对数正态模型已在大量应用中得到广泛使用。尽管该模型在快速运动中的物理和生物学意义已得到充分验证，但在处理连续、长程复杂运动时暴露出若干不足。为缓解这些问题，受运动等价理论和假设性视觉反馈机制的启发，本文提出了一种全新的西格玛对数正态参数提取框架——iDeLog。具体而言，iDeLog包含两个步骤：第一步受运动等价模型影响，从轨迹中独立推导由虚拟点与角度定义的初始动作计划，同时从速度中推导出一系列对数正态分布序列；第二步基于符合开环运动控制假设的视觉反馈机制，通过迭代移动动作计划中的虚拟目标点，以提升观测轨迹与重建轨迹及其速度之间的匹配度。在手写签名实验中，与西格玛对数正态模型的先前版本相比，iDeLog取得了显著更优的结果。