Problem

Intraoperative tracking of surgical instruments is an inevitable task of computer-assisted surgery. An optical tracking system often fails to precisely reconstruct the dynamic location and pose of a surgical tool due to the acquisition noise and measurement variance. Embedding a Kalman filter (KF) or any of its extensions such as extended and unscented Kalman filters (EKF and UKF) with the optical tracker resolves this issue by reducing the estimation variance and regularizing the temporal behavior. However, the current KF implementations are computationally burdensome and hence takes long execution time which hinders real-time surgical tracking.

Aim

This paper introduces a fast and computationally efficient implementation of linear KF to improve the measurement accuracy of an optical tracking system with high temporal resolution.

Methods

Instead of the surgical tool as a whole, our KF framework tracks each individual fiducial mounted on it using a Newtonian model. In addition to simulated dataset, we validate our technique against real data obtained from a high frame-rate commercial optical tracking system. We also perform experiments wherein a diffusive material (such as a drop of blood) blocks one of the fiducials and show that KF can substantially reduce the tracking error.

Results

The proposed KF framework substantially stabilizes the tracking behavior in all of our experiments and reduces the mean-squared error (MSE) by a factor of 26.84, from the order of \(10^{-1}\) to \(10^{-2}\) mm\(^{2}\). In addition, it exhibits a similar performance to UKF, but with a much smaller computational complexity.

中文翻译：

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使用卡尔曼滤波器对外科手术阵列进行快速而稳固的定位

问题

术中跟踪手术器械是计算机辅助手术的必然任务。由于采集噪声和测量差异，光学跟踪系统通常无法精确地重建手术工具的动态位置和姿势。在光学跟踪器中嵌入卡尔曼滤波器（KF）或其任何扩展，例如扩展的和无味的卡尔曼滤波器（EKF和UKF），可以通过减少估计方差并规范化时间行为来解决此问题。但是，当前的KF实施在计算上很繁琐，因此执行时间长，这妨碍了实时手术跟踪。

目标

本文介绍了线性KF的快速且计算效率高的实现，以提高具有高时间分辨率的光学跟踪系统的测量精度。

方法

我们的KF框架使用牛顿模型来跟踪安装在其上的每个基准，而不是整个手术工具。除了模拟数据集之外，我们还针对从高帧频商用光学跟踪系统获得的真实数据验证了我们的技术。我们还进行了实验，其中扩散材料（例如一滴血）阻塞了基准点之一，并表明KF可以大大降低跟踪误差。

结果

拟议的KF框架在我们所有的实验中都基本稳定了跟踪行为，并将均方误差（MSE）降低了26.84倍，从\（10 ^ {-1} \）到\（10 ^ { -2} \） 毫米\（^ {2} \）。此外，它表现出与UKF相似的性能，但计算复杂度却小得多。