Kalman filter/deep-learning hybrid automatic boundary tracking of optical coherence tomography data for deep anterior lamellar ker a top last y (DALK)

基于卡尔曼滤波与深度学习的深层前板层角膜移植术（DALK）OCT数据自动边界跟踪

ABSTRACT

摘要

Deep anterior lamellar ker a top last y (DALK) is a highly challenging partial thickness cornea transplant surgery that replaces the anterior cornea above Descemet’s membrane (DM) with a donor cornea. In our previous work, we proposed the design of an optical coherence tomography (OCT) sensor integrated needle to acquire real-time M-mode images to provide depth feedback during OCT-guided needle insertion during Big Bubble DALK procedures. Machine learning and deep learning techniques were applied to M-mode images to automatically identify the DM in OCT M-scan data. However, such segmentation methods often produce inconsistent or jagged segmentation of the DM which reduces the model accuracy. Here we present a Kalman filter based OCT M-scan boundary tracking algorithm in addition to AIbased precise needle guidance to improve automatic DM segmentation for OCT-guided DALK procedures. By using the Kalman filter, the proposed method generates a smoother layer segmentation result from OCT M-mode images for more accurate tracking of the DM layer and epithelium. Initial ex vivo testing demonstrates that the proposed approach significantly increases the segmentation accuracy compared to conventional methods without the Kalman filter. Our proposed model can provide more consistent and precise depth sensing results, which has great potential to improve surgical safety and ultimately contributes to better patient outcomes.

深层前板层角膜移植术 (DALK) 是一种极具挑战性的部分厚度角膜移植手术，它使用供体角膜替换位于 Descemet 膜 (DM) 以上的前角膜。在之前的工作中，我们提出了一种集成光学相干断层扫描 (OCT) 传感器的针头设计，用于在 Big Bubble DALK 手术中获取实时的 M 模式图像，以在 OCT 引导下针头插入时提供深度反馈。我们将机器学习和深度学习技术应用于 M 模式图像，以自动识别 OCT M 扫描数据中的 DM。然而，此类分割方法通常会产生不一致的或锯齿状的 DM 分割，从而降低了模型的准确性。本文提出了一种基于卡尔曼滤波器的 OCT M 扫描边界跟踪算法，结合基于 AI 的精确针头引导，以改进 OCT 引导的 DALK 手术中的自动 DM 分割。通过使用卡尔曼滤波器，该方法从 OCT M 模式图像中生成了更平滑的层分割结果，从而更准确地跟踪 DM 层和上皮层。初步的离体测试表明，与没有卡尔曼滤波器的传统方法相比，该方法显著提高了分割精度。我们提出的模型可以提供更一致和精确的深度感知结果，这具有提高手术安全性的巨大潜力，并最终有助于改善患者的预后。

Keywords: Kalman filter, cornea transplant, OCT, DALK, image segmentation

关键词：卡尔曼滤波器 (Kalman filter)，角膜移植，OCT，DALK，图像分割

1. INTRODUCTION

1. 引言

The DALK is a partial thickness corneal transplant procedure that offers significant advantages over full-thickness transplants, including reduced risk of graft rejection and better preservation of endo the li al cell density [1]. The DALK technique specifically replaces the anterior stroma above DM while leaving the endothelium intact, making it a preferred option for treating conditions such as ker a to con us, stromal scarring, and other corneal path o logie s [2]. However, the success of this procedure hinges on the precise separation of the deep stroma from DM, a process that is technically challenging due to the delicate nature of the tissue and the micron-scale accuracy required.

DALK 是一种部分厚度角膜移植手术，相比全厚度移植具有显著优势，包括降低移植物排斥风险和更好地保留内皮细胞密度 [1]。DALK 技术特别替换了 DM 以上的前基质层，同时保持内皮层完整，使其成为治疗如圆锥角膜、基质瘢痕和其他角膜病变 [2] 等疾病的首选方案。然而，该手术的成功关键在于将深层基质与 DM 精确分离，这一过程由于组织的脆弱性和所需的微米级精度而具有较高的技术挑战性。

The Big Bubble technique [3] is a widely adopted method for DALK, where a needle is inserted into the corneal stroma to inject air and p neum o dissect the layers. Accurate placement of the needle is critical to avoid perforation of the DM, which would necessitate conversion to a full-thickness transplant, negating the benefits of DALK. The OCT has emerged as a transformative imaging modality in ophthalmic surgery [4][5], providing high-resolution, crosssectional images of corneal layers. By integrating an OCT sensor with the needle, our previous work demonstrated the potential of real-time depth feedback to guide needle insertion during DALK procedures. Machine learning models, particularly deep learning approaches like U-Net, were employed to segment corneal layers in OCT M-scan data, enabling autonomous or semi-autonomous needle guidance. However, these methods are often challenged by signal noise, motion artifacts, and data inconsistencies, which can lead to jagged or inaccurate segmentation of the DM and epithelium boundary as shown in Figure 1 deep learning approaches like U-Net based approach , were employed to segment corneal layers in OCT M-scan data, enabling autonomous or semi-autonomous needle guidance. However, these methods are often challenged by signal

大气泡技术 (The Big Bubble Technique) [3] 是广泛采用的 DALK 方法，其中将针插入角膜基质中注入空气以分离层次。准确放置针头对于避免穿透后弹力层 (DM) 至关重要，穿透 DM 将需要转换为全厚度移植，从而抵消 DALK 的优势。OCT 已成为眼科手术中的一种变革性成像方式 [4][5]，提供了角膜层的高分辨率横截面图像。通过将 OCT 传感器与针头集成，我们之前的工作展示了在 DALK 手术过程中利用实时深度反馈指导针插入的潜力。机器学习模型，特别是像 U-Net 这样的深度学习方法，被用于在 OCT M-scan 数据中分割角膜层，从而实现自主或半自主的针引导。然而，这些方法经常受到信号噪声、运动伪影和数据不一致的挑战，这可能导致 DM 和上皮边界的分割不平滑或不准确，如图 1 所示。

To address these challenges, we propose a novel Kalman filter/deep-learning hybrid (KDH) automatic boundary tracking approach that combines deep learning-based segmentation with a Kalman filter. The Kalman filter’s predictive capabilities smooth out segmentation artifacts and enhance the robustness of boundary tracking, making it particularly suited for noisy and dynamic surgical environments [6][7]. By integrating this method into the OCT-guided DALK workflow, the system improved the consistency and accuracy of DM and epithelium segmentation, ultimately enhancing the safety and efficacy of the procedure. Experiments demonstrate significant improvements in segmentation accuracy and robustness, highlighting the potential of this KDH approach to advance the state of OCT-guided microsurgery.

为了解决这些挑战，我们提出了一种新颖的卡尔曼滤波/深度学习混合（KDH）自动边界跟踪方法，该方法将基于深度学习的分割与卡尔曼滤波相结合。卡尔曼滤波的预测能力能够平滑分割伪影，并增强边界跟踪的鲁棒性，使其特别适用于噪声和动态的手术环境 [6][7]。通过将这种方法整合到 OCT 引导的 DALK 工作流程中，系统提高了 DM 和上皮分割的一致性和准确性，最终提升了手术的安全性和有效性。实验表明，分割准确性和鲁棒性得到了显著改善，突显了这种 KDH 方法在推动 OCT 引导显微手术状态方面的潜力。

Figure 1. Example of the inconsistent or jagged segmentation of the DM and epithelium

图 1: DM 和上皮组织不一致或锯齿状分割的示例

2. METHODS

2. 方法

2.1 Data Collection

2.1 数据收集

The dataset for this study consisted of ex vivo corneal samples collected from 12 rabbit eyes [8][9], acquired using a custom-built OCT imaging system. Each sample was subjected to a Big Bubble DALK procedure to simulate clinical conditions. M-mode OCT images were captured during the procedure, focusing on the stromal layers and Descemet’s membrane. A total of 250 OCT images were collected, of which 200 were used for training and 50 for testing. Ground truth labels for DM and epithelium boundaries were manually annotated by experienced ophthalmologists [1], ensuring accuracy and reliability of the dataset. Preprocessing steps included image normalization, denoising, and augmentation to enhance segmentation robustness.

本研究所用的数据集由12只兔眼的离体角膜样本组成 [8][9], 这些样本是通过定制的OCT成像系统获取的。每个样本都进行了大泡法深板层角膜移植 (Big Bubble DALK) 手术以模拟临床条件。在手术过程中采集了M模式 OCT 图像, 重点关注基质层和德赛梅膜 (Descemet’s membrane, DM)。总共收集了250张 OCT 图像, 其中200张用于训练, 50张用于测试。DM 和上皮边界的真实标签由经验丰富的眼科医生手动标注 [1], 确保了数据集的准确性和可靠性。预处理步骤包括图像归一化、去噪和增强, 以提高分割的鲁棒性。

2.2 Deep learning Based Segmentation

2.2 基于深度学习的分割

The deep learning-based segmentation approach used a U-Net [5] architecture as shown in Figure 2 (a), which is widely regarded for its effectiveness in biomedical image segmentation. The network consists of a contracting path and an expansive path, enabling it to capture contextual information while maintaining spatial resolution. Input OCT M-scan images were pre processed with normalization and denoising techniques to enhance the signal-to-noise ratio (SNR). The U-Net’s encoder-decoder structure, combined with skip connections, facilitated precise localization of boundaries within the corneal tissue.

基于深度学习的分割方法使用了 U-Net [5] 架构，如图 2(a) 所示，该架构因其在生物医学图像分割中的有效性而广受认可。网络由收缩路径和扩展路径组成，使其在保持空间分辨率的同时能够捕捉上下文信息。输入的 OCT M 扫描图像通过归一化和去噪技术进行了预处理，以提高信噪比 (SNR)。U-Net 的编码器-解码器结构结合跳跃连接，有助于精确定位角膜组织内的边界。

Training was performed on 200 annotated ex vivo M-scans using a $20%$ cross-validation split to minimize over fitting. The loss function used cross-entropy loss coefficient to handle class imbalance and ensure accurate boundary segmentation. Despite its ability to detect DM and epithelium boundaries, the U-Net occasionally produced jagged and inconsistent segmentation s due to signal noise and fluctuation in the OCT data. This limitation motivated the integration of the Kalman filter in the following steps to smooth the segmentation results and improve tracking consistency.

使用 20% 的交叉验证分割对 200 张标注的离体 M 扫描图进行训练，以最小化过拟合。损失函数采用交叉熵损失系数来处理类别不平衡问题，并确保准确的边界分割。尽管 U-Net 能够检测到 DM 和上皮边界，但由于 OCT 数据中的信号噪声和波动，偶尔会产生锯齿状和不一致的分割结果。这一局限性促使了在后续步骤中集成卡尔曼滤波器，以平滑分割结果并提高跟踪一致性。

Figure 2. (a) Modified U-Net architecture (b) Illustration of Kalman Filter Integration

图 2: (a) 改进的 U-Net 架构 (b) 卡尔曼滤波器集成示意图

2.3 Kalman Filter Integration

2.3 卡尔曼滤波 (Kalman Filter) 集成

To enhance the accuracy and robustness of corneal layers’ segmentation, we integrated the Kalman filter into the workflow to address the limitations of purely deep learning-based methods as shown in Figure 2 (b). The Kalman filter was configured with a state transition matrix $F=1$ , an observation matrix $H=1$ , a process noise covariance $Q=1!\times!10^{-5}$ , and an observation noise covariance $R=1$ . This configuration provided a well-balanced tradeoff between the smoothing effect and the responsiveness of the filter. The prediction and update formulas are defined as:

为了提高角膜层分割的准确性和鲁棒性，我们将卡尔曼滤波器 (Kalman filter) 集成到工作流程中，以解决纯粹基于深度学习方法的局限性，如图 2 (b) 所示。卡尔曼滤波器的配置包括状态转移矩阵 $F=1$、观测矩阵 $H=1$、过程噪声协方差 $Q=1!\times!10^{-5}$ 和观测噪声协方差 $R=1$。这种配置在平滑效果和滤波器的响应性之间提供了良好的平衡。预测和更新公式定义如下：

A sliding window technique was employed to refine the observation inputs further. For the initial 50 data points, the standard Kalman update was applied to establish a reliable state estimate. As additional data accumulated, the observation input was adaptively adjusted using a weighted average of the most recent 50 data points with $70%$ weight and the preceding 50 data points with $30%$ weight. This adaptive approach as shown in Figure 2 (b) ensured responsiveness to new data while maintaining stability, resulting in an ameliorate and consistent line for the corneal layers.

采用滑动窗口技术进一步优化观测输入。对于最初的 50 个数据点，应用标准的卡尔曼更新来建立可靠的状态估计。随着数据的累积，使用最近 50 个数据点的加权平均值（权重为 70%）和前 50 个数据点的加权平均值（权重为 30%）自适应调整观测输入。如图 2 (b) 所示，这种自适应方法确保了对新数据的响应性，同时保持了稳定性，从而为角膜层生成了一条改善且一致的线条。

During segmentation, the Kalman filter utilized predictions from the deep learning model as inputs, dynamically refining the positions of the DM and epithelium boundaries in real-time. The integration of the Kalman filter significantly minimize noise and artifacts, ensuring smooth and accurate boundary tracking even under dynamic surgical conditions.

在分割过程中，Kalman滤波器利用深度学习模型的预测作为输入，实时动态调整DM和上皮边界的位置。Kalman滤波器的集成显著减少了噪声和伪影，即使在动态手术条件下也能确保边界跟踪的平滑和准确。

3. EXPERIMENTS AND RESULTS

3. 实验与结果

3.1 Data Description

3.1 数据描述

In the experiments, the ex vivo dataset was divided into 200 image pairs for training and 50 image pairs for testing. To accommodate the requirements of M-mode OCT data and real-time tracking, each $512,\times,512$ image pair was automatically cropped into patches of size $16,\times,512,\times,32$ for input into the network. These patches were normalized using the mean and standard deviation computed from their respective training sets. During inference, the network reconstructed the processed patches back int