Unsupervised Deformable Image Registration for Respiratory Motion Compensation in Ultrasound Images ^††thanks: ¹Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA (abhiman2, aorekhov, choset, jgaleotti)@andrew.cmu.edu

Let $I_{f}$ and $I_{m}$ be the fixed and moving ultrasound images, respectively from the same respiratory cycle. We denote a displacement field (DF) as $u_{fm}=g_{\theta}(I_{f},I_{m})$, where $g_{\theta}$ is the function we seek to model with our network and the subscript $\theta$ denotes RAFT’s [4] network parameters. RAFT is a state-of-the-art optical flow estimation network, but no prior work has shown the application of RAFT on ultrasound images, which are inherently noisier than RGB images[5]. RAFT is also needs labelled ground truth displacement fields for training. Acquiring ground truth for ultrasound images is time-consuming and labor-intensive, so we seek to make the training unsupervised. We do this by passing the output of RAFT through a Spatial Transformer Network (STN) [6] to generate a reconstructed deformed image $I_{f}^{\prime}=\textrm{STN}(u_{fm},I_{m})$. We then use a cyclic loss function, denoted as ($\mathcal{L}_{\textrm{cyclic-us}}$), to compare $I_{f}$ to $I_{f}^{\prime}$ and $I_{m}$ to $I_{m}^{\prime}$ using multi-scale structural similarity (MS-SSIM), where $I_{f}^{\prime}=\textrm{STN}(u_{fm},I_{m})$ and $I_{m}^{\prime}=\textrm{STN}(u_{mf^{\prime}},I_{f^{\prime}})$. We also add a smoothness loss term to regularize the flow prediction.

We use U-RAFT to track the displacement of every pixel in the video sequence and therefore capture the periodic movement of the tissue during respiratory motion. The first frame in the video sequence is $I_{f}$ and the rest of the frames are the moving images $I_{m}$. For the frame $i$ in the video sequence, we calculate the net displacement of the pixel at location $x^{*},y^{*}$ as, $d_{x^{*},y^{*},i}=||u_{f,m_{i}}(x^{*},y^{*})||$, where $||.||$ is the $L_{2}$ norm. We then pass the sequence of moving images $I_{m_{i}}$ to STN along with $u_{f,m_{i}}$ to retrieve the static sequence of images $I_{f_{i}}^{\prime}=STN(u_{f,m_{i}},I_{m_{i}})$. Furthermore, we compute the Fast Fourier Transform (FFT) of $d_{x^{*},y^{*}}$ over time to calculate the per-pixel displacement frequency.

The study collected ultrasound images on three live anesthetized pigs for experiments in a controlled lab setting under the supervision of clinicians. The vascular ultrasound images from two of the pigs were used for training a U-RAFT, while lung ultrasound images from the third pig were used for testing. A robotic ultrasound system was used for data collection, including a UR3e manipulator, a Fukuda Denshi portable point-of-care ultrasound scanner, and a six-axis force/torque sensor. The training dataset was collected while palpating with the robot in a sinusoidal force profile, with a minimum and maximum force of 2 N and 10 N, respectively, while the testing dataset was collected by keeping the ultrasound probe static.

Table I provides the mean displacement of pixels for all the frames before and after applying for respiratory compensation. Figure 2 shows the net displacement of one of the pixels for the whole video sequence around a critical landmark before and after the application of the compensation. Furthermore, we also calculate the respiration rate, via the FFT, by tracking pixels near the rib cage in the ultrasound images. We calculated the respiration rate to be approximately $18$ beats per minute, which is consistent with the recorded breathing rate of approximately $19$ bpm during the experiment.