# Automatic 3D MRI-Ultrasound Registration for Image Guided Arthroscopy
## 1 Introduction  
Knee arthroscopy is a minimally invasive surgery (MIS) commonly used to treat intra-articular knee disorders [1]. The procedure is performed by inserting an arthroscope and a surgical tool into the knee joint through small incisions. The setup allows the surgeon to inspect the joint through the arthroscopic view displayed on a screen while altering the leg position to allow the scope to capture the required tissues. Despite offering several clinical advantages, arthroscopic procedures face long-standing challenges such as physically-demanding ergonomics during patient manipulation, lack of depth perception, limitedfield of view, and counter-intuitive hand-eye coordination between scope and surgical instruments.Even with skilled operator manipulation, a complex procedure like this can cause unintended trauma and post-operative complications [2; 3; 4]. To overcome these setbacks, an image guidance platform which uses both intra-operative and pre-operative imaging, in particular US and MRI, is proposed in [5]. This image guidance platform enables the surgeon to track and visualize both the target tissue distribution and the position of the surgical tool(s) in real-time. Intra-operative US is currently the only non-invasive, non-ionizing, imaging modality compatible with the knee arthroscopy surgical setup that can offer real-time imaging for guidance during the surgery [6; 7]. However, US can only offer a limited field of view [8], with complex image interpretation. On the other hand, MRI provides a superior soft-tissue contrast, high resolution, as well as field of view covering the entire surgical site (total knee). Pre-operative MRI allows the surgeon to derive and use the information missing from the intra-operative US, enabling a comprehensive view of the bony and soft tissues. Therefore, the combination of both the modalities would synergistically integrate high contrast, large field-of-view, semantically labelable pre-operative MRI data into the fast, intra-operative, partial view 3D US and enable image-guided robotic surgery or MIS. This fusion not only provides a better visualization of structures of interest but also safely enhances the level of automation of MIS. This requires a quick and automatic registration of intra-operative US with pre-operative MRI. Though relatively new for arthroscopy, multi-modal registration of US and MRI has been previously studied in the field of brain surgery where intra-operative US is used to track brain shift and tumor resection. The MICCAI Challenge CuRIOUS provided a public platform to benchmark MRI-US registration on the RESECT dataset [9]. A total of six fully automated registration algorithms are presented in this challenge [10]. These algorithms were tested on 12 patient volumes and the least registration error, which is \(1.57\pm 0.96\) mm, was reported by the team ImFusion who performed rigid registration using the LC\({}^{2}\) metric [11]. Another recent work [12] proposed combined segmentation based MRI-US registration approach in image-guided neurosurgery. Completely automatic registration of US and MRI volumes is a complex problem with no satisfactory solution so far [11]. It is primarily because of the entirely different principles used to capture the information in the two modalities [11]. Hence, the direct registration of the two modalities is not easily achievable in the image intensity domain using traditional metrics like the sum of squared distances, mutual information [13] or correlation [14]. Gradient-based methods have also been used, but they tend to discard valuable MRI intensity information [15]. Specifically targeting the multi-modal registration, a similarity measure, LC\({}^{2}\), was proposed in [11], which is invariant to local changes with respect to brightness, contrast, etc. The metric was initially designed for US-CT [16] and later adapted to US-MRI registration. The other challenging aspect of automating the MRI-US registration is the initialization.