Similarity Registration Problems for 2D/3D Ultrasound Calibration
We propose a minimal solution for the similarity registration (rigid pose and scale) between two sets of 3D lines, and also between a set of co-planar points and a set of 3D lines. The first problem is solved up to 8 discrete solutions with a minimum of 2
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Introduction
Ultrasound (US) is a low-cost and real-time medical imaging technique in minimally invasive surgery and in percutaneous procedures. It observes information under the surface, so it is used to locate invisible details about vessels, nerves, or tumours. By tracking the pose of a 2D ultrasound probe (2D US) we can render 3D reconstructions from a collection of 2D slices [1], while a tracked 3D probe (3D US) is able to build large and detailed 3D models from a set of 3D scans [2]. Both 2D US and 3D US can also be used to guide other tracked medical instruments, such as biopsy needles [3], and fuse data with other imaging modalities such as endoscopes. Freehand 3D ultrasound generally refers to the extrinsic calibration between a hand-held US probe and a pose tracking device. This calibration aims at determining the rigid transformation between the US scan and the tracked marker as well as the scale factor that converts the US scan to metric coordinates, i.e. a similarity transformation. This is usually achieved by scanning a known calibration object (phantom) immersed in either water or a tissue mimicking c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VI, LNCS 9910, pp. 171–187, 2016. DOI: 10.1007/978-3-319-46466-4 11
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Fig. 1. (a) Scanning a tracked needle with a US probe; (b) a 2D US probe detects a cross section of the needle; (c) a 3D US detects a line segment.
gel. Since the speed of sound in water is different than in tissue, sometimes an alcoholic solution is used to obtain a more realistic US scale. A multitude of calibration phantoms with different shapes have been proposed in the literature [4], including intersecting wires [5], a single plane [6,7], a stylus [1,8,9], and 3D printed objects [10]. Although these methods focus on 2D US calibration, some extensions to 3D US using similar phantoms have been proposed as well [11,12] (Fig. 1). In this paper we focus on using a tracked needle as the calibration phantom. Our main motivation is towards assisted guidance and motion analysis in fetal interventions that require the extraction of in utero samples with a biopsy needle. It thus becomes a practical solution to use the same needle as a calibration object, avoiding the need to introduce new objects in the operating room and the additional burden of their sterilization. The tracked needle is detected by the pose tracking system as a 3D line, and it is scanned either as a line (3D US) or as a point (2D US). By scanning the needle under different poses, we formulate the 3D US calibration as the similarity registration between two sets of 3D lines and the 2D US calibration as the similarity registration between co-planar 3D points and 3D lines. In this paper we propose a minimal solver to the similarity registration between two sets of 3D lines. We will also show that the registration between co-planar 3D points and 3D lines is a sub-problem of the same formulation and therefore the same minimal solver can be applied. Addit
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