Epipolar Consistency in Fluoroscopy for Image-Based Tracking

Abstract

Geometry and physics of absorption imaging impose certain constraints on X-ray projections. Various consistency conditions have been derived in the Computed Tomography (CT) community under the assumption of specific scanner trajectories. They can be exploited, for example, in truncation and motion correction. Recently, the Epipolar Consistency Conditions (ECC) [1] have been derived from the epipolar geometry between two arbitrary flat-panel projections. The fact that they make no assumption on trajectory enables us to apply the ECC to patient tracking in fluoroscopy for interventional radiology. For the first time, we perform 3D tracking of an object solely based on the consistency between 2D X-ray shots. The core idea is that before an intervention under fluoroscopy, between two and five reference images of the region of interest are acquired from different angles. We suggest, that an optimization of the ECC of an unseen image with respect to a few reference images enables us determine a rigid 3D pose of an object or patient.The ECC are based on the observation, that certain lines in X-ray images contain redundant information. Intuitively, integrating over a line in a projection image is roughly the same as integrating over the corresponding plane E of absorption coefficients through the object. The plane E is the plane through the source position which intersects the detector in the respective line. For the projection matrices P 0 , P 1 ∈ R 3×4 , the epipolar lines l 0 , l 1 ∈ P 2 are special lines in the two images, whose corresponding epipolar plane E is the same [2]:There are two redundant ways to compute the plane integral over E from either l 0 or l 1 , respectively. Epipolar Consistency can thus be quantified by taking several epipolar planes and measuring the difference between these redundant line integrals. Let ρ I (l) = ρ I (α,t) denote the Radon transform of the projection image I at line l of angle α to the image u-axis and distance t to the origin. The Epipolar Consistency Conditions statewhere the derivative d dt in direction of line normals accounts for non-parallel ray geometries [1].In this work, we assume to have a fluoroscopic video of a patient and a set of reference projections of known projection geometry. Patient movement results in inconsistencies of the fluoroscopic image I 0 with respect to the reference projections. Our goal is to estimate patient motion by minimizing these inconsistencies. A 6-DOF rigid motion is represented by the parameter vector ϕ . For each reference image I i we definite a metric over a set of epipolar planes E = {E 1 , . . . ,which should be minimized over patient motion ϕ . There are several assumptions involved in the ECC. Among those, first, an absorption-only model for X-ray physics is assumed when computing the "ray-sums", which neglects scatter and other non-linear effects of intensity. Second, the method is based on line-integrals in the projection images. Information is therefore obtained only in an orthogonal direction to these lines. It is essential,...

Cone-beam consistency conditions for planar trajectories with parallel and perpendicular detectors

“…However, we are mainly interested in sources on a trajectory in R 3 , not on a two-or threedimensional manifold.…”

Range Imaging for Motion Compensation in C-Arm Cone-Beam CT of Knees under Weight-Bearing Conditions

“…Results showed improved sharpness at the bone outline, but a motion free supine scan might not always be available. Moreover, epipolar and Fourier consistency conditions, which minimize the inconsistency in the projection data, have been investigated for this application [22][23][24].…”

Comparative Evaluation of Cone-Beam Consistency Conditions for Mono-Material Beam Hardening Correction in Flat Detector Computed Tomography

“…that can be enforced on cone-beam projection pairs have gained traction in recent years. The pair-wise or epipolar [8] cone-beam consistency conditions yield numerous redundant values from each projection pair, making the robust estimation of model parameters feasible. Besides, they eliminate the need for a perfect circular X-ray source trajectory in axial scans.…”

“…The intermediate function values of each Radon plane can be computed from the projections acquired at various rotation angles if the plane intersects corresponding detectors. If we consider a pair of projections, numerous planes intersecting the detectors and containing the line connecting two source positions can be found, providing a vector of redundant values or conditions [11] [8]. In this paper, the conditions derived from the intermediate functions [12] [13] are termed as Grangeat (GCC) and Smith Consistency Conditions (SCC).…”

“…In addition, Fan-Beam Consistency Conditions (FBCC) can be reformulated as pairwise conditions and can be enforced on cone-beam projections as described in [14] and [15]. Many applications of pairwise cone-beam consistency conditions can be found in the literature including misalignment correction (GCC) [11], 3D rigid motion compensation (GCC) [16], image-based tracking in fluoroscopy (GCC) [8], geometric calibration (FBCC) [17] and 2D-3D registration (GCC) [18].…”