Biopsy-needle depth estimation in limited-angle tomography using multiple view geometry

Introduction Recently, compressed-sensing based algorithms have enabled volume reconstruction from projection images acquired over a relatively small angle 휃휃<20∘ [1]. These methods yield depth estimation of surgical tools, such as biopsy needles, with respect to anatomical structures. However, they are computationally expensive and time consuming, rendering them unattractive for image-guided interventions. Papalazarou proposed to apply depth estimation algorithms for multi-camera systems on projection data from C-arm X-ray systems [2]. Inspired by this work, we propose an alternative approach for depth estimation of biopsy needles during image-guided interventions, in which we split the problem in two parts (i.e. needle depth estimation and volume reconstruction) and solve them independently. Methodology The proposed system consists of three steps: (1) needle extraction, (2) depth estimation and (3) volume reconstruction. In the first step, we detect the biopsy needle in the projection images and remove it by interpolation. Next, we employ epipolar geometry, see Figure 1, to find point-to-point correspondences in the projection images to triangulate the 3D position of the needle in the volume. In the last step, we use the filtered projection images to reconstruct the local anatomical structures and indicate the position of the needle in this volume. We have adjusted the widely used Filtered Backprojection algorithm, such that it fits in the geometrical framework as proposed by Papalazarou [2]. Results For validation of the algorithm, we have recorded a full CT scan (180∘ + fan angle) of a phantom with an inserted biopsy needle. Using the full sinogram, a 5123 voxel ground truth volume is constructed. Next, all subsets of two images with angular difference 훿훿훿 of the sinogram are used for evaluation of the proposed algorithm. Finally, the depth estimation error is computed as the average difference between the estimated position of the needle and the position of the needle in the ground truth volume. The average error for different angles is given in Table 1. Conclusions Based on the results of this initial phantom study, we conclude that multiple view geometry offers an attractive alternative to time consuming iterative methods for the depth estimation of surgical tools during C-arm-based image-guided interventions