We present a general method to estimate the fundamental matrix from a pair of images under perspective projection without the need for image point correspondences. Our method is particularly well-suited for transmission imaging, where state-of-the-art feature detection and matching approaches generally do not perform well. Estimation of the fundamental matrix plays a central role in auto-calibration methods for reflection imaging. Such methods are currently not applicable to transmission imaging. Furthermore, our method extends an existing technique proposed for reflection imaging which potentially avoids the outlier-prone feature matching step from an orthographic projection model to a perspective model. Our method exploits the idea that under a linear attenuation model line integrals along corresponding epipolar lines are equal if we compute their derivatives in orthogonal direction to their common epipolar plane. We use the fundamental matrix to parametrize this equality. Our method estimates the matrix by formulating a non-convex optimization problem, minimizing an error in our measurement of this equality. We believe this technique will enable the application of the large body of work on image-based camera pose estimation to transmission imaging leading to more accurate and more general motion compensation and auto-calibration algorithms, particularly in medical X-ray and Computed Tomography imaging.

Rotational coronary angiography using C-arm angiography systems enables intra-procedural 3-D imaging that is considered beneficial for diagnostic assessment and interventional guidance. Despite previous efforts, rotational angiography was not yet successfully established in clinical practice for coronary artery procedures due to challenges associated with substantial intra-scan respiratory and cardiac motion. While gating handles cardiac motion during reconstruction, respiratory motion requires compensation. State-of-the-art algorithms rely on 3-D / 2-D registration that requires an uncompensated reconstruction of sufficient quality. To overcome this limitation, we investigate two prior-free respiratory motion estimation methods based on the optimization of: 1) epipolar consistency conditions (ECCs) and 2) a task-based auto-focus measure (AFM). The methods assess redundancies in projection images or impose favorable properties of 3-D space, respectively, and are used to estimate the respiratory motion of the coronary arteries within rotational angiograms. We evaluate our algorithms on the publicly available CAVAREV benchmark and on clinical data. We quantify reductions in error due to respiratory motion compensation using a dedicated reconstruction domain metric. Moreover, we study the improvements in image quality when using an analytic and a novel temporal total variation regularized algebraic reconstruction algorithm. We observed substantial improvement in all figures of merit compared with the uncompensated case. Improvements in image quality presented as a reduction of double edges, blurring, and noise. Benefits of the proposed corrections were notable even in cases suffering little corruption from respiratory motion, translating to an improvement in the vessel sharpness of (6.08 ± 4.46)% and (14.7 ± 8.80)% when the ECC-based and the AFM-based compensation were applied. On the CAVAREV data, our motion compensation approach exhibits an improvement of (27.6 ± 7.5)% and (97.0 ± 17.7)% when the ECC and AFM were used, respectively. At the time of writing, our method based on AFM is leading the CAVAREV scoreboard. Both motion estimation strategies are purely image-based and accurately estimate the displacements of the coronary arteries due to respiration. While current evidence suggests the superior performance of AFM, future work will further investigate the use of ECC in the context of angiography as they solely rely on geometric calibration and projection-domain images.

Geometry and physics of absorption imaging impose certain constraints on X-ray projections. Recently, the Epipolar Consistency Conditions (ECC) have been introduced and applied to motion correction in flat-detector computed tomography (CT). They are based on redundant information in transmission images along epipolar lines. Unlike other consistency conditions for CT scans, they act directly on an arbitrary pair of X-ray images. This paper proposes an application of ECC to 3D patient tracking in interventional radiology. We evaluate the proposed method against 2D-3D registration with a previously acquired CT. Our experiments on synthetic data based on a patient CT and phantom data from an interventional C-arm demonstrate that our method is able to compensate online for rotations of up to ±10° and translations of ±25 mm between consecutive frames. We successfully track rotations of as much as 45° over 45 images. The outstanding property of the approach is that no 3D scan is required for tracking a 3D object in space. We show, that small rotations of about 3° in space and translations of about 50 mm can be tracked based on just two reference X-ray images. Since the proposed approach works directly on X-ray images, it exceeds regular 2D-3D registration with a CT in an order of magnitude in computational speed. We conclude that ECC are a simple and effective new tool for pre-aligment and online patient tracking for fluoroscopic sequences.

This paper presents the derivation of the Epipolar Consistency Conditions (ECC) between two X-ray images from the Beer-Lambert law of X-ray attenuation and the Epipolar Geometry of two pinhole cameras, using Grangeat's theorem. We motivate the use of Oriented Projective Geometry to express redundant line integrals in projection images and define a consistency metric, which can be used, for instance, to estimate patient motion directly from a set of X-ray images. We describe in detail the mathematical tools to implement an algorithm to compute the Epipolar Consistency Metric and investigate its properties with detailed random studies on both artificial and real FD-CT data. A set of six reference projections of the CT scan of a fish were used to evaluate accuracy and precision of compensating for random disturbances of the ground truth projection matrix using an optimization of the consistency metric. In addition, we use three X-ray images of a pumpkin to prove applicability to real data. We conclude, that the metric might have potential in applications related to the estimation of projection geometry. By expression of redundancy between two arbitrary projection views, we in fact support any device or acquisition trajectory which uses a cone-beam geometry. We discuss certain geometric situations, where the ECC provide the ability to correct 3D motion, without the need for 3D reconstruction.

Fundus imaging is one of the most frequently used modalities for screening, diagnosis of eye diseases and some vascular abnormalities. Due to its wide availability, automatic evaluation of fundus images offers great potential benefits to current clinical practice. The basis of many automatic evaluations or diagnosis is the segmentation of the eye background, most notably, the detection of the optic disk and the segmentation of the retinal vessel tree. In this work we propose a variant of the fast radial symmetry transform (FRST), adapted to its application in the detection of the optic disk in fundus images. We evaluated and compared the performance of our method to the standard FRST and the similar, gradient based circular Hough transform using 45 images of a high resolution database with gold standard information available. We demonstrated in our experiments that the proposed method outperforms the state-of-the-art algorithms with 0.051 ± 0.073 optic disk diameter localization error in average.

Visual discomfort is a major problem for head-mounted displays and other stereo displays. One effect that is known to reduce visual comfort is double vision, which can occur due to high disparities. Previous studies suggest that adding artificial out-of-focus blur increases the fusional limits, where the left and right image can be fused without double vision. We investigate the effect of adding artificial out-of-focus blur on visual discomfort using two different setups. One uses a stereo monitor and an eye tracker to change the depth of focus based on the gaze of the user. The other one uses a video-see through head mounted display. A study involving 18 subjects showed that the viewing comfort when using blur is significantly higher in both setups for virtual scenes. However we can not confirm without doubt that the higher viewing comfort is only related to an increase of the fusional limits, as many subjects reported that double vision did not occur during the experiment. Results for additional photographed images that have been shown to the subjects were less significant. A first prototype of an AR system extracting a depth map from stereo images and adding artificial out-of-focus blur is presented.