Radial Distortion Self-Calibration

In cameras with radial distortion, straight lines in space are in general mapped to curves in the image. Although epipolar geometry also gets distorted, there is a set of special epipolar lines that remain straight, namely those that go through the distortion center. By finding these straight epipolar lines in camera pairs we can obtain constraints on the distortion center(s) without any calibration object or plumbline assumptions in the scene. Although this holds for all radial distortion models we conceptually prove this idea using the division distortion model and the radial fundamental matrix which allow for a very simple closed form solution of the distortion center from two views (same distortion) or three views (different distortions). The non-iterative nature of our approach makes it immune to local minima and allows finding the distortion center also for cropped images or those where no good prior exists. Besides this, we give comprehensive relations between different undistortion models and discuss advantages and drawbacks.

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

One-sided Radial-Fundamental Matrix Estimation

For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsic parameters are assumed to be known, whereas the second view has unknown distortion and calibration parameters. This situation arises e.g. when one would like to register archive imagery to recently taken photos. A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework. However, only very few existing solutions apply to the calibrated-uncalibrated setting. We propose a simple and numerically stable two-step scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers. We demonstrate the performance on synthetic and real datasets.

Variations of the soft tissue thicknesses external to the ribs in Pectus Excavatum patients

Background: Surgical repair of pectus excavatum (PE) has become more popular due to improvements in the minimally invasive Nuss procedure. The pre-surgical assessment of PE patients requires Computerized Tomography (CT), as the malformation characteristics vary from patient to patient. Objective: This work aims to characterize soft tissue thickness (STT) external to the ribs among PE patients. It also presents a comparative analysis between the anterior chest wall surface before and after surgical correction. Methods: Through surrounding tissue segmentation in CT data, STT values were calculated at different lines along the thoracic wall, with a reference point in the intersection of coronal and median planes. The comparative analysis between the two 3D anterior chest surfaces sets a surgical correction influence area (SCIA) and a volume of interest (VOI) based on image processing algorithms, 3D surface algorithms, and registration methods. Results: There are always variations between left and right side STTs (2.54±2.05 mm and 2.95±2.97 mm for female and male patients, respectively). STTs are dependent on age, sex, and body mass index of each patient. On female patients, breast tissue induces additional errors in bar manual

Variations of the soft tissue thicknesses external to the ribs in pectus excavatum patients

Background: Surgical repair of pectus excavatum (PE) has become more popular due to improvements in the minimally invasive Nuss procedure. The pre-surgical assessment of PE patients requires Computerized Tomography (CT), as the malformation characteristics vary from patient to patient. Objective: This work aims to characterize soft tissue thickness (STT) external to the ribs among PE patients. It also presents a comparative analysis between the anterior chest wall surface before and after surgical correction. Methods: Through surrounding tissue segmentation in CT data, STT values were calculated at different lines along the thoracic wall, with a reference point in the intersection of coronal and median planes. The comparative analysis between the two 3D anterior chest surfaces sets a surgical correction influence area (SCIA) and a volume of interest (VOI) based on image processing algorithms, 3D surface algorithms, and registration methods. Results: There are always variations between left and right side STTs (2.54±2.05 mm and 2.95±2.97 mm for female and male patients, respectively). STTs are dependent on age, sex, and body mass index of each patient. On female patients, breast tissue induces additional errors in bar manual

Dense motion field estimation from myocardial boundary displacements

Minimally invasive cardiovascular interventions guided by multiple imaging modalities are rapidly gaining clinical acceptance for the treatment of several cardiovascular diseases. These images are typically fused with richly detailed pre-operative scans through registration techniques, enhancing the intra-operative clinical data and easing the image-guided procedures. Nonetheless, rigid models have been used to align the different modalities, not taking into account the anatomical variations of the cardiac muscle throughout the cardiac cycle. In the current study, we present a novel strategy to compensate the beat-to-beat physiological adaptation of the myocardium. Hereto, we intend to prove that a complete myocardial motion field can be quickly recovered from the displacement field at the myocardial boundaries, therefore being an efficient strategy to locally deform the cardiac muscle. We address this hypothesis by comparing three different strategies to recover a dense myocardial motion field from a sparse one, namely, a diffusion-based approach, thin-plate splines, and multiquadric radial basis functions. Two experimental setups were used to validate the proposed strategy. First, an in silico validation was carried out on synthetic motion fields obtained from two realistic simulated ultrasound sequences. Then, 45 mid-ventricular 2D sequences of cine magnetic resonance imaging were processed to further evaluate the different approaches. The results showed that accurate boundary tracking combined with dense myocardial recovery via interpolation/ diffusion is a potentially viable solution to speed up dense myocardial motion field estimation and, consequently, to deform/compensate the myocardial wall throughout the cardiac cycle. Copyright © 2015 John Wiley & Sons, Ltd.