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.

Thoracic wall reconstruction using ultrasound images to model/bend the thoracic prosthesis for correction of pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior thoracic wall. The surgical correction of such deformity, using Nuss procedure, consists in the placement of a personalized convex prosthesis into sub-sternal position to correct the deformity. The aim of this work is the CT-scan substitution by ultrasound imaging for the pre-operative diagnosis and pre-modeling of the prosthesis, in order to avoid patient radiation exposure. To accomplish this, ultrasound images are acquired along an axial plane, followed by a rigid registration method to obtain the spatial transformation between subsequent images. These images are overlapped to reconstruct an axial plane equivalent to a CT-slice. A phantom was used to conduct preliminary experiments and the achieved results were compared with the corresponding CT-data, showing that the proposed methodology can be capable to create a valid approximation of the anterior thoracic wall, which can be used to model/bend the prosthesis

Assessment of 3D scanners for modeling Pectus Carinatum corrective bar

Pectus Carinatum (PC) is a chest deformity consisting on the anterior protrusion of the sternum and adjacent costal cartilages. Non-operative corrections, such as the orthotic compression brace, require previous information of the patient chest surface, to improve the overall brace fit. This paper focuses on the validation of the Kinect scanner for the modelling of an orthotic compression brace for the correction of Pectus Carinatum. To this extent, a phantom chest wall surface was acquired using two scanner systems – Kinect and Polhemus FastSCAN – and compared through CT. The results show a RMS error of 3.25mm between the CT data and the surface mesh from the Kinect sensor and 1.5mm from the FastSCAN sensor

Assessment of 3D scanners for modeling pectus carinatum corrective bar

Pectus Carinatum (PC) is a chest deformity consisting on the anterior protrusion of the sternum and adjacent costal cartilages. Non-operative corrections, such as the orthotic compression brace, require previous information of the patient chest surface, to improve the overall brace fit. This paper focuses on the validation of the Kinect scanner for the modelling of an orthotic compression brace for the correction of Pectus Carinatum. To this extent, a phantom chest wall surface was acquired using two scanner systems – Kinect and Polhemus FastSCAN – and compared through CT. The results show a RMS error of 3.25mm between the CT data and the surface mesh from the Kinect sensor and 1.5mm from the FastSCAN sensor.

An Electromagnetic Tracker System for the design of a dental superstructure

Nowadays, different techniques are available for manufacturing full-arch implant-supported prosthesis, many of them based on an impression procedure. Nevertheless, the long-term success of the prosthesis is highly influenced by the accuracy during such process, being affected by factors such as the impression material, implant position, angulation and depth. This paper investigates the feasibility of a 3D electromagnetic motion tracking system as an acquisition method for modeling such prosthesis. To this extent, we propose an implant acquisition method at the patient mouth, using a specific prototyped tool coupled with a tracker sensor, and a set of calibration procedures (for distortion correction and tool calibration), that ultimately obtains combined measurements of the implant’s position and angulation, and eliminating the use of any impression material. However, in the particular case of the evaluated tracking system, the order of magnitude of the obtained errors invalidates its use for this specific application.

Electromagnetic tracker feasibility in the design of a dental superstructure for edentulous patients

The success of the osseointegration concept and the Brånemark protocol is highly associated to the accuracy in the production of an implant-supported prosthesis. One of most critical steps for long-term success of these prosthesis is the accuracy obtained during the impression procedure, which is affected by factors such as the impression material, implant position, angulation and depth. This paper investigates the feasibility of 3D electromagnetic motion tracking systems as an acquisition method for modeling full-arch implant-supported prosthesis. To this extent, we propose an implant acquisition method at the patient mouth and a calibration procedure, based on a 3D electromagnetic tracker that obtains combined measurements of implant’s position and angulation, eliminating the use of any impression material. Three calibration algorithms (namely linear interpolation, higher-order polynomial and Hardy multiquadric) were tested to compensate for the electromagnetic tracker distortions introduced by the presence of nearby metals. Moreover, implants from different suppliers were also tested to study its impact on tracking accuracy. The calibration methodology and the algorithms employed proved to implement a suitable strategy for the evaluation of novel dental impression techniques. However, in the particular case of the evaluated electromagnetic tracking system, the order of magnitude of the obtained errors invalidates its use for the full-arch modeling of implant-supported prosthesis.

Real-time hand tracking for rehabilitation and character animation

Hand and finger tracking has a major importance in healthcare, for rehabilitation of hand function required due to a neurological disorder, and in virtual environment applications, like characters animation for on-line games or movies. Current solutions consist mostly of motion tracking gloves with embedded resistive bend sensors that most often suffer from signal drift, sensor saturation, sensor displacement and complex calibration procedures. More advanced solutions provide better tracking stability, but at the expense of a higher cost. The proposed solution aims to provide the required precision, stability and feasibility through the combination of eleven inertial measurements units (IMUs). Each unit captures the spatial orientation of the attached body. To fully capture the hand movement, each finger encompasses two units (at the proximal and distal phalanges), plus one unit at the back of the hand. The proposed glove was validated in two distinct steps: a) evaluation of the sensors’ accuracy and stability over time; b) evaluation of the bending trajectories during usual finger flexion tasks based on the intra-class correlation coefficient (ICC). Results revealed that the glove was sensitive mainly to magnetic field distortions and sensors tuning. The inclusion of a hard and soft iron correction algorithm and accelerometer and gyro drift and temperature compensation methods provided increased stability and precision. Finger trajectories evaluation yielded high ICC values with an overall reliability within application’s satisfying limits. The developed low cost system provides a straightforward calibration and usability, qualifying the device for hand and finger tracking in healthcare and animation industries.

A-scan ultrasound system for real-time puncture safety assessment during percutaneous nephrolithotomy

Background: Kidney stone is a major universal health problem, affecting 10% of the population worldwide. Percutaneous nephrolithotomy is a first-line and established procedure for disintegration and removal of renal stones. Its surgical success depends on the precise needle puncture of renal calyces, which remains the most challenging task for surgeons. This work describes and tests a new ultrasound based system to alert the surgeon when undesirable anatomical structures are in between the puncture path defined through a tracked needle. Methods: Two circular ultrasound transducers were built with a single 3.3-MHz piezoelectric ceramic PZT SN8, 25.4 mm of radius and resin-epoxy matching and backing layers. One matching layer was designed with a concave curvature to work as an acoustic lens with long focusing. The A-scan signals were filtered and processed to automatically detect reflected echoes. Results: The transducers were mapped in water tank and tested in a study involving 45 phantoms. Each phantom mimics different needle insertion trajectories with a percutaneous path length between 80 and 150 mm. Results showed that the beam cross-sectional area oscillates around the ceramics radius and it was possible to automatically detect echo signals in phantoms with length higher than 80 mm. Conclusions: This new solution may alert the surgeon about anatomical tissues changes during needle insertion, which may decrease the need of X-Ray radiation exposure and ultrasound image evaluation during percutaneous puncture.