Registration techniques for computer assisted orthopaedic surgery

The registration of 3D preoperative medical data to patients is a key task in developing computer assisted surgery systems. In computer assisted surgery, the patient in the operation theatre must be aligned with the coordinate system in which the preoperative data has been acquired, so that the planned surgery based on the preoperative data can be carried out under the guidance of the computer assisted surgery system.The aim of this research is to investigate registration algorithms for developing computer assisted bone surgery systems. We start with reference mark registration. New interpretations are given to the development of well knowm algorithms based on singular value decomposition, polar decomposition techniques and the unit quaternion representation of the rotation matrix. In addition, a new algorithm is developed based on the estimate of the rotation axis. For non-land mark registration, we first develop iterative closest line segment and iterative closest triangle patch registrations, similar to the well known iterative closest point registration, when the preoperative data are dense enough. We then move to the situation where the preoperative data are not dense enough. Implicit fitting is considered to interpolate the gaps between the data . A new ellipsoid fitting algorithm and a new constructive implicit fitting strategy are developed. Finally, a region to region matching procedure is proposed based on our novel constructive implicit fitting technique. Experiments demonstrate that the new algorithm is very stable and very efficient

Content based image pose manipulation

This thesis proposes the application of space-frequency transformations to the domain of pose estimation in images. This idea is explored using the Wavelet Transform with illustrative applications in pose estimation for face images, and images of planar scenes. The approach is based on examining the spatial frequency components in an image, to allow the inherent scene symmetry balance to be recovered. For face images with restricted pose variation (looking left or right), an algorithm is proposed to maximise this symmetry in order to transform the image into a fronto-parallel pose. This scheme is further employed to identify the optimal frontal facial pose from a video sequence to automate facial capture processes. These features are an important pre-requisite in facial recognition and expression classification systems. The under lying principles of this spatial-frequency approach are examined with respect to images with planar scenes. Using the Continuous Wavelet Transform, full perspective planar transformations are estimated within a featureless framework. Restoring central symmetry to the wavelet transformed images in an iterative optimisation scheme removes this perspective pose. This advances upon existing spatial approaches that require segmentation and feature matching, and frequency only techniques that are limited to affine transformation recovery. To evaluate the proposed techniques, the pose of a database of subjects portraying varying yaw orientations is estimated and the accuracy is measured against the captured ground truth information. Additionally, full perspective homographies for synthesised and imaged textured planes are estimated. Experimental results are presented for both situations that compare favourably with existing techniques in the literature

Vision-based Autonomous Navigation using Moon and Earth images

This document explores the possibility of a novel approach to trajectory determination based on optical observation of nearby celestial bodies, and describes its development, implementation and testing. The initial idea was spurred by the need to give the Orion capsule, the next-generation manned spacecraft currently in development at NASA, a backup autonomous positioning system. Among other missions, Orion is designed to transport a crew to and from the Moon. The presence of individuals on board tightens the safety requirements, and therefore it is necessary to provide a backup positioning system in case contact with ground is lost. However, rather that develop and install specific hardware on the craft, this work attempts to use data form a pre-existing sensor, an optic camera, for position estimation. This research consists of three main sections: first, analysis of the images captured by camera, to identify the geometrical features of interest of the observed celestial bodies (namely apparent radius, center position and orientation). Second, estimate of these properties with various best fitting algorithms, and derivation of orientation and position of the spacecraft in an inertial frame. And last, best fitting of the gathered position data with a newly developed algorithm based on Bézier functions. Each of these parts are discussed in detail. Results show that the image processing algorithm developed is capable to meet the accuracy requirements imposed by the mission, and that Bézier functions are a suitable tool to efficiently interpolate space trajectories, favorably comparing to more complex techniques like Iterative Batch Least Square and Extended Kalman Filter

The Three-Dimensional Circumstellar Environment of SN 1987A

We present the detailed construction and analysis of the most complete map to date of the circumstellar environment around SN 1987A, using ground and space-based imaging from the past 16 years. PSF-matched difference-imaging analyses of data from 1988 through 1997 reveal material between 1 and 28 ly from the SN. Careful analyses allows the reconstruction of the probable circumstellar environment, revealing a richly-structured bipolar nebula. An outer, double-lobed ``Peanut,'' which is believed to be the contact discontinuity between red supergiant and main sequence winds, is a prolate shell extending 28 ly along the poles and 11 ly near the equator. Napoleon's Hat, previously believed to be an independent structure, is the waist of this Peanut, which is pinched to a radius of 6 ly. Interior to this is a cylindrical hourglass, 1 ly in radius and 4 ly long, which connects to the Peanut by a thick equatorial disk. The nebulae are inclined 41\degr south and 8\degr east of the line of sight, slightly elliptical in cross section, and marginally offset west of the SN. From the hourglass to the large, bipolar lobes, echo fluxes suggest that the gas density drops from 1--3 cm^{-3} to >0.03 cm^{-3}, while the maximum dust-grain size increases from ~0.2 micron to 2 micron, and the Si:C dust ratio decreases. The nebulae have a total mass of ~1.7 Msun. The geometry of the three rings is studied, suggesting the northern and southern rings are located 1.3 and 1.0 ly from the SN, while the equatorial ring is elliptical (b/a < 0.98), and spatially offset in the same direction as the hourglass.Comment: Accepted for publication in the ApJ Supplements. 38 pages in apjemulate format, with 52 figure

A mathematical framework for contact detection between quadric and superquadric surfaces

The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C2 continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton-Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C2 continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super)ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.Fundação para a Ciência e a Tecnologia (FCT

Guided Medical Data Segmentation Using Structure-Aligned Planar Contours

Segmentation of 3D/4D biological images is a critical step for a wide range of applications such as treatment planning, quantitative analysis, virtual simulations, and rendering visualizations. Automatic segmentation methods are becoming more reliable, but many experts still rely on manual intervention which makes segmentation a time and resource intensive bottleneck. Marking boundary contours in 3D images can be difficult when images are often noisy or the delineation of biological tissue is unclear. Non-parallel contours can be more accurate and reduce the amount of marking necessary, but require extra effort to ensure boundary consistency and maintain spatial orientation. This dissertation focuses three problems that pertain to drawing non-parallel contour networks and generating a segmentation surface from those networks. First a guided structure-aligned segmentation system is detailed that utilizes prior structure knowledge from past segmentations of similar data. It employs a contouring protocol to aid in navigating the volume data and support using arbitrarily-oriented contouring planes placed to capture or follow the global structure shape. A user study is provided to test how well novices perform segmentation using this system. The following two problems then aim to improve different aspects of this system. A new deformation approach to reconstruction is discussed which deforms previous segmentation meshes to fit protocol drawn contours from new data instances in order to obtain accurate segmentations that have the correct topology and general shape and preserves fine details. The focus is on the problem of finding a correspondence between a mesh and a set of contours describing a similar shape. And finally, a new robust algorithm that resolves inconsistencies in contour networks is detailed. Inconsistent contours are faster and less demanding to draw, and they allow the segmenter to focus on drawing boundaries and not maintaining consistency. However, inconsistency is detrimental to most reconstruction algorithms, so the network must be fixed as a post process after drawing