Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy

The Cramer-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramer-Rao lower bound for the estimation of a feature's position (e.g. of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g. the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramer-Rao lower bound are given. Under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental data

Computer image registration techniques applied to nuclear medicine images

Modern medicine has been using imaging as a fundamental tool in a wide range of applications. Consequently, the interest in automated registration of images from either the same or different modalities has increased. In this chapter, computer techniques of image registration are reviewed, and cover both their classification and the main steps involved. Moreover, the more common geometrical transforms, optimization and interpolation algorithms are described and discussed. The clinical applications examined emphases nuclear medicine

Orientation Uncertainty Characteristics of Some Pose Measuring Systems

We investigate the performance of pose measuring systems which determine an object’s pose from measurement of a few fiducial markers attached to the object. Such systems use point-based, rigid body registration to get the orientation matrix. Uncertainty in the fiducials’ measurement propagates to the uncertainty of the orientation matrix. This orientation uncertainty then propagates to points on the object’s surface. This propagation is anisotropic, and the direction along which the uncertainty is the smallest is determined by the eigenvector associated with the largest eigenvalue of the orientation data’s covariance matrix. This eigenvector in the coordinate frame defined by the fiducials remains almost fixed for any rotation of the object. However, the remaining two eigenvectors vary widely and the direction along which the propagated uncertainty is the largest cannot be determined from the object’s pose. Conditions that result in such a behavior and practical consequences of it are presented

Comparing Measured and Theoretical Target Registration Error of an Optical Tracking System

The goal of this thesis is to experimentally measure the accuracy of an optical tracking system used in commercial surgical navigation systems. We measure accuracy by constructing a mechanism that allows a tracked target to move with spherical motion (i.e., there exists a single point on the mechanism—the center of the sphere—that does not change position when the tracked target is moved). We imagine that the center of the sphere is the tip of a surgical tool rigidly attached to the tracked target. The location of the tool tip cannot be measured directly by the tracking system (because it is impossible to attach a tracking marker to the tool tip) and must be calculated using the measured location and orientation of the tracking target. Any measurement error in the tracking system will cause the calculated position of the tool tip to change as the target is moved; the spread of the calculated tool tip positions is a measurement of tracking error called the target registration error (TRE). The observed TRE will be compared to an analytic model of TRE to assess the predictions of the analytic model

Exploring the developing preterm brain with diffusion tensor magnetic resonance imaging

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Image Guidance in Telemanipulator Assisted Urology Surgery

This thesis outlines the development of an image guided surgery system, intended for use in \davinci assisted radical prostatectomy but more generally applicable to laparoscopic urology surgery. We defined the key performance parameter of the system as the accuracy of overlaying modelled anatomy onto the surgical scene. This thesis is primarily concerned with determining the system accuracy based on an analysis of the system's components. A common error measure was defined for all system components. This is an on screen error (measured in pixels) based on the error in projecting a single point lying near the apex of the prostate with the endoscope in a typical surgical pose. In this case the projected point was approximately 200 mm from the endoscope lens. An intraoperative coordinate system is first defined as the coordinate system of an optical tracking system used to track the endoscope. The MRI image of the patient is transformed into the intraoperative coordinate system. Prior to surgery the endoscope is calibrated and during surgery the endoscope is tracked, defining a transform from the coordinates of the optical tracking system to the endoscope screen. This transform is used to project the MRI image onto the endoscope video display. The early part of the thesis describes a novel algorithm for registering MRI to ultrasound images of the bone which was used to put the MRI image into the intraoperative coordinate system. Using this algorithm avoids the need for fiducial markers. The table below shows the errors (as on screen pixel RMS) due to using this algorithm. An approximate value as RMS distance error at the prostate apex point is also included