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

Design study for LANDSAT-D attitude control system

The gimballed Ku-band antenna system for communication with TDRS was studied. By means of an error analysis it was demonstrated that the antenna cannot be open loop pointed to TDRS by an onboard programmer, but that an autotrack system was required. After some tradeoffs, a two-axis, azimuth-elevation type gimbal configuration was recommended for the antenna. It is shown that gimbal lock only occurs when LANDSAT-D is over water where a temporary loss of the communication link to TDRS is of no consequence. A preliminary gimbal control system design is also presented. A digital computer program was written that computes antenna gimbal angle profiles, assesses percent antenna beam interference with the solar array, and determines whether the spacecraft is over land or water, a lighted earth or a dark earth, and whether the spacecraft is in eclipse

Euler's fluid equations: Optimal Control vs Optimization

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the \emph {same} Euler fluid equations, although their Lagrangian parcel dynamics are \emph{different}. This is a result of the \emph{gauge freedom} in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.Comment: 12 page

Analytical derivation of elasticity in breast phantoms for deformation tracking

Patient-specific biomedical modeling of the breast is of interest for medical applications such as image registration, image guided procedures and the alignment for biopsy or surgery purposes. The computation of elastic properties is essential to simulate deformations in a realistic way. This study presents an innovative analytical method to compute the elastic modulus and evaluate the elasticity of a breast using magnetic resonance (MRI) images of breast phantoms.An analytical method for elasticity computation was developed and subsequently validated on a series of geometric shapes, and on four physical breast phantoms that are supported by a planar frame. This method can compute the elasticity of a shape directly from a set of MRI scans. For comparison, elasticity values were also computed numerically using two different simulation software packages.Application of the different methods on the geometric shapes shows that the analytically derived elongation differs from simulated elongation by less than 9% for cylindrical shapes, and up to 18% for other shapes that are also substantially vertically supported by a planar base. For the four physical breast phantoms, the analytically derived elasticity differs from numeric elasticity by 18% on average, which is in accordance with the difference in elongation estimation for the geometric shapes. The analytic method has shown to be multiple orders of magnitude faster than the numerical methods.It can be concluded that the analytical elasticity computation method has good potential to supplement or replace numerical elasticity simulations in gravity-induced deformations, for shapes that are substantially supported by a planar base perpendicular to the gravitational field. The error is manageable, while the calculation procedure takes less than one second as opposed to multiple minutes with numerical methods. The results will be used in the MRI and Ultrasound Robotic Assisted Biopsy (MURAB) project

Error in target-based georeferencing and registration in terrestrial laser scanning

Terrestrial laser scanning (TLS) has been used widely for various applications, such as measurement of movement caused by natural hazards and Earth surface processes. In TLS surveying, registration and georeferencing are two essential steps, and their accuracy often determines the usefulness of TLS surveys. So far, evaluation of registration and georeferencing errors has been based on statistics obtained from the data processing software provided by scanner manufacturers. This paper demonstrates that these statistics are incompetent measures of the actual registration and georeferencing errors in TLS data and, thus, should no longer be used in practice. To seek a suitable replacement, an investigation of the spatial pattern and the magnitude of the actual registration and georeferencing errors in TLS data points was undertaken. This led to the development of a quantitative means of estimating the registration- or georeferencing-induced positional error in point clouds. The solutions proposed can aid in the planning of TLS surveys where a minimum accuracy requirement is known, and are of use for subsequent analysis of the uncertainty in TLS datasets

Discontinuity preserving image registration for breathing induced sliding organ motion

Image registration is a powerful tool in medical image analysis and facilitates the clinical routine in several aspects. It became an indispensable device for many medical applications including image-guided therapy systems. The basic goal of image registration is to spatially align two images that show a similar region of interest. More speci�cally, a displacement �eld respectively a transformation is estimated, that relates the positions of the pixels or feature points in one image to the corresponding positions in the other one. The so gained alignment of the images assists the doctor in comparing and diagnosing them. There exist di�erent kinds of image registration methods, those which are capable to estimate a rigid transformation or more generally an a�ne transformation between the images and those which are able to capture a more complex motion by estimating a non-rigid transformation. There are many well established non-rigid registration methods, but those which are able to preserve discontinuities in the displacement �eld are rather rare. These discontinuities appear in particular at organ boundaries during the breathing induced organ motion. In this thesis, we make use of the idea to combine motion segmentation with registration to tackle the problem of preserving the discontinuities in the resulting displacement �eld. We introduce a binary function to represent the motion segmentation and the proposed discontinuity preserving non-rigid registration method is then formulated in a variational framework. Thus, an energy functional is de�ned and its minimisation with respect to the displacement �eld and the motion segmentation will lead to the desired result. In theory, one can prove that for the motion segmentation a global minimiser of the energy functional can be found, if the displacement �eld is given. The overall minimisation problem, however, is non-convex and a suitable optimisation strategy has to be considered. Furthermore, depending on whether we use the pure L1-norm or an approximation of it in the formulation of the energy functional, we use di�erent numerical methods to solve the minimisation problem. More speci�cally, when using an approximation of the L1-norm, the minimisation of the energy functional with respect to the displacement �eld is performed through Brox et al.'s �xed point iteration scheme, and the minimisation with respect to the motion segmentation with the dual algorithm of Chambolle. On the other hand, when we make use of the pure L1-norm in the energy functional, the primal-dual algorithm of Chambolle and Pock is used for both, the minimisation with respect to the displacement �eld and the motion segmentation. This approach is clearly faster compared to the one using the approximation of the L1-norm and also theoretically more appealing. Finally, to support the registration method during the minimisation process, we incorporate additionally in a later approach the information of certain landmark positions into the formulation of the energy functional, that makes use of the pure L1-norm. Similarly as before, the primal-dual algorithm of Chambolle and Pock is then used for both, the minimisation with respect to the displacement �eld and the motion segmentation. All the proposed non-rigid discontinuity preserving registration methods delivered promising results for experiments with synthetic images and real MR images of breathing induced liver motion