Nonrigid Registration Using Regularization that Accomodates Local Tissue Rigidity

Regularized nonrigid medical image registration algorithms usually estimate the deformation by minimizing a cost function, consisting of a similarity measure and a penalty term that discourages “unreasonable” deformations. Conventional regularization methods enforce homogeneous smoothness properties of the deformation field; less work has been done to incorporate tissue-type-specific elasticity information. Yet ignoring the elasticity differences between tissue types can result in non-physical results, such as bone warping. Bone structures should move rigidly (locally), unlike the more elastic deformation of soft issues. Existing solutions for this problem either treat different regions of an image independently, which requires precise segmentation and incurs boundary issues; or use an empirical spatial varying “filter” to “correct” the deformation field, which requires the knowledge of a stiffness map and departs from the cost-function formulation. We propose a new approach to incorporate tissue rigidity information into the nonrigid registration problem, by developing a space variant regularization function that encourages the local Jacobian of the deformation to be a nearly orthogonal matrix in rigid image regions, while allowing more elastic deformations elsewhere. For the case of X-ray CT data, we use a simple monotonic increasing function of the CT numbers (in HU) as a “rigidity index” since bones typically have the highest CT numbers. Unlike segmentation-based methods, this approach is flexible enough to account for partial volume effects. Results using a B-spline deformation parameterization illustrate that the proposed approach improves registration accuracy in inhale-exhale CT scans with minimal computational penalty.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85935/1/Fessler216.pd

Image Guided Respiratory Motion Analysis: Time Series and Image Registration.

The efficacy of Image guided radiation therapy (IGRT) systems relies on accurately extracting, modeling and predicting tumor movement with imaging techniques. This thesis investigates two key problems associated with such systems: motion modeling and image processing. For thoracic and upper abdominal tumors, respiratory motion is the dominant factor for tumor movement. We have studied several special structured time series analysis techniques to incorporate the semi-periodicity characteristics of respiratory motion. The proposed methods are robust towards large variations among fractions and populations; the algorithms perform stably in the presence of sparse radiographic observations with noise. We have proposed a subspace projection method to quantitatively evaluate the semi-periodicity of a given observation trace; a nonparametric local regression approach for real-time prediction of respiratory motion; a state augmentation scheme to model hysteresis; and an ellipse tracking algorithm to estimate the trend of respiratory motion in real time. For image processing, we have focused on designing regularizations to account for prior information in image registration problems. We investigated a penalty function design that accommodates tissue-type-dependent elasticity information. We studied a class of discontinuity preserving regularizers that yield smooth deformation estimates in most regions, yet allow discontinuities supported by data. We have further proposed a discriminate regularizer that preserves shear discontinuity, but discourages folding or vacuum generating flows. In addition, we have initiated a preliminary principled study on the fundamental performance limit of image registration problems. We proposed a statistical generative model to account for noise effect in both source and target images, and investigated the approximate performance of the maximum-likelihood estimator corresponding to the generative model and the commonly adopted M-estimator. A simple example suggests that the approximation is reasonably accurate. Our studies in both time series analysis and image registration constitute essential building-blocks for clinical applications such as adaptive treatment. Besides their theoretical interests, it is our sincere hope that with further justifications, the proposed techniques would realize its clinical value, and improve the quality of life for patients.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60673/1/druan_1.pd