QUANTITATIVE THREE DIMENSIONAL ELASTICITY IMAGING

Neoplastic tissue is typically highly vascularized, contains abnormal concentrations of extracellular proteins (e.g. collagen, proteoglycans) and has a high interstitial fluid pres- sure compared to most normal tissues. These changes result in an overall stiffening typical of most solid tumors. Elasticity Imaging (EI) is a technique which uses imaging systems to measure relative tissue deformation and thus noninvasively infer its mechanical stiffness. Stiffness is recovered from measured deformation by using an appropriate mathematical model and solving an inverse problem. The integration of EI with existing imaging modal- ities can improve their diagnostic and research capabilities. The aim of this work is to develop and evaluate techniques to image and quantify the mechanical properties of soft tissues in three dimensions (3D). To that end, this thesis presents and validates a method by which three dimensional ultrasound images can be used to image and quantify the shear modulus distribution of tissue mimicking phantoms. This work is presented to motivate and justify the use of this elasticity imaging technique in a clinical breast cancer screening study. The imaging methodologies discussed are intended to improve the specificity of mammography practices in general. During the development of these techniques, several issues concerning the accuracy and uniqueness of the result were elucidated. Two new algorithms for 3D EI are designed and characterized in this thesis. The first provides three dimensional motion estimates from ultrasound images of the deforming ma- terial. The novel features include finite element interpolation of the displacement field, inclusion of prior information and the ability to enforce physical constraints. The roles of regularization, mesh resolution and an incompressibility constraint on the accuracy of the measured deformation is quantified. The estimated signal to noise ratio of the measured displacement fields are approximately 1800, 21 and 41 for the axial, lateral and eleva- tional components, respectively. The second algorithm recovers the shear elastic modulus distribution of the deforming material by efficiently solving the three dimensional inverse problem as an optimization problem. This method utilizes finite element interpolations, the adjoint method to evaluate the gradient and a quasi-Newton BFGS method for optimiza- tion. Its novel features include the use of the adjoint method and TVD regularization with piece-wise constant interpolation. A source of non-uniqueness in this inverse problem is identified theoretically, demonstrated computationally, explained physically and overcome practically. Both algorithms were test on ultrasound data of independently characterized tissue mimicking phantoms. The recovered elastic modulus was in all cases within 35% of the reference elastic contrast. Finally, the preliminary application of these techniques to tomosynthesis images showed the feasiblity of imaging an elastic inclusion.

EVALUATION OF HARMONIC MOTION ELASTOGRAPHY AND ACOUSTO-­OPTIC IMAGING FOR MONITORING LESION FORMATION BY HIGH INTENSITY FOCUSED ULTRASOUND

Malignant or benign tumors may be ablated with high‐intensity focused ultrasound (HIFU). This technique, known as focused ultrasound surgery (FUS), has been actively investigated for decades, but slow to be implemented and difficult to control due to lack of real‐time feedback during ablation. Two methods of imaging and monitoring HIFU lesions during formation were implemented simultaneously, in order to investigate the efficacy of each and to increase confidence in the detection of the lesion. The first, Acousto‐Optic Imaging (AOI) detects the increasing optical absorption and scattering in the lesion. The intensity of a diffuse optical field in illuminated tissue is mapped at the spatial resolution of an ultrasound focal spot, using the acousto‐optic effect. The second, Harmonic Motion Imaging (HMI), detects the changing stiffness in the lesion. The HIFU beam is modulated to force oscillatory motion in the tissue, and the amplitude of this motion, measured by ultrasound pulse‐echo techniques, is influenced by the stiffness. Experiments were performed on store‐bought chicken breast and freshly slaughtered bovine liver. The AOI results correlated with the onset and relative size of forming lesions much better than prior knowledge of the HIFU power and duration. For HMI, a significant artifact was discovered due to acoustic nonlinearity. The artifact was mitigated by adjusting the phase of the HIFU and imaging pulses. A more detailed model of the HMI process than previously published was made using finite element analysis. The model showed that the amplitude of harmonic motion was primarily affected by increases in acoustic attenuation and stiffness as the lesion formed and the interaction of these effects was complex and often counteracted each other. Further biological variability in tissue properties meant that changes in motion were masked by sample‐to‐sample variation. The HMI experiments predicted lesion formation in only about a quarter of the lesions made. In simultaneous AOI/HMI experiments it appeared that AOI was a more robust method for lesion detection.

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

Skin Color-Based Video Segmentation under Time-Varying Illumination

A novel approach for real-time skin segmentation in video sequences is described. The approach enables reliable skin segmentation despite wide variation in illumination during tracking. An explicit second order Markov model is used to predict evolution of the skin-color (HSV) histogram over time. Histograms are dynamically updated based on feedback from the current segmentation and predictions of the Markov model. The evolution of the skin-color distribution at each frame is parameterized by translation, scaling and rotation in color space. Consequent changes in geometric parameterization of the distribution are propagated by warping and resampling the histogram. The parameters of the discrete-time dynamic Markov model are estimated using Maximum Likelihood Estimation, and also evolve over time. The accuracy of the new dynamic skin color segmentation algorithm is compared to that obtained via a static color model. Segmentation accuracy is evaluated using labeled ground-truth video sequences taken from staged experiments and popular movies. An overall increase in segmentation accuracy of up to 24% is observed in 17 out of 21 test sequences. In all but one case the skin-color classification rates for our system were higher, with background classification rates comparable to those of the static segmentation.

Discovering Clusters in Motion Time-Series Data

A new approach is proposed for clustering time-series data. The approach can be used to discover groupings of similar object motions that were observed in a video collection. A finite mixture of hidden Markov models (HMMs) is fitted to the motion data using the expectation-maximization (EM) framework. Previous approaches for HMM-based clustering employ a k-means formulation, where each sequence is assigned to only a single HMM. In contrast, the formulation presented in this paper allows each sequence to belong to more than a single HMM with some probability, and the hard decision about the sequence class membership can be deferred until a later time when such a decision is required. Experiments with simulated data demonstrate the benefit of using this EM-based approach when there is more "overlap" in the processes generating the data. Experiments with real data show the promising potential of HMM-based motion clustering in a number of applications.

Deformable Prototypes for Encoding Shape Categories in Image Databases

We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.

A Geometric Approach to Slot Alignment in Wireless Sensor Networks

Traditionally, slotted communication protocols have employed guard times to delineate and align slots. These guard times may expand the slot duration significantly, especially when clocks are allowed to drift for longer time to reduce clock synchronization overhead. Recently, a new class of lightweight protocols for statistical estimation in wireless sensor networks have been proposed. This new class requires very short transmission durations (jam signals), thus the traditional approach of using guard times would impose significant overhead. We propose a new, more efficient algorithm to align slots. Based on geometrical properties of space, we prove that our approach bounds the slot duration by only a constant factor of what is needed. Furthermore, we show by simulation that this bound is loose and an even smaller slot duration is required, making our approach even more efficient.

System F with Constraint Types

System F is a type system that can be seen as both a proof system for second-order propositional logic and as a polymorphic programming language. In this work we explore several extensions of System F by types which express subtyping constraints. These systems include terms which represent proofs of subtyping relationships between types. Given a proof that one type is a subtype of another, one may use a coercion term constructor to coerce terms from the first type to the second. The ability to manipulate type constraints as first-class entities gives these systems a lot of expressive power, including the ability to encode generalized algebraic data types and intensional type analysis. The main contributions of this work are in the formulation of constraint types and a proof of strong normalization for an extension of System F with constraint types.

On the Stable Paths Problem and a Restricted Variant

Interdomain routing on the Internet is performed using route preference policies specified independently, and arbitrarily by each Autonomous System in the network. These policies are used in the border gateway protocol (BGP) by each AS when selecting next-hop choices for routes to each destination. Conflicts between policies used by different ASs can lead to routing instabilities that, potentially, cannot be resolved no matter how long BGP is run. The Stable Paths Problem (SPP) is an abstract graph theoretic model of the problem of selecting nexthop routes for a destination. A stable solution to the problem is a set of next-hop choices, one for each AS, that is compatible with the policies of each AS. In a stable solution each AS has selected its best next-hop given that the next-hop choices of all neighbors are fixed. BGP can be viewed as a distributed algorithm for solving SPP. In this report we consider the stable paths problem, as well as a family of restricted variants of the stable paths problem, which we call F stable paths problems. We show that two very simple variants of the stable paths problem are also NP-complete. In addition we show that for networks with a DAG topology, there is an efficient centralized algorithm to solve the stable paths problem, and that BGP always efficiently converges to a stable solution on such networks.

Deformable Shape Detection and Description via Model-Based Region Grouping

A method for deformable shape detection and recognition is described. Deformable shape templates are used to partition the image into a globally consistent interpretation, determined in part by the minimum description length principle. Statistical shape models enforce the prior probabilities on global, parametric deformations for each object class. Once trained, the system autonomously segments deformed shapes from the background, while not merging them with adjacent objects or shadows. The formulation can be used to group image regions based on any image homogeneity predicate; e.g., texture, color, or motion. The recovered shape models can be used directly in object recognition. Experiments with color imagery are reported.

Fast, Reliable Head Tracking under Varying Illumination

An improved technique for 3D head tracking under varying illumination conditions is proposed. The head is modeled as a texture mapped cylinder. Tracking is formulated as an image registration problem in the cylinder's texture map image. To solve the registration problem in the presence of lighting variation and head motion, the residual error of registration is modeled as a linear combination of texture warping templates and orthogonal illumination templates. Fast and stable on-line tracking is then achieved via regularized, weighted least squares minimization of the registration error. The regularization term tends to limit potential ambiguities that arise in the warping and illumination templates. It enables stable tracking over extended sequences. Tracking does not require a precise initial fit of the model; the system is initialized automatically using a simple 2-D face detector. The only assumption is that the target is facing the camera in the first frame of the sequence. The warping templates are computed at the first frame of the sequence. Illumination templates are precomputed off-line over a training set of face images collected under varying lighting conditions. Experiments in tracking are reported.

Estimation and Prediction of Evolving Color Distributions for Skin Segmentation Under Varying Illumination

A novel approach for real-time skin segmentation in video sequences is described. The approach enables reliable skin segmentation despite wide variation in illumination during tracking. An explicit second order Markov model is used to predict evolution of the skin color (HSV) histogram over time. Histograms are dynamically updated based on feedback from the current segmentation and based on predictions of the Markov model. The evolution of the skin color distribution at each frame is parameterized by translation, scaling and rotation in color space. Consequent changes in geometric parameterization of the distribution are propagated by warping and re-sampling the histogram. The parameters of the discrete-time dynamic Markov model are estimated using Maximum Likelihood Estimation, and also evolve over time. Quantitative evaluation of the method was conducted on labeled ground-truth video sequences taken from popular movies.

Recursive Estimation of Motion and Planar Structure

A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the number of feature points needed to estimate the state. Experiments with synthetic data and real imagery illustrate the system performance. The experiments confirm that the specialized formulation provides improved accuracy, stability to observation noise, and rate of convergence in estimation for the case where the tracked points lie on a plane.

Inferring Body Pose without Tracking Body Parts

A novel approach for estimating articulated body posture and motion from monocular video sequences is proposed. Human pose is defined as the instantaneous two dimensional configuration (i.e., the projection onto the image plane) of a single articulated body in terms of the position of a predetermined set of joints. First, statistical segmentation of the human bodies from the background is performed and low-level visual features are found given the segmented body shape. The goal is to be able to map these, generally low level, visual features to body configurations. The system estimates different mappings, each one with a specific cluster in the visual feature space. Given a set of body motion sequences for training, unsupervised clustering is obtained via the Expectation Maximation algorithm. Then, for each of the clusters, a function is estimated to build the mapping between low-level features to 3D pose. Currently this mapping is modeled by a neural network. Given new visual features, a mapping from each cluster is performed to yield a set of possible poses. From this set, the system selects the most likely pose given the learned probability distribution and the visual feature similarity between hypothesis and input. Performance of the proposed approach is characterized using a new set of known body postures, showing promising results.

Index Trees for Efficient Deformable Shape-based Retrieval

An improved method for deformable shape-based image indexing and retrieval is described. A pre-computed index tree is used to improve the speed of our previously reported on-line model fitting method; simple shape features are used as keys in a pre-generated index tree of model instances. In addition, a coarse to fine indexing scheme is used at different levels of the tree to further improve speed while maintaining matching accuracy. Experimental results show that the speedup is significant, while accuracy of shape-based indexing is maintained. A method for shape population-based retrieval is also described. The method allows query formulation based on the population distributions of shapes in each image. Results of population-based image queries for a database of blood cell micrographs are shown.