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.

Estimating 3D Body Pose Using Uncalibrated Cameras

An approach for estimating 3D body pose from multiple, uncalibrated views is proposed. First, a mapping from image features to 2D body joint locations is computed using a statistical framework that yields a set of several body pose hypotheses. The concept of a "virtual camera" is introduced that makes this mapping invariant to translation, image-plane rotation, and scaling of the input. As a consequence, the calibration matrices (intrinsics) of the virtual cameras can be considered completely known, and their poses are known up to a single angular displacement parameter. Given pose hypotheses obtained in the multiple virtual camera views, the recovery of 3D body pose and camera relative orientations is formulated as a stochastic optimization problem. An Expectation-Maximization algorithm is derived that can obtain the locally most likely (self-consistent) combination of body pose hypotheses. Performance of the approach is evaluated with synthetic sequences as well as real video sequences of human motion.

Specialized Mappings Architecture with Applications to Vision-based Estimation of Articulated Body Pose

A fundamental task of vision systems is to infer the state of the world given some form of visual observations. From a computational perspective, this often involves facing an ill-posed problem; e.g., information is lost via projection of the 3D world into a 2D image. Solution of an ill-posed problem requires additional information, usually provided as a model of the underlying process. It is important that the model be both computationally feasible as well as theoretically well-founded. In this thesis, a probabilistic, nonlinear supervised computational learning model is proposed: the Specialized Mappings Architecture (SMA). The SMA framework is demonstrated in a computer vision system that can estimate the articulated pose parameters of a human body or human hands, given images obtained via one or more uncalibrated cameras. The SMA consists of several specialized forward mapping functions that are estimated automatically from training data, and a possibly known feedback function. Each specialized function maps certain domains of the input space (e.g., image features) onto the output space (e.g., articulated body parameters). A probabilistic model for the architecture is first formalized. Solutions to key algorithmic problems are then derived: simultaneous learning of the specialized domains along with the mapping functions, as well as performing inference given inputs and a feedback function. The SMA employs a variant of the Expectation-Maximization algorithm and approximate inference. The approach allows the use of alternative conditional independence assumptions for learning and inference, which are derived from a forward model and a feedback model. Experimental validation of the proposed approach is conducted in the task of estimating articulated body pose from image silhouettes. Accuracy and stability of the SMA framework is tested using artificial data sets, as well as synthetic and real video sequences of human bodies and hands.

Estimating Human Body Pose from a Single Image via the Specialized Mappings Architecture

A non-linear supervised learning architecture, the Specialized Mapping Architecture (SMA) and its application to articulated body pose reconstruction from single monocular images is described. The architecture is formed by a number of specialized mapping functions, each of them with the purpose of mapping certain portions (connected or not) of the input space, and a feedback matching process. A probabilistic model for the architecture is described along with a mechanism for learning its parameters. The learning problem is approached using a maximum likelihood estimation framework; we present Expectation Maximization (EM) algorithms for two different instances of the likelihood probability. Performance is characterized by estimating human body postures from low level visual features, showing promising results.

Spatiotemporal Gesture Segmentation

Spotting patterns of interest in an input signal is a very useful task in many different fields including medicine, bioinformatics, economics, speech recognition and computer vision. Example instances of this problem include spotting an object of interest in an image (e.g., a tumor), a pattern of interest in a time-varying signal (e.g., audio analysis), or an object of interest moving in a specific way (e.g., a human's body gesture). Traditional spotting methods, which are based on Dynamic Time Warping or hidden Markov models, use some variant of dynamic programming to register the pattern and the input while accounting for temporal variation between them. At the same time, those methods often suffer from several shortcomings: they may give meaningless solutions when input observations are unreliable or ambiguous, they require a high complexity search across the whole input signal, and they may give incorrect solutions if some patterns appear as smaller parts within other patterns. In this thesis, we develop a framework that addresses these three problems, and evaluate the framework's performance in spotting and recognizing hand gestures in video. The first contribution is a spatiotemporal matching algorithm that extends the dynamic programming formulation to accommodate multiple candidate hand detections in every video frame. The algorithm finds the best alignment between the gesture model and the input, and simultaneously locates the best candidate hand detection in every frame. This allows for a gesture to be recognized even when the hand location is highly ambiguous. The second contribution is a pruning method that uses model-specific classifiers to reject dynamic programming hypotheses with a poor match between the input and model. Pruning improves the efficiency of the spatiotemporal matching algorithm, and in some cases may improve the recognition accuracy. The pruning classifiers are learned from training data, and cross-validation is used to reduce the chance of overpruning. The third contribution is a subgesture reasoning process that models the fact that some gesture models can falsely match parts of other, longer gestures. By integrating subgesture reasoning the spotting algorithm can avoid the premature detection of a subgesture when the longer gesture is actually being performed. Subgesture relations between pairs of gestures are automatically learned from training data. The performance of the approach is evaluated on two challenging video datasets: hand-signed digits gestured by users wearing short sleeved shirts, in front of a cluttered background, and American Sign Language (ASL) utterances gestured by ASL native signers. The experiments demonstrate that the proposed method is more accurate and efficient than competing approaches. The proposed approach can be generally applied to alignment or search problems with multiple input observations, that use dynamic programming to find a solution.