Multi-scale space-variant FRep cellular structures

Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

Image processing for plastic surgery planning

This thesis presents some image processing tools for plastic surgery planning. In particular, it presents a novel method that combines local and global context in a probabilistic relaxation framework to identify cephalometric landmarks used in Maxillofacial plastic surgery. It also uses a method that utilises global and local symmetry to identify abnormalities in CT frontal images of the human body. The proposed methodologies are evaluated with the help of several clinical data supplied by collaborating plastic surgeons

Continuous-variable quantum neural networks

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks

Segmentation and Fracture Detection in CT Images for Traumatic Pelvic Injuries

In recent decades, more types and quantities of medical data have been collected due to advanced technology. A large number of significant and critical information is contained in these medical data. High efficient and automated computational methods are urgently needed to process and analyze all available medical data in order to provide the physicians with recommendations and predictions on diagnostic decisions and treatment planning. Traumatic pelvic injury is a severe yet common injury in the United States, often caused by motor vehicle accidents or fall. Information contained in the pelvic Computed Tomography (CT) images is very important for assessing the severity and prognosis of traumatic pelvic injuries. Each pelvic CT scan includes a large number of slices. Meanwhile, each slice contains a large quantity of data that may not be thoroughly and accurately analyzed via simple visual inspection with the desired accuracy and speed. Hence, a computer-assisted pelvic trauma decision-making system is needed to assist physicians in making accurate diagnostic decisions and determining treatment planning in a short period of time. Pelvic bone segmentation is a vital step in analyzing pelvic CT images and assisting physicians with diagnostic decisions in traumatic pelvic injuries. In this study, a new hierarchical segmentation algorithm is proposed to automatically extract multiplelevel bone structures using a combination of anatomical knowledge and computational techniques. First, morphological operations, image enhancement, and edge detection are performed for preliminary bone segmentation. The proposed algorithm then uses a template-based best shape matching method that provides an entirely automated segmentation process. This is followed by the proposed Registered Active Shape Model (RASM) algorithm that extracts pelvic bone tissues using more robust training models than the Standard ASM algorithm. In addition, a novel hierarchical initialization process for RASM is proposed in order to address the shortcoming of the Standard ASM, i.e. high sensitivity to initialization. Two suitable measures are defined to evaluate the segmentation results: Mean Distance and Mis-segmented Area to quantify the segmentation accuracy. Successful segmentation results indicate effectiveness and robustness of the proposed algorithm. Comparison of segmentation performance is also conducted using both the proposed method and the Snake method. A cross-validation process is designed to demonstrate the effectiveness of the training models. 3D pelvic bone models are built after pelvic bone structures are segmented from consecutive 2D CT slices. Automatic and accurate detection of the fractures from segmented bones in traumatic pelvic injuries can help physicians detect the severity of injuries in patients. The extraction of fracture features (such as presence and location of fractures) as well as fracture displacement measurement, are vital for assisting physicians in making faster and more accurate decisions. In this project, after bone segmentation, fracture detection is performed using a hierarchical algorithm based on wavelet transformation, adaptive windowing, boundary tracing and masking. Also, a quantitative measure of fracture severity based on pelvic CT scans is defined and explored. The results are promising, demonstrating that the proposed method not only capable of automatically detecting both major and minor fractures, but also has potentials to be used for clinical applications

Hypothesis Validation of Far-Wall Brightness in Carotid-Artery Ultrasound for Feature-Based IMT Measurement Using a Combination of Level-Set Segmentation and Registration

Intima-media thickness (IMT) is now being considered as an indicator of atherosclerosis. Our group has developed several feature-based IMT measurement algorithms such as the Completely Automated Layer EXtraction (CALEX) (which is a class of patented AtheroEdge Systems from Global Biomedical Technologies, Inc., CA, USA). These methods are based on the hypothesis that the highest pixel intensities are in the far wall of the common carotid artery (CCA) or the internal carotid artery (ICA). In this paper, we verify that this hypothesis holds true for B-mode longitudinal ultrasound (US) images of the carotid wall. This patented methodology consists of generating the composite image (the arithmetic sum of images) from the database by first registering the carotid image frames with respect to a nearly straight carotid-artery frame from the same database using: 1) B-spline-based nonrigid registration and 2) affine registration. Prior to registration, we segment the carotid-artery lumen using a level-set-based algorithm followed by morphological image processing. The binary lumen images are registered, and the transformations are applied to the original grayscale CCA images. We evaluated our technique using a database of 200 common carotid images of normal and pathologic carotids. The composite image presented the highest intensity distribution in the far wall of the CCA/ICA, validating our hypothesis. We have also demonstrated the accuracy and improvement in the IMT segmentation result with our CALEX 3.0 system. The CALEX system, when run on newly acquired US images, shows the IMT error of about 30 mu m. Thus, we have shown that the CALEX algorithm is able to exploit the far-wall brightness for accurate IMT measurements

Exact Simulation of Wishart Multidimensional Stochastic Volatility Model

In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of the conditional characteristic function of the log-price given volatility level. In particular, we found an explicit expression for the conditional characteristic function for the Heston model. We perform numerical experiments to demonstrate the performance and accuracy of our method. As a result of numerical experiments, it is shown that our new method is much faster and reliable than Euler discretization method.Comment: 27 page