Non-Parametric Mixture Model Based Evolution of Level Sets and Application to Medical Images

We present a novel region-based curve evolution algorithm which has three primary contributions: (i) non-parametric estimation of probability distributions using the recently developed NP windows method; (ii) an inequality-constrained least squares method to model the image histogram with a mixture of nonparametric probability distributions; and (iii) accommodation of the partial volume effect, which is primarily due to low resolution images, and which often poses a significant challenge in medical image analysis (our primary application area). We first approximate the image intensity histogram as a mixture of non-parametric probability density functions (PDFs), justifying its use with respect to medical image analysis. The individual densities in the mixture are estimated using the recent NP windows PDF estimation method, which builds a continuous representation of discrete signals. A Bayesian framework is then formulated in which likelihood probabilities are given by the non-parametric PDFs and prior probabilities are calculated using an inequality constrained least squares method. The non-parametric PDFs are then learnt and the segmentation solution is spatially regularised using a level sets framework. The log ratio of the posterior probabilities is used to drive the level set evolution. As background to our approach, we recall related developments in level set methods. Results are presented for a set of synthetic and natural images as well as simulated and real medical images of various anatomical organs. Results on a range of images show the effectiveness of the proposed algorithm.     

Characterizing users’ check-in activities using their scores in a location-based social network

Analysis of users’ check-ins in location-based social networks (LBSNs, also called GeoSocial Networks), such as Foursquare and Yelp, is essential to understand users’ mobility patterns and behaviors. However, most empirical results of users’ mobility patterns reported in the current literature are based on users’ sampled and nonconsecutive public check-ins. Additionally, such analyses take no account of the noise or false information in the dataset, such as dishonest check-ins created by users. These empirical results may be biased and hence may bring side effects to LBSN services, such as friend and venue recommendations. Foursquare, one of the most popular LBSNs, provides a feature called a user’s score. A user’s score is an aggregate measure computed by the system based on more accurate and complete check-ins of the user. It reflects a snapshot of the user’s temporal and spatial patterns from his/her check-ins. For example, a high user score indicates that the user checked in at many venues regularly or s/he visited a number of new venues. In this paper, we show how a user’s score can be used as an alternative way to investigate the user’s mobility patterns. We first characterize a set of properties from the time series of a user’s consecutive weekly scores. Based on these properties, we identify different types of users by clustering users’ common check-in patterns using non-negative matrix factorization (NMF). We then analyze the correlations between the social features of user clusters and users’ check-in patterns. We present several interesting findings. For example, users with high scores (more mobile) tend to have more friends (more social). Our empirical results demonstrate how to uncover interesting spatio-temporal patterns by utilizing the aggregate measures released by a LBSN service.     

A Unified Variational Volume Registration Method Based on Automatically Learned Brain Structures

We introduce a new volumetric registration technique that effectively combines active surfaces with the finite element method. The method simultaneously aligns multi-label automatic structural segmentation results, which can be obtained by the application of existing segmentation software, to produce an anatomically accurate 3D registration. This registration is obtained by the minimization of a single energy functional. Just like registering raw images, obtaining a 3D registration this way still requires solving a fundamentally ill-posed problem. We explain through academic examples as well as an MRI dataset with manual anatomical labels, which are hidden from the registration method, how the quality of a registration method can be measured and the advantages our approach offers.     

Decision-theoretic planning with generalized first-order decision diagrams

Many tasks in AI require representation and manipulation of complex functions. First-Order Decision Diagrams (FODD) are a compact knowledge representation expressing functions over relational structures. They represent numerical functions that, when constrained to the Boolean range, use only existential quantification. Previous work has developed a set of operations for composition and for removing redundancies in FODDs, thus keeping them compact, and showed how to successfully employ FODDs for solving large-scale stochastic planning problems through the formalism of relational Markov decision processes (RMDP). In this paper, we introduce several new ideas enhancing the applicability of FODDs. More specifically, we first introduce Generalized FODDs (GFODD) and composition operations for them, generalizing FODDs to arbitrary quantification. Second, we develop a novel approach for reducing (G)FODDs using model checking. This yields – for the first time – a reduction that maximally reduces the diagram for the FODD case and provides a sound reduction procedure for GFODDs. Finally we show how GFODDs can be used in principle to solve RMDPs with arbitrary quantification, and develop a complete solution for the case where the reward function is specified using an arbitrary number of existential quantifiers followed by an arbitrary number of universal quantifiers.     

A Linear Variational System for Modelling From Curves

We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.     

Effective visualization of complex vascular structures using a non-parametric vessel detection method

The effective visualization of vascular structures is critical for diagnosis, surgical planning as well as treatment evaluation. In recent work, we have developed an algorithm for vessel detection that examines the intensity profile around each voxel in an angiographic image and determines the likelihood that any given voxel belongs to a vessel; we term this the "vesselness coefficient" of the voxel. Our results show that our algorithm works particularly well for visualizing branch points in vessels. Compared to standard Hessian based techniques, which are fine-tuned to identify long cylindrical structures, our technique identifies branches and connections with other vessels. Using our computed vesselness coefficient, we explore a set of techniques for visualizing vasculature. Visualizing vessels is particularly challenging because not only is their position in space important for clinicians but it is also important to be able to resolve their spatial relationship. We applied visualization techniques that provide shape cues as well as depth cues to allow the viewer to differentiate between vessels that are closer from those that are farther. We use our computed vesselness coefficient to effectively visualize vasculature in both clinical neurovascular x-ray computed tomography based angiography images, as well as images from three different animal studies. We conducted a formal user evaluation of our visualization techniques with the help of radiologists, surgeons, and other expert users. Results indicate that experts preferred distance color blending and tone shading for conveying depth over standard visualization techniques.     

Texture-based feature tracking for effective time-varying data visualization

Analyzing, visualizing, and illustrating changes within time-varying volumetric data is challenging due to the dynamic changes occurring between timesteps. The changes and variations in computational fluid dynamic volumes and atmospheric 3D datasets do not follow any particular transformation. Features within the data move at different speeds and directions making the tracking and visualization of these features a difficult task. We introduce a texture-based feature tracking technique to overcome some of the current limitations found in the illustration and visualization of dynamic changes within time-varying volumetric data. Our texture-based technique tracks various features individually and then uses the tracked objects to better visualize structural changes. We show the effectiveness of our texture-based tracking technique with both synthetic and real world time-varying data. Furthermore, we highlight the specific visualization, annotation, registration, and feature isolation benefits of our technique. For instance, we show how our texture-based tracking can lead to insightful visualizations of time-varying data. Such visualizations, more than traditional visualization techniques, can assist domain scientists to explore and understand dynamic changes.     

Generalized Lévy-walk model for DNA nucleotide sequences

We propose a generalized Lévy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Lévy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length lj) within these correlated sequences. In the generalized Lévy-walk model, the lj are chosen from a power-law distribution P(lj) varies as lj(-mu). The correlation exponent alpha is related to mu through alpha = 2-mu/2 if 2 < mu < 3. The model is consistent with the finding of "repetitive elements" of variable length interspersed within noncoding DNA.     

Deformable M-Reps for 3D Medical Image Segmentation

M-reps (formerly called DSLs) are a multiscale medial means for modeling and rendering 3D solid geometry. They are particularly well suited to model anatomic objects and in particular to capture prior geometric information effectively in deformable models segmentation approaches. The representation is based on figural models, which define objects at coarse scale by a hierarchy of figures—each figure generally a slab representing a solid region and its boundary simultaneously. This paper focuses on the use of single figure models to segment objects of relatively simple structure.A single figure is a sheet of medial atoms, which is interpolated from the model formed by a net, i.e., a mesh or chain, of medial atoms (hence the name m-reps), each atom modeling a solid region via not only a position and a width but also a local figural frame giving figural directions and an object angle between opposing, corresponding positions on the boundary implied by the m-rep. The special capability of an m-rep is to provide spatial and orientational correspondence between an object in two different states of deformation. This ability is central to effective measurement of both geometric typicality and geometry to image match, the two terms of the objective function optimized in segmentation by deformable models. The other ability of m-reps central to effective segmentation is their ability to support segmentation at multiple levels of scale, with successively finer precision. Objects modeled by single figures are segmented first by a similarity transform augmented by object elongation, then by adjustment of each medial atom, and finally by displacing a dense sampling of the m-rep implied boundary. While these models and approaches also exist in 2D, we focus on 3D objects.The segmentation of the kidney from CT and the hippocampus from MRI serve as the major examples in this paper. The accuracy of segmentation as compared to manual, slice-by-slice segmentation is reported.