CLASSIFICATION OF NEUROANATOMICAL STRUCTURES BASED ON NON-EUCLIDEAN GEOMETRIC OBJECT PROPERTIES

Studying the observed morphological differences in neuroanatomical structures between individuals with neurodevelopmental disorders and a control group of typically developing individuals has been an important objective. Researchers study the differences with two goals: to assist an accurate diagnosis of the disease and to gain insights into underlying mechanisms of the disease that cause such changes. Shape classification is commonly utilized in such studies. An effective classification is difficult because it requires 1) a choice of an object model that can provide rich geometric object properties (GOPs) relevant for a given classification task, and 2) a choice of a statistical classification method that accounts for the non-Euclidean nature of GOPs. I lay out my methodological contributions to address the aforementioned challenges in the context of early diagnosis and detection of Autism Spectrum Disorder (ASD) in infants based on shapes of hippocampi and caudate nuclei; morphological deviations in these structures between individuals with ASD and typically developing individuals have been reported in the literature. These contributions respectively lead to 1) an effective modeling of shapes of objects of interest and 2) an effective classification. As the first contribution for modeling shapes of objects, I propose a method to obtain a set of skeletal models called s-reps from a set of 3D objects. First, the method iteratively deforms the object surface via Mean Curvature Flow (MCF) until the deformed surface is approximately ellipsoidal. Then, an s-rep of the approximate ellipsoid is obtained analytically. Finally, the ellipsoid s-rep is deformed via a series of inverse MCF transformations. The method has two important properties: 1) it is fully automatic, and 2) it yields a set of s-reps with good correspondence across the set. The method is shown effective in generating a set of s-reps for a few neuroanatomical structures. As the second contribution with respect to modeling shapes of objects, I introduce an extension to the current s-rep for representing an object with a narrowing sharp tail. This includes a spoke interpolation method for interpolating a discrete s-rep of an object with a narrowing sharp tail into a continuous object. This extension is necessary for representing surface geometry of objects whose boundary has a singular point. I demonstrate that this extension allows appropriate surface modeling of a narrowing sharp tail region of the caudate nucleus. In addition, I show that the extension is beneficial in classifying autistic and non-autistic infants at high risk of ASD based on shapes of caudate nuclei. As the first contribution with respect to statistical methods, I propose a novel shape classification framework that uses the s-rep to capture rich localized geometric descriptions of an object, a statistical method called Principal Nested Spheres (PNS) analysis to handle the non-Euclidean s-rep GOPs, and a classification method called Distance Weighted Discrimination (DWD). I evaluate the effectiveness of the proposed method in classifying autistic and non-autistic infants based on either hippocampal shapes or caudate shapes in terms of the Area Under the ROC curve (AUC). In addition, I show that the proposed method is superior to commonly used shape classification methods in the literature. As my final methodological contribution, I extend the proposed shape classification method to perform the classifcation task based on temporal shape differences. DWD learns a class separation direction based on the temporal shape differences that are obtained by taking differences of the temporal pair of Euclideanized s-reps. In the context of early diagnosis and detection of ASD in young infants, the proposed temporal shape difference classification produces some interesting results; the temporal differences in shapes of hippocampi and caudate nuclei do not seem to be as predictive as the cross-sectional shape of these structures alone.Doctor of Philosoph

New Estimation Strategies for Demand Threshold Models in the Southern United States

This paper estimates demand threshold models using both first generation log-log models and second generation Tobit models to zip code areas in the Southern US. Results of own-place demographic and economic variables were consistent with previous studies but impacts of neighboring zip codes contrasted previous studies.Demand Threshold Analysis, Central Place Theory, Demand and Price Analysis, R120,

Three essays on the role of amenities as an economic development strategy

It is well known that an amenity is a key driving engine to regional economic growth. However, the site-specific nature of an amenity can characterize them as public goods. Due to this characteristic, local governments have difficulty optimally supplying amenities. This dissertation tries to find relationships between an amenity and economic growth. Three empirical papers comprise the original research in this dissertation. The findings of the meta-analysis in the first essay suggest little methodological diversity exists among researchers linking amenities to economic growth., I do find that employment growth is more likely related to man-made amenities even in research on rural areas than natural amenities. Further, incorporating spatial estimators into amenity research improves modeling performance while reducing the net impact of amenities on economic growth. The second essay indicates a distinctive distribution between man-made amenities and natural amenities over counties of the United States. While man-made amenities are agglomerated in urban areas, natural amenities show heterogeneous dispersion. Both agricultural land and conservation land show an inverse relationship to man-made amenities across space. From an analysis using a local government’s public policy along with an areas’ physical attributes, I find government tax policy having the greatest effect on film location decisions with natural amenities having little impact. The third essay analyzed the impact of a tax incentive program targeted to film industries on local economies using a quasi-experimental approach. This last essay provided three findings. First, this chapter found meaningful methodological specifications that should be considered in regional studies using a quasi-experimental approach. They are appropriate consideration of control periods, spatial units of comparison, and validities of dummy variables representing extraneous shocks. Second, the impact of the film industry tax program on local economies is insignificant for most industries. Third, the influence of tax subsidy policy on local economies is limited to a central area but is not beneficial to its adjacent areas

Non-Euclidean classification of medically imaged objects via s-reps

AbstractClassifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes full advantage of the geometry of the manifold on which these non-Euclidean geometric object properties (GOPs) live. Our method is evaluated via the task of classifying 3D hippocampi between schizophrenics and healthy controls. We address three central questions. 1) Does adding shape features increase discriminative power over the more standard classification based only on global volume? 2) If so, does our skeletal representation provide greater discriminative power than a conventional boundary point distribution model (PDM)? 3) Especially, is Euclideanization of non-Euclidean shape properties important in achieving high discriminative power? Measuring the capability of a method in terms of area under the receiver operator characteristic (ROC) curve, we show that our proposed method achieves strongly better classification than both the classification method based on global volume alone and the s-rep-based classification method without proper Euclideanization of non-Euclidean GOPs. We show classification using Euclideanized s-reps is also superior to classification using PDMs, whether the PDMs are first Euclideanized or not. We also show improved performance with Euclideanized boundary PDMs over non-linear boundary PDMs. This demonstrates the benefit that proper Euclideanization of non-Euclidean GOPs brings not only to s-rep-based classification but also to PDM-based classification

The Role of Amenities in a Regional Economy: A Meta-Analysis Approach

This paper seeks to address whether and how amenities are related to regional economic growth by using meta-analysis. Findings imply which amenity-related economic growth strategy should be taken into consideration when interpreting research results from diverse studies. Research results are summarized as follows. First, research methodologies do not deviate much from the mainstream. Second, spatial autocorrelation correction components seem to yield contradictory results to a conventional logic but they in fact restore neighborhood effects. Last, different types of amenities (natural v.s. man-made) have distinctive relationships with economic growth. Natural amenity growth derives lower-wage employment growth, while man-made amenities drive creative class growth. The results from meta-analysis on amenity-related economic growth provide policy decision makers with more consistent understanding than each literature's various political implication

New Estimation Strategies for Demand Threshold Models in the Southern United States

This paper estimates demand threshold models using both first generation log-log models and second generation Tobit models to zip code areas in the Southern US. Results of own-place demographic and economic variables were consistent with previous studies but impacts of neighboring zip codes contrasted previous studies

Non-Euclidean classification of medically imaged objects via s-reps

Classifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes full advantage of the geometry of the manifold on which these non-Euclidean geometric object properties (GOPs) live. Our method is evaluated via the task of classifying 3D hippocampi between schizophrenics and healthy controls. We address three central questions. 1) Does adding shape features increase discriminative power over the more standard classification based only on global volume? 2) If so, does our skeletal representation provide greater discriminative power than a conventional boundary point distribution model (PDM)? 3) Especially, is Euclideanization of non-Euclidean shape properties important in achieving high discriminative power? Measuring the capability of a method in terms of area under the receiver operator characteristic (ROC) curve, we show that our proposed method achieves strongly better classification than both the classification method based on global volume alone and the s-rep-based classification method without proper Euclideanization of non-Euclidean GOPs. We show classification using Euclideanized s-reps is also superior to classification using PDMs, whether the PDMs are first Euclideanized or not. We also show improved performance with Euclideanized boundary PDMs over non-linear boundary PDMs. This demonstrates the benefit that proper Euclideanization of non-Euclidean GOPs brings not only to s-rep-based classification but also to PDM-based classification