Browsing by Author "Peterson, Christopher, committee member"
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Item Open Access A local characterization of domino evacuation-shuffling(Colorado State University. Libraries, 2024) McCann, Jacob, author; Gillespie, Maria, advisor; Peterson, Christopher, committee member; Huang, Dongzhou, committee memberWe consider linear intersection problems in the Grassmanian (the space of k-dimensional subspaces of Cn), where the dimension of the intersection is 2. These spaces are called Schubert surfaces. We build of the previous work of Speyer [1] and Gillespie and Levinson [2]. Speyer showed there is a combinatorial interpretation for what happens to fibers of Schubert intersections above a "wall crossing", where marked points corresponding to the coordinates of partitions coincide. Building off Speyer's work, Levinson showed there is a combinatorial operation associated with the monodromy operator on Schubert curves, involving rectification, promotion, and shuffling of Littlewood-Richardson Young Tableaux, which overall is christened evacuation-shuffling. Gillespie and Levinson [2] further developed a localization of the evacuation-shuffling algorithm for Schubert curves. We fully develop a local description of the monodromy operator on certain classes of curves embedded inside Schubert surfaces [3].Item Open Access A quantum H*(T)-module via quasimap invariants(Colorado State University. Libraries, 2024) Lee, Jae Hwang, author; Shoemaker, Mark, advisor; Cavalieri, Renzo, advisor; Gillespie, Maria, committee member; Peterson, Christopher, committee member; Hulpke, Alexander, committee member; Chen, Hua, committee memberFor X a smooth projective variety, the quantum cohomology ring QH*(X) is a deformation of the usual cohomology ring H*(X), where the product structure is modified to incorporate quantum corrections. These correction terms are defined using Gromov-Witten invariants. When X is toric with geometric quotient description V//T, the cohomology ring H*(V//T) also has the structure of a H*(T)-module. In this paper, we introduce a new deformation of the cohomology of X using quasimap invariants with a light point. This defines a quantum H*(T)-module structure on H*(X) through a modified version of the WDVV equations. We explicitly compute this structure for the Hirzebruch surface of type 2. We conjecture that this new quantum module structure is isomorphic to the natural module structure of the Batyrev ring for a semipositive toric variety.Item Open Access Acoustic monitoring system for frog population estimation using in-situ progressive learning(Colorado State University. Libraries, 2013) Aboudan, Adam, author; Azimi-Sadjadi, Mahmood R., advisor; Fristrup, Kurt, committee member; Peterson, Christopher, committee memberFrog populations are considered excellent bio-indicators and hence the ability to monitor changes in their populations can be very useful for ecological research and environmental monitoring. This thesis presents a new population estimation approach based on the recognition of individual frogs of the same species, namely the Pseudacris Regilla (Pacific Chorus Frog), which does not rely on the availability of prior training data. An in-situ progressive learning algorithm is developed to determine whether an incoming call belongs to a previously detected individual frog or a newly encountered individual frog. A temporal call overlap detector is also presented as a pre-processing tool to eliminate overlapping calls. This is done to prevent the degrading of the learning process. The approach uses Mel-frequency cepstral coefficients (MFCCs) and multivariate Gaussian models to achieve individual frog recognition. In the first part of this thesis, the MFCC as well as the related linear predictive cepstral coefficients (LPCC) acoustic feature extraction processes are reviewed. The Gaussian mixture models (GMM) are also reviewed as an extension to the classical Gaussian modeling used in the proposed approach. In the second part of this thesis, the proposed frog population estimation system is presented and discussed in detail. The proposed system involves several different components including call segmentation, feature extraction, overlap detection, and the in-situ progressive learning process. In the third part of the thesis, data description and system performance results are provided. The process of synthetically generating test sequences of real frog calls, which are applied to the proposed system for performance analysis, is described. Also, the results of the system performance are presented which show that the system is successful in distinguishing individual frogs, hence capable of providing reasonable estimates of the frog population. The system can readily be transitioned for the purpose of actual field studies.Item Open Access An empathic avatar in task-driven human-computer interaction(Colorado State University. Libraries, 2020) Wang, Heting, author; Beveridge, Ross, advisor; Ortega, Francisco, advisor; Sharp, Julia, committee member; Peterson, Christopher, committee memberIn Human-Computer Interaction, it is difficult to give machines emotional intelligence to resemble human affects, such as the ability of empathy. This thesis presents our work of an emotionally expressive avatar named Diana that can recognize human affects, and show her empathy by using dynamic facial expressions. Diana's behaviors and facial expressions were modeled from Human-Human multimodal interactions to help to provide human-like perceptions in users. Specifically, we designed her empathic facial expressions as a linear combination of the action units in the Facial Action Coding System [1], with the action units that were previously found to improve the accuracy and judgments of human likeness. Our work studies the role of affect between a human and Diana working together in a blocks world. We first conducted an elicitation study to extract naturally occurring gestures from naive human pairs. The pair of human collaborated on a task remotely through video communication to build wooden blocks. The video footage of their interactions composed a dataset named EGGNOG [2]. We provided descriptive and statistical analysis of the affective metrics between human signalers and builders in EGGNOG. The metrics included measures of valence (positive or negative experience) and intensities of 7 basic emotions (joy, fear, disgust, anger, surprise, and contempt). We found: 1) Overall the signalers had a broader range of valence and showed more varied emotions than the builders. 2) The intensity of signalers' joy was greater than that in builders, indicating a happier signaler than a builder. 3) For individuals, the person was happier to act as a signaler in a task than act as a builder. Additionally, valence was more associated with a person's role in a task and less associated with personality traits. Other emotions were all weak and no significant difference was found between signalers and builders. To adapt to the user's affects in the later Human-Avatar interaction, we modeled Diana's empathic behaviors based upon findings in EGGNOG and the Appraisal theory [3]. We created a Demo mode of Diana whose affective states, i.e., facial expressions that simulated empathy, dynamically transitioned between 5 finite states (neutral, joy, sympathy, concentration, and confusion) with respect to the user's affects and gestures. We also created a Mimicry mode of Diana who mimicked the user's instant facial expressions. Human subject studies involving three modes of this avatar (Demo, Mimicry, and Emotionless) were conducted with 21 participants. The difference in votes from a 5-point Likert scale perception questionnaire or a NASA TLX perceived load survey was both statistically insignificant. However, compared to the Mimicry Diana and the Emotionless Diana, a descriptive analysis indicated users spent more time engaging with the empathic Diana, and both the Demo and Mimicry mode of Diana were preferred by users over the Emotionless Diana. Some participants commented about Diana's facial expressions as natural and friendly while 3 other participants were elicited uncomfortable feelings and mentioned the Uncanny Valley effect. Results indicated our approach of adding affects to Diana was perceived differently by different people and received both positive and negative feedback. Our work provided another implementable direction of the human-centered user interfaces with complex affective states. However, there was no evidence that the empathic facial expressions were more preferred by participants than the mimicked facial expressions. In the future, Diana's empathic facial expressions may be refined by modeling more human-like action unit movements with the help of deep learning networks, and the user perception in subjective reports may get improved.Item Open Access Anomaly detection in terrestrial hyperspectral video using variants of the RX algorithm(Colorado State University. Libraries, 2012) Schwickerath, Anthony N., author; Kirby, Michael, advisor; Peterson, Christopher, committee member; Anderson, Charles, committee memberThere is currently interest in detecting the use of chemical and biological weapons using hyperspectral sensors. Much of the research in this area assumes the spectral signature of the weapon is known in advance. Unfortunately, this may not always be the case. To obviate the reliance on a library of known target signatures, we instead view this as an anomaly detection problem. In this thesis, the RX algorithm, a benchmark anomaly detection algorithm for multi- and hyper-spectral data is reviewed, as are some standard extensions. This class of likelihood ratio test-based algorithms is generally applied to aerial imagery for the identification of man-made artifacts. As such, the model assumes that the scale is relatively consistent and that the targets (roads, cars) also have fixed sizes. We apply these methods to terrestrial video of biological and chemical aerosol plumes, where the background scale and target size both vary, and compare preliminary results. To explore the impact of parameter choice on algorithm performance, we also present an empirical study of the standard RX algorithm applied to synthetic targets of varying sizes over a range of settings.Item Open Access Avoiding singularities during homotopy continuation(Colorado State University. Libraries, 2017) Hodges, Timothy E., author; Bates, Daniel J., advisor; Böhm, A. P., committee member; Hulpke, Alexander, committee member; Peterson, Christopher, committee memberIn numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1,x2,...xn). This is done through a process called homotopy continuation. During this process, it is possible to encounter areas of ill-conditioning. These areas can cause failure of homotopy continuation or an increase in run time. In this thesis, we formalize where these areas of ill-conditioning can happen, and give a novel method for avoiding them. In addition, future work and possible improvements to the method are proposed. We also report on related developments in the Bertini software package. In addition, we discuss new infrastructure and heuristics for tuning configurations during homotopy continuation.Item Open Access Counting with convolutional neural networks(Colorado State University. Libraries, 2021) Shastri, Viraj, author; Beveridge, J. Ross, advisor; Blanchard, Nathaniel, committee member; Peterson, Christopher, committee memberIn this work, we tackle the question: Can neural networks count? More precisely, given an input image with a certain number of objects, can a neural network tell how many are there? To study this, we create a synthetic dataset consisting of black and white images with variable numbers of white triangles on a black background, oriented right-side up, down, left or right. We train a network to count the right-side up triangles; specifically, we see this as a closed-set classification problem where the class is the number of right-side up triangles in the image. These evaluations show that our networks, even in their simplest designs, are able to count a particular object in an image with a very small epsilon of approximation. We conclude that the neural networks are enforced with more complex learning capabilities than given credit for.Item Open Access Gale duality, decoupling, parameter homotopies, and monodromy(Colorado State University. Libraries, 2014) Niemerg, Matthew E., author; Bates, Daniel J., advisor; Shipman, Patrick, committee member; Peterson, Christopher, committee member; Lee, Chihoon, committee memberNumerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial systems. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 10 years ago. We will give an introduction and overview of numerical algebraic geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials and associated software called galeDuality; describe a software module of bertini named paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; give two examples that are parametric polynomial systems on which the aforementioned software is used; and finally describe two novel algorithms, decoupling and a heuristic that makes use of monodromy.Item Open Access Improving gesture recognition through spatial focus of attention(Colorado State University. Libraries, 2018) Narayana, Pradyumna, author; Draper, Bruce A., advisor; Beveridge, Ross J., committee member; Anderson, Charles W., committee member; Peterson, Christopher, committee memberGestures are a common form of human communication and important for human computer interfaces (HCI). Most recent approaches to gesture recognition use deep learning within multi- channel architectures. We show that when spatial attention is focused on the hands, gesture recognition improves significantly, particularly when the channels are fused using a sparse network. We propose an architecture (FOANet) that divides processing among four modalities (RGB, depth, RGB flow, and depth flow), and three spatial focus of attention regions (global, left hand, and right hand). The resulting 12 channels are fused using sparse networks. This architecture improves performance on the ChaLearn IsoGD dataset from a previous best of 67.71% to 82.07%, and on the NVIDIA dynamic hand gesture dataset from 83.8% to 91.28%. We extend FOANet to perform gesture recognition on continuous streams of data. We show that the best temporal fusion strategies for multi-channel networks depends on the modality (RGB vs depth vs flow field) and target (global vs left hand vs right hand) of the channel. The extended architecture achieves optimum performance using Gaussian Pooling for global channels, LSTMs for focused (left hand or right hand) flow field channels, and late Pooling for focused RGB and depth channels. The resulting system achieves a mean Jaccard Index of 0.7740 compared to the previous best result of 0.6103 on the ChaLearn ConGD dataset without first pre-segmenting the videos into single gesture clips. Human vision has α and β channels for processing different modalities in addition to spatial attention similar to FOANet. However, unlike FOANet, attention is not implemented through separate neural channels. Instead, attention is implemented through top-down excitation of neurons corresponding to specific spatial locations within the α and β channels. Motivated by the covert attention in human vision, we propose a new architecture called CANet (Covert Attention Net), that merges spatial attention channels while preserving the concept of attention. The focus layers of CANet allows it to focus attention on hands without having dedicated attention channels. CANet outperforms FOANet by achieving an accuracy of 84.79% on ChaLearn IsoGD dataset while being efficient (≈35% of FOANet parameters and ≈70% of FOANet operations). In addition to producing state-of-the-art results on multiple gesture recognition datasets, this thesis also tries to understand the behavior of multi-channel networks (a la FOANet). Multi- channel architectures are becoming increasingly common, setting the state of the art for performance in gesture recognition and other domains. Unfortunately, we lack a clear explanation of why multi-channel architectures outperform single channel ones. This thesis considers two hypotheses. The Bagging hypothesis says that multi-channel architectures succeed because they average the result of multiple unbiased weak estimators in the form of different channels. The Society of Experts (SoE) hypothesis suggests that multi-channel architectures succeed because the channels differentiate themselves, developing expertise with regard to different aspects of the data. Fusion layers then get to combine complementary information. This thesis presents two sets of experiments to distinguish between these hypotheses and both sets of experiments support the SoE hypothesis, suggesting multi-channel architectures succeed because their channels become specialized. Finally we demonstrate the practical impact of the gesture recognition techniques discussed in this thesis in the context of a sophisticated human computer interaction system. We developed a prototype system with a limited form of peer-to-peer communication in the context of blocks world. The prototype allows the users to communicate with the avatar using gestures and speech and make the avatar build virtual block structures.Item Open Access Joint shape and motion estimation from echo-based sensor data(Colorado State University. Libraries, 2018) Pine, Samuel J., author; Cheney, Margaret, advisor; Bates, Daniel, committee member; Fosdick, Bailey, committee member; Peterson, Christopher, committee memberGiven a set of time-series data collected from echo-based ranging sensors, we study the problem of jointly estimating the shape and motion of the target under observation when the sensor positions are also unknown. Using an approach first described by Stuff et al., we model the target as a point configuration in Euclidean space and estimate geometric invariants of the configuration. The geometric invariants allow us to estimate the target shape, from which we can estimate the motion of the target relative to the sensor position. This work will unify the various geometric- invariant based shape and motion estimation literature under a common framework, and extend that framework to include results for passive, bistatic sensor systems.Item Open Access Machine learning models towards elucidating the plant intron retention code(Colorado State University. Libraries, 2017) Sneham, Swapnil, author; Ben-Hur, Asa, advisor; Chitsaz, Hamidreza, committee member; Peterson, Christopher, committee memberAlternative Splicing is a process that allows a single gene to encode multiple proteins. Intron Retention (IR) is a type of alternative splicing which is mainly prevalent in plants, but has been shown to regulate gene expression in various organisms and is often involved in rare human diseases. Despite its important role, not much research has been done to understand IR. The motivation behind this research work is to better understand IR and how it is regulated by various biological factors. We designed a combination of 137 features, forming an "intron retention code", to reveal the factors that contribute to IR. Using random forest and support vector machine classifiers, we show the usefulness of these features for the task of predicting whether an intron is subject to IR or not. An analysis of the top-ranking features for this task reveals a high level of similarity of the most predictive features across the three plant species, demonstrating the conservation of the factors that determine IR. We also found a high level of similarity to the top features contributing to IR in mammals. The task of predicting the response to drought stress proved more difficult, with lower levels of accuracy and lower levels of similarity across species, suggesting that additional features need to be considered for predicting condition-specific IR.Item Open Access Persistence and simplicial metric thickenings(Colorado State University. Libraries, 2024) Moy, Michael, author; Adams, Henry, advisor; Patel, Amit, committee member; Peterson, Christopher, committee member; Ben-Hur, Asa, committee memberThis dissertation examines the theory of one-dimensional persistence with an emphasis on simplicial metric thickenings and studies two particular filtrations of simplicial metric thickenings in detail. It gives self-contained proofs of foundational results on one-parameter persistence modules of vector spaces, including interval decomposability, existence of persistence diagrams and barcodes, and the isometry theorem. These results are applied to prove the stability of persistent homology for sublevel set filtrations, simplicial complexes, and simplicial metric thickenings. The filtrations of simplicial metric thickenings studied in detail are the Vietoris–Rips and anti-Vietoris–Rips metric thickenings of the circle. The study of the Vietoris–Rips metric thickenings is motivated by persistent homology and its use in applied topology, and it builds on previous work on their simplicial complex counterparts. On the other hand, the study of the anti-Vietoris–Rips metric thickenings is motivated by their connections to graph colorings. In both cases, the homotopy types of these spaces are shown to be odd-dimensional spheres, with dimensions depending on the scale parameters.Item Open Access Practical aspects of designing and developing a multimodal embodied agent(Colorado State University. Libraries, 2021) Bangar, Rahul, author; Beveridge, Ross, advisor; Ortega, Francisco R., advisor; Peterson, Christopher, committee memberThis thesis reviews key elements that went into the design and construction of the CSU CwC Embodied agent, also known as the Diana System. The Diana System has been developed over five years by a joint team of researchers at three institutions – Colorado State University, Brandeis University and the University of Florida. Over that time, I contributed to this overall effort and in this thesis, I present a practical review of key elements involved in designing and constructing the system. Particular attention is paid to Diana's multimodal capabilities that engage asynchronously and concurrently to support realistic interactions with the user. Diana can communicate in visual as well as auditory modalities. She can understand a variety of hand gestures for object manipulation, deixis, etc. and can gesture in return. Diana can also hold a conversation with the user in spoken and/or written English. Gestures and speech are often at play simultaneously, supplementing and complementing each other. Diana conveys her attention through several non-verbal cues like slower blinking when inattentive, keeping her gaze on the subject of her attention, etc. Finally, her ability to express emotions with facial expressions adds another crucial human element to any user interaction with the system. Central to Diana's capabilities is a blackboard architecture coordinating a hierarchy of modular components, each controlling a part of Diana's perceptual, cognitive, and motor abilities. The modular design facilitates contributions from multiple disciplines, namely VoxSim/VoxML with Text-to-speech/Automatic Speech Recognition systems for natural language understanding, deep neural networks for gesture recognition, 3D computer animation systems, etc. – all integrated within the Unity game engine to create an embodied, intelligent agent that is Diana. The primary contribution of this thesis is to provide a detailed explanation of Diana's internal working along with a thorough background of the research that supports these technologies.Item Open Access Reevaluating the photophysics and electronic structure of Cr(III) and V(II) complexes: the implications of distortion on the excited state manifold(Colorado State University. Libraries, 2020) Portillo, Romeo I., author; Shores, Matthew P., advisor; Rappé, Anthony K., committee member; Chen, Eugene Y.-X., committee member; Peterson, Christopher, committee memberPresented in this dissertation are investigations into the electronic structure of chromium and vanadium complexes targeted towards photocatalysis. These studies have focused on two primary features in the excited state manifold: the energy of the excited state and the relative distortion of the excited state to the ground state. Chapter 1 provides a background on how the study of electron transfer led to the development of inorganic photocatalysis. The chapter includes the progression of photocatalysts design from [Ru(bpy)3]2+ to modern alternatives focusing on Earth-abundant reagents. Additionally, I provide my perspective on these advances and criticism of prevalent methodologies. Chapter 2 discusses the synthesis and characterization of polypyridyl-containing Cr(III) complexes. Each complex exhibits spectroscopic signatures of an unusual 4(3IL) excited state, a mixed excited state between a paramagnetic ligand and metal center. Calculations provide insight into the character of this excited state, suggesting this 4(3IL) excited state may be the lowest spinallowed excited state in some of these complexes. The minimal distortion in these excited states limit the degrees of freedom for non-radiative decay compared to the metal-based 4T2 excited state. Chapter 3 discusses the synthesis and characterization of two V(II) polypyridyl complexes. Here, I reevaluate the proposed excited state manifold in the literature which claims that the 4MLCT is the lowest energy excited state. Spectroelectrochemical and picosecond-resolved spectroscopic techniques reveal a short-lived excited state, presumably 2MLCT. A new excited state manifold is presented, suggesting doublet excited states are relevant to the understanding of V(II) photophysics. Chapter 4 discusses the differences in the electronic structure of isoelectronic V(II) and Cr(III) polypyridyls. While several factors contribute to these differences, the identity and energies of the relevant excited states lead to a completely different excited state manifold between the two systems. The chapter summarizes the work of Chapters 2 and 3. Chapter 5 discusses the synthesis and electronic structure of a tripodal ligand scaffold bound to V(II) and V(III). The differences between the hexacoordinate V(II) and heptacoordinate V(III) further our understanding of the apical nitrogen's role on the electronics of the complex. Additionally, we exploit the utility of the SHAPE program to quantify structural distortion and correlate to the species' electronic structure. Chapter 6 discusses the electronic structure of a similar vanadium tripodal complex, [V((5-CO2Me)py)3tren]2+ . This complex displays spectroscopic signals of both a V(II) complex with a neutral ligand and V(III) complex with a ligand radical. Different phenomena are proposed, but neither provide a complete explanation of the results. Chapter 7 summarizes the investigations into V(II) and Cr(III) photophysics. Additionally, I discuss how SHAPE may be used in other fields and identify important structural motifs through machine learning.Item Open Access Scalable learning of actions from unlabeled videos(Colorado State University. Libraries, 2013) O'Hara, Stephen, author; Draper, Bruce A., advisor; Howe, Adele, committee member; Anderson, Charles, committee member; Peterson, Christopher, committee memberEmerging applications in human-computer interfaces, security, and robotics have a need for understanding human behavior from video data. Much of the research in the field of action recognition evaluates methods using relatively small data sets, under controlled conditions, and with a small set of allowable action labels. There are significant challenges in trying to adapt existing action recognition models to less structured and larger-scale data sets. Those challenges include: the recognition of a large vocabulary of actions, the scalability to learn from a large corpus of video data, the need for real-time recognition on streaming video, and the requirement to operate in settings with uncontrolled lighting, a variety of camera angles, dynamic backgrounds, and multiple actors. This thesis focuses on scalable methods for classifying and clustering actions with minimal human supervision. Unsupervised methods are emphasized in order to learn from a massive amount of unlabeled data, and for the potential to retrain models with minimal human intervention when adapting to new settings or applications. Because many applications of action recognition require real-time performance, and training data sets can be large, scalable methods for both learning and detection are beneficial. The specific contributions from this dissertation include a novel method for Approximate Nearest Neighbor (ANN) indexing of general metric spaces and the application of this structure to a manifold-based action representation. With this structure, nearest-neighbor action recognition is demonstrated to be comparable or superior to existing methods, while also being fast and scalable. Leveraging the same metric space indexing mechanism, a novel clustering method is introduced for discovering action exemplars in data.Item Open Access Sparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman iterative techniques(Colorado State University. Libraries, 2012) Rohrbacker, Nicholas, author; Kirby, Michael, advisor; Peterson, Christopher, committee member; Liu, Jiangguo, committee member; Ben-Hur, Asa, committee memberIn this dissertation we propose Split Bregman algorithms for several multivariate analytic techniques for dimensionality reduction and feature selection including Sparse Principal Components Analysis, Bisparse Singular Value Decomposition (BSSVD) and Bisparse Singular Value Decomposition with an ℓ1-constrained classifier BSSVDℓ1. For each of these problems we construct and solve a new optimization problem using these Bregman iterative techniques. Each of the proposed optimization problems contain one or more ℓ1-regularization terms to enforce sparsity in the solutions. The use of the ℓ1-norm to enforce sparsity is a widely used technique, however, its lack of differentiability makes it more difficult to solve problems including these types of terms. Bregman iterations make these solutions possible without the addition of variables and algorithms such as the Split Bregman algorithm makes additional penalty terms and multiple ℓ1 terms feasible, a trait that is not present in other state of the art algorithms such as the fixed point continuation algorithm. It is also shown empirically to be faster than another iterative solver for total variation image denoising, another ℓ1-regularized problem, in. We also link sparse Principal Components to cluster centers, denoise Hyperspectral Images using the BSSVD, identify and remove ambiguous observations from a classification problem using the algorithm and detect anomalistic subgraphs using Sparse Eigenvectors of the Modularity Matrix.Item Open Access Unsupervised video segmentation using temporal coherence of motion(Colorado State University. Libraries, 2015) Alsaaran, Hessah, author; Draper, Bruce A., advisor; Beveridge, J. Ross, advisor; Whitley, Darrell, committee member; Peterson, Christopher, committee memberSpatio-temporal video segmentation groups pixels with the goal of representing moving objects in scenes. It is a difficult task for many reasons: parts of an object may look very different from each other, while parts of different objects may look similar and/or overlap. Of particular importance to this dissertation, parts of non-rigid objects such as animals may move in different directions at the same time. While appearance models are good for segmenting visually distinct objects and traditional motion models are good for segmenting rigid objects, there is a need for a new technique to segment objects that move non-rigidly. This dissertation presents a new unsupervised motion-based video segmentation approach. It segments non-rigid objects based on motion temporal coherence (i.e. the correlations of when points move), instead of motion magnitude and direction as in previous approaches. The hypothesis is that although non-rigid objects can move their parts in different directions, their parts tend to move at the same time. In the experiments, the proposed approach achieves better results than related state-of-the-art approaches on a video of zebras in the wild, and on 41 videos from the VSB100 dataset.Item Open Access Vietoris–Rips metric thickenings and Wasserstein spaces(Colorado State University. Libraries, 2020) Mirth, Joshua, author; Adams, Henry, advisor; Peterson, Christopher, committee member; Patel, Amit, committee member; Eykholt, Richard, committee memberIf the vertex set, X, of a simplicial complex, K, is a metric space, then K can be interpreted as a subset of the Wasserstein space of probability measures on X. Such spaces are called simplicial metric thickenings, and a prominent example is the Vietoris–Rips metric thickening. In this work we study these spaces from three perspectives: metric geometry, optimal transport, and category theory. Using the geodesic structure of Wasserstein space we give a novel proof of Hausmann's theorem for Vietoris–Rips metric thickenings. We also prove the first Morse lemma in Wasserstein space and relate it to the geodesic perspective. Finally we study the category of simplicial metric thickenings and determine effects of certain limits and colimits on homotopy type.