Change Detection in Stochastic Shape Dynamical Models with Applications in Activity Modeling and Abnormality Detection

摘要: Title of Dissertation: Change Detection in Stochastic Shape Dynamical Models with Applications Activity Modeling and Abnormality Namrata Vaswani, Doctor Philosophy, 2004 Dissertation directed by: Professor Rama Chellappa Department Electrical Computer Engineering The goal this research is to model an “activity” performed by a group moving interacting objects (which can be people or cars robots different rigid components the human body) use these models for abnormal activity detection, tracking segmentation. Previous approaches modeling include co-occurrence statistics (individual joint histograms) Dynamic Bayesian Networks, neither which applicable when number large. We treat as point (referred “landmarks”) propose their changing configuration deforming “shape” using ideas from Kendall’s shape theory discrete landmarks. A continuous state HMM defined landmark dynamics “activity”. landmarks at given time forms observation vector corresponding scaled Euclidean motion parameters form hidden vector. dynamical linear Gauss-Markov on “velocity”. “shape velocity” manifold tangent space that point. Particle filters are used track HMM, i.e. estimate observations. An change model, could slow drastic whose unknown. Drastic changes easily detected increase error negative log likelihood current past (OL). But usually get missed. have proposed statistic detection called ELL Expectation Log Likelihood observations) shown analytically experimentally complementary behavior OL changes. established stability (monotonic decrease) errors approximating changed observations particle filter optimal unchanged system. Asymptotic under stronger assumptions. Finally, it upper bound increasing function “rate change” derivatives all orders, its implications discussed. Another contribution thesis subspace algorithm pattern classification, we call Principal Components’ Null Space Analysis (PCNSA). PCNSA was motivated (PCA) approximates Bayes classifier Gaussian distributions unequal covariance matrices. derived classification probability expressions compared performance Linear Discriminant (LDA) both experimentally. action retrieval, object/face recognition