iii Abstract Motivated by problems in image processing involving segmentation and detection of multiple instances of complex objects, this dissertation explores the use of marked Poisson point processes within a Bayesian nonparametric framework. The Poisson point process underlies a wide range of combinatorial stochastic processes and as such has been a key object driving research in Bayesian nonparametrics. We explore Poisson point processes in combination with probabilistic shape and

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... e priors for detection/segmentation of objects/patterns in 1D, 2D and 3D frameworks. This probabilistic formulation encompasses uncertainty in number, location, shape and appearance of the feature of interest, be it in images or time-series data (detection/segmentation of objects of interest). In images, this model can simultaneously detect and segment objects of interest. The generative process of the model can be explained as sampling a random number of objects at random locations from a Poisson process. The shape of each object is sampled from a shape model. The appearance inside and outside the shape boundary is sampled from an appearance model with foreground and background parameters respectively. The Poisson intensity parameter can either be homogeneous (uniform) or non-homogeneous. A non-homogeneous Poisson prior provides the flexibility to incorporate spatial context information regarding where the high or low concentration areas occur. We model the non-homogeneous Poisson intensity with a log-Gaussian Cox process. For shape, any probabilistic model can be used. We describe examples of both, parametric and complex shape priors. Appearance features can be simple intensity values of the image or higher level features such as texture. This dissertation was made possible with the help and support from professors, research staff, graduate students, friends, family and coffee shops of Boston and Cambridge. I thank my advisor Jennifer Dy for her guidance and encouragement. Her high frequency of meetings, personal attention, suggestions and support have helped me immensely to mature as a graduate student. I thank her for giving me the opportunity to be a part of her talented research team and graduate students. I thank Ralf Birken, Ming Wang, Sara Wadia-Fascetti, and the VOTERS project for accepting me into their program and mentoring me. The VOTERS project gave me the opportunity to peek into a wide range of research developments in other fields as well. I thank my co-advisor Ralf Birken for his guidance and patience in helping me through the graduate study. I thank the BSPIRAL group and specifically professors, Dana Brooks and Deniz Erdogmus for encouraging us to interact and present a wide variety of materials to the group. It has helped me learn the art of digesting new material quickly and asking right questions. I thank Michael Jordan for his ideas and help in making this dissertation possible. I thank Milind Rajadhyaksha and Kivanc Kose for their support and help in providing me data and their insight. I thank Gunar Schirner for his guidance and mentoring that helped me understand and develop the camera system i in VOTERS project. I thank my friends Rameez Ahmed, Foram Thakkar, Abhishek Dey and Shruti (also my roommate) for their support, and making my graduate life in Boston memorable. I thank my lab mates,