Point-set matching defines the task in computer vision of identifying a one-to-one alignment between two sets of points. Existing techniques rely on simple relationships between point-sets in order to efficiently find optimal correspondences between larger sets. Modern methodology precludes application to more challenging point-set matching tasks which benefit from interdependent modeling. This thesis addresses a gap in combinatorial optimization literature by enhancing leading methods in both graph matching and multiple object tracking (MOT) to more flexibly use data-driven point-set matching models. Presented contributions are inspired by Caenorhabditis elegans, a transparent free-living roundworm frequently studied in developmental biology and neurobiology. The C. elegans embryo, containing around 550 cells at hatch, can be used for cell tracking studies to understand how cell movement drives the development of specific embryonic tissues and organ functions. The development of muscle cells complicates analyses during late-stage development, as embryos begin twitching due to muscular activity. The sporadic twitches cause cells to move violently and unpredictably, invalidating traditional cell tracking approaches. The embryo possesses seam cells, a set of 20 cells which together act as fiducial markers to approximate the coiled embryo's body. Novel optimization algorithms and data-driven hypergraphical models leveraging the correlated movement among seam cells are used to forward research on C. elegans embryogenesis. We contribute two optimization algorithms applicable in differing conditions to interdependent point-set matching. The first algorithm, Exact Hypergraph Matching (EHGM), exactly solves the n-adic assignment problem by casting the problem as hypergraph matching. The algorithm obtains solutions to highly interdependent seam cell identification models. The second optimization algorithm, Multiple Hypothesis Hypergraph Tracking (MHHT), adapts traditional multiple hypothesis tracking with hypergraphical data association. Results from both studies highlight improved performance over established methods while providing adaptable optimization tools for multiple academic communities.

The canonical point-set matching task is solved efficiently under strict assumptions of frame-to-frame transformations. Challenging situations arising from non-rigid displacements between frames will complicate established methods. Particularly, limitations in fluorescence microscopy paired with muscular twitching in late-stage embryonic C. elegans yield adversarial point-set matching tasks. Seam cell identification is cast as an assignment problem; detected cells in images are uniquely identified through a combinatorial optimization algorithm. Existing graph matching methods are underequipped to contextualize the coiled embryonic position in sparsely imaged samples. Both the lack of an effective point-set matching model and an efficient algorithm for solving the resulting optimization problem limit computationally driven solutions to identify seam cells in acquired image volumes. We cast the n-adic problem as hypergraph matching and present an exact algorithm to solve the resulting optimization problem. EHGM adapts the branch-and-bound paradigm to dynamically identify a globally optimal correspondence; it is the first algorithm capable of solving the underlying optimization problem. Our algorithm and accompanying data-driven hypergraphical models identify seam cells more accurately than established point-set matching methods.

The final hours of embryogenesis encompass the moments in which C. elegans assumes motor control and begins exhibiting behavior. Rapid imaging of the seam cells provides insight into the embryo’s movement as a proxy for behavior. However, seam cell tracking is especially challenging due to both muscular twitching and the low dose required to gently image the embryo without perturbing development. Current methods in MOT rely on independent object trajectories undergoing smooth motion to effectively track large numbers of objects. Multiple Hypothesis Tracking (MHT) is the foremost method for challenging MOT tasks, yet the method cannot model correlated object movements. We contribute Multiple Hypothesis Hypergraph Tracking (MHHT) as an extension of MHT, which performs interdependent object tracking by jointly representing objects as a hypergraph. We apply MHHT to track seam cell nuclei during late-stage embryogenesis. Data-driven hypergraphical models more accurately track seam cells than traditional MHT based approaches. Analysis of time-lapse embryonic postures and behavioral motifs reveal a stereotyped developmental progression in C. elegans. Further analysis uncovers late-stage motility defects in unc-13 mutants.