| Correlation Filters are a class of classifiers, which are specifically optimized to produce sharp peaks in the correlation output, primarily to achieve accurate localization of targets in scenes. While correlation filtering theory has been very widely researched, there exists plenty of scope for extending and adapting correlation filter theory to non-traditional settings and applications of correlation filters. Towards this purpose, we propose to study the following advances to correlation filter theory. First, traditional correlation filter designs are limited to scalar feature representations of objects. In this thesis we propose a new margin based correlation filter formulation for vector feature representations of objects thereby enabling new applications and scenarios where correlation filters can be used. Second, traditional correlation filters have been designed to classify images spanning a subspace, while a typical image and its various distortions span an arbitrary and unknown low-dimensional manifold. We propose local linear subspace models to approximate this unknown non-linear manifold by a combination of multiple linear subspaces allowing us to explicitly control the trade-off between the computational complexity and discriminative capacity of object detection models. Third, traditionally correlation filters have been designed to produce a single sharp peak in the correlation output, mainly to achieve accurate localization of targets. In this thesis we extend the filter design paradigm to structured prediction tasks i.e., tasks that involve predicting structured outputs (outputs with complex internal structure like object bounding boxes in images) instead of a small or simple set (like a single binary or real output) through the application of biometric key-binding which is posed as a structured prediction problem. Finally, we consider an application where the task of pattern detection is only a sub-problem of a larger problem requiring multiple pattern detectors along with availability of structural constraints in the form of a prior on the detector outputs. |
