Recognizing objects from images and videos has been a long standing problem in computer vision. The recent surge in the prevalence of visual cameras has given rise to two main challenges where, (i) it is important to understand different sources of object variations in more unconstrained scenarios, and (ii) rather than describing an object in isolation, efficient learning methods for modeling object-scene `contextual' relations are required to resolve visual ambiguities.

This dissertation addresses some aspects of these challenges, and consists of two parts. First part of the work focuses on obtaining object descriptors that are largely preserved across certain sources of variations, by utilizing models for image formation and local image features. Given a single instance of an object, we investigate the following three problems. (i) Representing a 2D projection of a 3D non-planar shape invariant to articulations, when there are no self-occlusions. We propose an articulation invariant distance that is preserved across piece-wise affine transformations of a non-rigid object parts', under a weak perspective imaging model, and then obtain a shape context-like descriptor to perform recognition; (ii) Understanding the space of arbitrary' blurred images of an object, by representing an unknown blur kernel of a known maximum size using a complete set of orthonormal basis functions spanning that space, and showing that subspaces resulting from convolving a clean object and its blurred versions with these basis functions are equal under some assumptions. We then view the invariant subspaces as points on a Grassmann manifold, and use statistical tools that account for the underlying non-Euclidean nature of the space of these invariants to perform recognition across blur; (iii) Analyzing the robustness of local feature descriptors to different illumination conditions. We perform an empirical study of these descriptors for the problem of face recognition under lighting change, and show that the direction of image gradient largely preserves object properties across varying lighting conditions.

The second part of the dissertation utilizes information conveyed by large quantity of data to learn contextual information shared by an object (or an entity) with its surroundings. (i) We first consider a supervised two-class problem of detecting lane markings from road video sequences, where we learn relevant feature-level contextual information through a machine learning algorithm based on boosting. We then focus on unsupervised object classification scenarios where, (ii) we perform clustering using maximum margin principles, by deriving some basic properties on the affinity of a pair of points' belonging to the same cluster using the information conveyed by all' points in the system, and (iii) then consider correspondence-free adaptation of statistical classifiers across domain shifting transformations, by generating meaningful `intermediate domains' that incrementally convey potential information about the domain change.