Change in viewpoint is one of the major factors for variation in object appearance across different images. Thus, view-invariant object recognition is a challenging and important image understanding task. In this paper, we propose a method that can match objects in images taken under different viewpoints. Unlike most methods in the literature, no restriction on camera orientations or internal camera parameters are imposed and no prior knowledge of 3D structure of the object is required. We prove that when two cameras take pictures of the same object from two different viewing angels, the relationship between every quadruple of points reduces to the special case of homography with two equal eigenvalues. Based on this property, we formulate the problem as an error function that indicates how likely two sets of 2D points are projections of the same set of 3D points under two different cameras. Comprehensive set of experiments were conducted to prove the robustness of the method to noise, and evaluate its performance on real-world applications, such as face and object recognition.
@cite_119: Kernel methods provide a powerful and unified framework for pattern discovery, motivating algorithms that can act on general types of data (e.g. strings, vectors or text) and look for general types of relations (e.g. rankings, classifications, regressions, clusters). The application areas range from neural networks and pattern recognition to machine learning and data mining. This book, developed from lectures and tutorials, fulfils two major roles: firstly it provides practitioners with a large toolkit of algorithms, kernels and solutions ready to use for standard pattern discovery problems in fields such as bioinformatics, text analysis, image analysis. Secondly it provides an easy introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new specific application, and covering all the necessary conceptual and mathematical tools to do so.
@cite_140: This paper presents a general multi-view feature extraction approach that we call Generalized Multiview Analysis or GMA. GMA has all the desirable properties required for cross-view classification and retrieval: it is supervised, it allows generalization to unseen classes, it is multi-view and kernelizable, it affords an efficient eigenvalue based solution and is applicable to any domain. GMA exploits the fact that most popular supervised and unsupervised feature extraction techniques are the solution of a special form of a quadratic constrained quadratic program (QCQP), which can be solved efficiently as a generalized eigenvalue problem. GMA solves a joint, relaxed QCQP over different feature spaces to obtain a single (non)linear subspace. Intuitively, GMA is a supervised extension of Canonical Correlational Analysis (CCA), which is useful for cross-view classification and retrieval. The proposed approach is general and has the potential to replace CCA whenever classification or retrieval is the purpose and label information is available. We outperform previous approaches for textimage retrieval on Pascal and Wiki text-image data. We report state-of-the-art results for pose and lighting invariant face recognition on the MultiPIE face dataset, significantly outperforming other approaches.
One common approach to tackle the varience in pose is to find latent spaces where the correlation between two views are maximized. Canonical correlation analysis(CCA) @cite_119 projects the data from two views into two low dimensional subspace which are highly correlated. @cite_140 have extended CCA method so that it exploits the labels of training data to find a more discriminative projection direction. Both of the mentioned methods can exploit kernels to model non-linearity. Although methods based on latent spaces have proven to be powerful tools for both multi-view image classification and multi-modal data classification, they require learning a projection direction for every viewpoint and their ability to generalize to unseen viewpoints is limited.