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.
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.
@cite_119 @cite_140
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This paper proposes a new approach for Cross Modal Matching, i.e. the matching of patterns represented in di erent modalities, when pairs of same di erent data are available for training (e.g. faces of same di erent persons). In this situation, standard approaches such as Partial Least Squares (PLS) or Canonical Correlation Analysis (CCA), map the data into a common latent space that maximizes the covariance, using the information brought by positive pairs only. Our contribution is a new metric learning algorithm, which alleviates this limitation by considering both positive and negative constraints and use them effi ciently to learn a discriminative latent space. The contribution is validated on several datasets for which the proposed approach consistently outperforms PLS CCA as well as more recent discriminative approaches. Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multi-view data, it ignores the high order statistics (correlation information) which can only be discovered by simultaneously exploring all features. Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the canonical correlation of multiple (more than two) views. Crucially, we prove that the main problem of multi-view canonical correlation maximization is equivalent to finding the best rank- @math approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained. In addition, a non-linear extension of TCCA is presented. Experiments on various challenge tasks, including large scale biometric structure prediction, internet advertisement classification, and web image annotation, demonstrate the effectiveness of the proposed method Linking two data sources is a basic building block in numerous computer vision problems. Canonical Correlation Analysis (CCA) achieves this by utilizing a linear optimizer in order to maximize the correlation between the two views. Recent work makes use of non-linear models, including deep learning techniques, that optimize the CCA loss in some feature space. In this paper, we introduce a novel, bi-directional neural network architecture for the task of matching vectors from two data sources. Our approach employs two tied neural network channels that project the two views into a common, maximally correlated space using the Euclidean loss. We show a direct link between the correlation-based loss and Euclidean loss, enabling the use of Euclidean loss for correlation maximization. To overcome common Euclidean regression optimization problems, we modify well-known techniques to our problem, including batch normalization and dropout. We show state of the art results on a number of computer vision matching tasks including MNIST image matching and sentence-image matching on the Flickr8k, Flickr30k and COCO datasets. Building a common representation for several related data sets is an important problem in multi-view learning. CCA and its extensions have shown that they are effective in finding the shared variation among all data sets. However, these models generally fail to exploit the common structure of the data when the views are with private information. Recently, methods explicitly modeling the information into shared part and private parts have been proposed, but they presume to know the prior knowledge about the latent space, which is usually impossible to obtain. In this paper, we propose a probabilistic model, which could simultaneously learn the structure of the latent space whilst factorize the information correctly, therefore the prior knowledge of the latent space is unnecessary. Furthermore, as a probabilistic model, our method is able to deal with missing data problem in a natural way. We show that our approach attains the performance of state-of-art methods on the task of human pose estimation when the motion capture view is completely missing, and significantly improves the inference accuracy with only a few observed data.