2,195 research outputs found

    Masking Strategies for Image Manifolds

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    We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes

    Regression on fixed-rank positive semidefinite matrices: a Riemannian approach

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    The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks

    Fine-grained Categorization and Dataset Bootstrapping using Deep Metric Learning with Humans in the Loop

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    Existing fine-grained visual categorization methods often suffer from three challenges: lack of training data, large number of fine-grained categories, and high intraclass vs. low inter-class variance. In this work we propose a generic iterative framework for fine-grained categorization and dataset bootstrapping that handles these three challenges. Using deep metric learning with humans in the loop, we learn a low dimensional feature embedding with anchor points on manifolds for each category. These anchor points capture intra-class variances and remain discriminative between classes. In each round, images with high confidence scores from our model are sent to humans for labeling. By comparing with exemplar images, labelers mark each candidate image as either a "true positive" or a "false positive". True positives are added into our current dataset and false positives are regarded as "hard negatives" for our metric learning model. Then the model is retrained with an expanded dataset and hard negatives for the next round. To demonstrate the effectiveness of the proposed framework, we bootstrap a fine-grained flower dataset with 620 categories from Instagram images. The proposed deep metric learning scheme is evaluated on both our dataset and the CUB-200-2001 Birds dataset. Experimental evaluations show significant performance gain using dataset bootstrapping and demonstrate state-of-the-art results achieved by the proposed deep metric learning methods.Comment: 10 pages, 9 figures, CVPR 201
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