15,346 research outputs found

    Learning to Convolve: A Generalized Weight-Tying Approach

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    Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter on a square pixel-grid is difficult. In this paper, we learn how to transform filters for use in the group convolution, focussing on roto-translation. For this, we learn a filter basis and all rotated versions of that filter basis. Filters are then encoded by a set of rotation invariant coefficients. To rotate a filter, we switch the basis. We demonstrate we can produce feature maps with low sensitivity to input rotations, while achieving high performance on MNIST and CIFAR-10.Comment: Accepted to ICML 201

    Learning with Algebraic Invariances, and the Invariant Kernel Trick

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    When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA

    Image registration with sparse approximations in parametric dictionaries

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    We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an estimate of the global transformation between sparse images by examining the set of relative geometrical transformations between the respective features. We propose a theoretical analysis of our registration algorithm and we derive performance guarantees based on two novel important properties of redundant dictionaries, namely the robust linear independence and the transformation inconsistency. We propose several illustrations and insights about the importance of these dictionary properties and show that common properties such as coherence or restricted isometry property fail to provide sufficient information in registration problems. We finally show with illustrative experiments on simple visual objects and handwritten digits images that our algorithm outperforms baseline competitor methods in terms of transformation-invariant distance computation and classification

    Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

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    Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission and processing power. Encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. By encoding and processing the image information in quantum-mechanical systems, we here demonstrate the framework of quantum image processing, where a pure quantum state encodes the image information: we encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Our quantum image representation reduces the required number of qubits compared to existing implementations, and we present image processing algorithms that provide exponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an image, we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image. This demonstrates the potential of quantum image processing for highly efficient image and video processing in the big data era.Comment: 13 pages, including 9 figures and 5 appendixe
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