15,346 research outputs found
Learning to Convolve: A Generalized Weight-Tying Approach
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
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
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
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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