24,766 research outputs found
Understanding the Limitations of CNN-based Absolute Camera Pose Regression
Visual localization is the task of accurate camera pose estimation in a known
scene. It is a key problem in computer vision and robotics, with applications
including self-driving cars, Structure-from-Motion, SLAM, and Mixed Reality.
Traditionally, the localization problem has been tackled using 3D geometry.
Recently, end-to-end approaches based on convolutional neural networks have
become popular. These methods learn to directly regress the camera pose from an
input image. However, they do not achieve the same level of pose accuracy as 3D
structure-based methods. To understand this behavior, we develop a theoretical
model for camera pose regression. We use our model to predict failure cases for
pose regression techniques and verify our predictions through experiments. We
furthermore use our model to show that pose regression is more closely related
to pose approximation via image retrieval than to accurate pose estimation via
3D structure. A key result is that current approaches do not consistently
outperform a handcrafted image retrieval baseline. This clearly shows that
additional research is needed before pose regression algorithms are ready to
compete with structure-based methods.Comment: Initial version of a paper accepted to CVPR 201
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
Applications of the Wavelet Multiplicity Function
This paper examines the wavelet multiplicity function. An explicit formula
for the multiplicity function is derived. An application to operator
interpolation is then presented. We conclude with several remarks regarding the
wavelet connectivity problem.Comment: 9 pages, AMS-Late
Weighted interpolation inequalities: a perturbation approach
We study optimal functions in a family of Caffarelli-Kohn-Nirenberg
inequalities with a power-law weight, in a regime for which standard
symmetrization techniques fail. We establish the existence of optimal
functions, study their properties and prove that they are radial when the power
in the weight is small enough. Radial symmetry up to translations is true for
the limiting case where the weight vanishes, a case which corresponds to a
well-known subfamily of Gagliardo-Nirenberg inequalities. Our approach is based
on a concentration-compactness analysis and on a perturbation method which uses
a spectral gap inequality. As a consequence, we prove that optimal functions
are explicit and given by Barenblatt-type profiles in the perturbative regime
Multiple sampling and interpolation in the classical Fock space
We study multiple sampling, interpolation and uniqueness for the classical
Fock space in the case of unbounded mul-tiplicities
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