13,338 research outputs found
A new ADMM algorithm for the Euclidean median and its application to robust patch regression
The Euclidean Median (EM) of a set of points in an Euclidean space
is the point x minimizing the (weighted) sum of the Euclidean distances of x to
the points in . While there exits no closed-form expression for the EM,
it can nevertheless be computed using iterative methods such as the Wieszfeld
algorithm. The EM has classically been used as a robust estimator of centrality
for multivariate data. It was recently demonstrated that the EM can be used to
perform robust patch-based denoising of images by generalizing the popular
Non-Local Means algorithm. In this paper, we propose a novel algorithm for
computing the EM (and its box-constrained counterpart) using variable splitting
and the method of augmented Lagrangian. The attractive feature of this approach
is that the subproblems involved in the ADMM-based optimization of the
augmented Lagrangian can be resolved using simple closed-form projections. The
proposed ADMM solver is used for robust patch-based image denoising and is
shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
No-reference Image Denoising Quality Assessment
A wide variety of image denoising methods are available now. However, the
performance of a denoising algorithm often depends on individual input noisy
images as well as its parameter setting. In this paper, we present a
no-reference image denoising quality assessment method that can be used to
select for an input noisy image the right denoising algorithm with the optimal
parameter setting. This is a challenging task as no ground truth is available.
This paper presents a data-driven approach to learn to predict image denoising
quality. Our method is based on the observation that while individual existing
quality metrics and denoising models alone cannot robustly rank denoising
results, they often complement each other. We accordingly design denoising
quality features based on these existing metrics and models and then use Random
Forests Regression to aggregate them into a more powerful unified metric. Our
experiments on images with various types and levels of noise show that our
no-reference denoising quality assessment method significantly outperforms the
state-of-the-art quality metrics. This paper also provides a method that
leverages our quality assessment method to automatically tune the parameter
settings of a denoising algorithm for an input noisy image to produce an
optimal denoising result.Comment: 17 pages, 41 figures, accepted by Computer Vision Conference (CVC)
201
Recombinator Networks: Learning Coarse-to-Fine Feature Aggregation
Deep neural networks with alternating convolutional, max-pooling and
decimation layers are widely used in state of the art architectures for
computer vision. Max-pooling purposefully discards precise spatial information
in order to create features that are more robust, and typically organized as
lower resolution spatial feature maps. On some tasks, such as whole-image
classification, max-pooling derived features are well suited; however, for
tasks requiring precise localization, such as pixel level prediction and
segmentation, max-pooling destroys exactly the information required to perform
well. Precise localization may be preserved by shallow convnets without pooling
but at the expense of robustness. Can we have our max-pooled multi-layered cake
and eat it too? Several papers have proposed summation and concatenation based
methods for combining upsampled coarse, abstract features with finer features
to produce robust pixel level predictions. Here we introduce another model ---
dubbed Recombinator Networks --- where coarse features inform finer features
early in their formation such that finer features can make use of several
layers of computation in deciding how to use coarse features. The model is
trained once, end-to-end and performs better than summation-based
architectures, reducing the error from the previous state of the art on two
facial keypoint datasets, AFW and AFLW, by 30\% and beating the current
state-of-the-art on 300W without using extra data. We improve performance even
further by adding a denoising prediction model based on a novel convnet
formulation.Comment: accepted in CVPR 201
Learning how to be robust: Deep polynomial regression
Polynomial regression is a recurrent problem with a large number of
applications. In computer vision it often appears in motion analysis. Whatever
the application, standard methods for regression of polynomial models tend to
deliver biased results when the input data is heavily contaminated by outliers.
Moreover, the problem is even harder when outliers have strong structure.
Departing from problem-tailored heuristics for robust estimation of parametric
models, we explore deep convolutional neural networks. Our work aims to find a
generic approach for training deep regression models without the explicit need
of supervised annotation. We bypass the need for a tailored loss function on
the regression parameters by attaching to our model a differentiable hard-wired
decoder corresponding to the polynomial operation at hand. We demonstrate the
value of our findings by comparing with standard robust regression methods.
Furthermore, we demonstrate how to use such models for a real computer vision
problem, i.e., video stabilization. The qualitative and quantitative
experiments show that neural networks are able to learn robustness for general
polynomial regression, with results that well overpass scores of traditional
robust estimation methods.Comment: 18 pages, conferenc
Topological analysis of scalar fields with outliers
Given a real-valued function defined over a manifold embedded in
, we are interested in recovering structural information about
from the sole information of its values on a finite sample . Existing
methods provide approximation to the persistence diagram of when geometric
noise and functional noise are bounded. However, they fail in the presence of
aberrant values, also called outliers, both in theory and practice.
We propose a new algorithm that deals with outliers. We handle aberrant
functional values with a method inspired from the k-nearest neighbors
regression and the local median filtering, while the geometric outliers are
handled using the distance to a measure. Combined with topological results on
nested filtrations, our algorithm performs robust topological analysis of
scalar fields in a wider range of noise models than handled by current methods.
We provide theoretical guarantees and experimental results on the quality of
our approximation of the sampled scalar field
- …