6,256 research outputs found
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
Photometric Depth Super-Resolution
This study explores the use of photometric techniques (shape-from-shading and
uncalibrated photometric stereo) for upsampling the low-resolution depth map
from an RGB-D sensor to the higher resolution of the companion RGB image. A
single-shot variational approach is first put forward, which is effective as
long as the target's reflectance is piecewise-constant. It is then shown that
this dependency upon a specific reflectance model can be relaxed by focusing on
a specific class of objects (e.g., faces), and delegate reflectance estimation
to a deep neural network. A multi-shot strategy based on randomly varying
lighting conditions is eventually discussed. It requires no training or prior
on the reflectance, yet this comes at the price of a dedicated acquisition
setup. Both quantitative and qualitative evaluations illustrate the
effectiveness of the proposed methods on synthetic and real-world scenarios.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence
(T-PAMI), 2019. First three authors contribute equall
Depth Super-Resolution Meets Uncalibrated Photometric Stereo
A novel depth super-resolution approach for RGB-D sensors is presented. It
disambiguates depth super-resolution through high-resolution photometric clues
and, symmetrically, it disambiguates uncalibrated photometric stereo through
low-resolution depth cues. To this end, an RGB-D sequence is acquired from the
same viewing angle, while illuminating the scene from various uncalibrated
directions. This sequence is handled by a variational framework which fits
high-resolution shape and reflectance, as well as lighting, to both the
low-resolution depth measurements and the high-resolution RGB ones. The key
novelty consists in a new PDE-based photometric stereo regularizer which
implicitly ensures surface regularity. This allows to carry out depth
super-resolution in a purely data-driven manner, without the need for any
ad-hoc prior or material calibration. Real-world experiments are carried out
using an out-of-the-box RGB-D sensor and a hand-held LED light source.Comment: International Conference on Computer Vision (ICCV) Workshop, 201
Maximum-a-posteriori estimation with Bayesian confidence regions
Solutions to inverse problems that are ill-conditioned or ill-posed may have
significant intrinsic uncertainty. Unfortunately, analysing and quantifying
this uncertainty is very challenging, particularly in high-dimensional
problems. As a result, while most modern mathematical imaging methods produce
impressive point estimation results, they are generally unable to quantify the
uncertainty in the solutions delivered. This paper presents a new general
methodology for approximating Bayesian high-posterior-density credibility
regions in inverse problems that are convex and potentially very
high-dimensional. The approximations are derived by using recent concentration
of measure results related to information theory for log-concave random
vectors. A remarkable property of the approximations is that they can be
computed very efficiently, even in large-scale problems, by using standard
convex optimisation techniques. In particular, they are available as a
by-product in problems solved by maximum-a-posteriori estimation. The
approximations also have favourable theoretical properties, namely they
outer-bound the true high-posterior-density credibility regions, and they are
stable with respect to model dimension. The proposed methodology is illustrated
on two high-dimensional imaging inverse problems related to tomographic
reconstruction and sparse deconvolution, where the approximations are used to
perform Bayesian hypothesis tests and explore the uncertainty about the
solutions, and where proximal Markov chain Monte Carlo algorithms are used as
benchmark to compute exact credible regions and measure the approximation
error
A Deep Primal-Dual Network for Guided Depth Super-Resolution
In this paper we present a novel method to increase the spatial resolution of
depth images. We combine a deep fully convolutional network with a non-local
variational method in a deep primal-dual network. The joint network computes a
noise-free, high-resolution estimate from a noisy, low-resolution input depth
map. Additionally, a high-resolution intensity image is used to guide the
reconstruction in the network. By unrolling the optimization steps of a
first-order primal-dual algorithm and formulating it as a network, we can train
our joint method end-to-end. This not only enables us to learn the weights of
the fully convolutional network, but also to optimize all parameters of the
variational method and its optimization procedure. The training of such a deep
network requires a large dataset for supervision. Therefore, we generate
high-quality depth maps and corresponding color images with a physically based
renderer. In an exhaustive evaluation we show that our method outperforms the
state-of-the-art on multiple benchmarks.Comment: BMVC 201
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