4,038 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection
Hierarchies, such as the tree of shapes, are popular representations for
image simplification and segmentation thanks to their multiscale structures.
Selecting meaningful level lines (boundaries of shapes) yields to simplify
image while preserving intact salient structures. Many image simplification and
segmentation methods are driven by the optimization of an energy functional,
for instance the celebrated Mumford-Shah functional. In this paper, we propose
an efficient approach to hierarchical image simplification and segmentation
based on the minimization of the piecewise-constant Mumford-Shah functional.
This method conforms to the current trend that consists in producing
hierarchical results rather than a unique partition. Contrary to classical
approaches which compute optimal hierarchical segmentations from an input
hierarchy of segmentations, we rely on the tree of shapes, a unique and
well-defined representation equivalent to the image. Simply put, we compute for
each level line of the image an attribute function that characterizes its
persistence under the energy minimization. Then we stack the level lines from
meaningless ones to salient ones through a saliency map based on extinction
values defined on the tree-based shape space. Qualitative illustrations and
quantitative evaluation on Weizmann segmentation evaluation database
demonstrate the state-of-the-art performance of our method.Comment: Pattern Recognition Letters, Elsevier, 201
Learning sparse representations of depth
This paper introduces a new method for learning and inferring sparse
representations of depth (disparity) maps. The proposed algorithm relaxes the
usual assumption of the stationary noise model in sparse coding. This enables
learning from data corrupted with spatially varying noise or uncertainty,
typically obtained by laser range scanners or structured light depth cameras.
Sparse representations are learned from the Middlebury database disparity maps
and then exploited in a two-layer graphical model for inferring depth from
stereo, by including a sparsity prior on the learned features. Since they
capture higher-order dependencies in the depth structure, these priors can
complement smoothness priors commonly used in depth inference based on Markov
Random Field (MRF) models. Inference on the proposed graph is achieved using an
alternating iterative optimization technique, where the first layer is solved
using an existing MRF-based stereo matching algorithm, then held fixed as the
second layer is solved using the proposed non-stationary sparse coding
algorithm. This leads to a general method for improving solutions of state of
the art MRF-based depth estimation algorithms. Our experimental results first
show that depth inference using learned representations leads to state of the
art denoising of depth maps obtained from laser range scanners and a time of
flight camera. Furthermore, we show that adding sparse priors improves the
results of two depth estimation methods: the classical graph cut algorithm by
Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page
Coherent multi-dimensional segmentation of multiview images using a variational framework and applications to image based rendering
Image Based Rendering (IBR) and in particular light field rendering has attracted a lot of
attention for interpolating new viewpoints from a set of multiview images. New images of
a scene are interpolated directly from nearby available ones, thus enabling a photorealistic
rendering. Sampling theory for light fields has shown that exact geometric information
in the scene is often unnecessary for rendering new views. Indeed, the band of the function
is approximately limited and new views can be rendered using classical interpolation
methods. However, IBR using undersampled light fields suffers from aliasing effects and
is difficult particularly when the scene has large depth variations and occlusions. In order
to deal with these cases, we study two approaches:
New sampling schemes have recently emerged that are able to perfectly reconstruct
certain classes of parametric signals that are not bandlimited but characterized by a finite
number of parameters. In this context, we derive novel sampling schemes for piecewise
sinusoidal and polynomial signals. In particular, we show that a piecewise sinusoidal signal
with arbitrarily high frequencies can be exactly recovered given certain conditions. These
results are applied to parametric multiview data that are not bandlimited.
We also focus on the problem of extracting regions (or layers) in multiview images
that can be individually rendered free of aliasing. The problem is posed in a multidimensional
variational framework using region competition. In extension to previous
methods, layers are considered as multi-dimensional hypervolumes. Therefore the segmentation
is done jointly over all the images and coherence is imposed throughout the
data. However, instead of propagating active hypersurfaces, we derive a semi-parametric
methodology that takes into account the constraints imposed by the camera setup and the
occlusion ordering. The resulting framework is a global multi-dimensional region competition that is consistent in all the images and efficiently handles occlusions. We show the
validity of the approach with captured light fields. Other special effects such as augmented
reality and disocclusion of hidden objects are also demonstrated
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
Rate-Distortion Efficient Piecewise Planar 3D Scene Representation from 2-D Images
Cataloged from PDF version of article.In any practical application of the 2-D-to-3-D conversion
that involves storage and transmission, representation effi-
ciency has an undisputable importance that is not reflected in the
attention the topic received. In order to address this problem, a
novel algorithm, which yields efficient 3-D representations in the
rate distortion sense, is proposed. The algorithm utilizes two views
of a scene to build a mesh-based representation incrementally, via
adding new vertices, while minimizing a distortion measure. The
experimental results indicate that, in scenes that can be approximated
by planes, the proposed algorithm is superior to the dense
depth map and, in some practical situations, to the block motion
vector-based representations in the rate-distortion sense
Optimising Spatial and Tonal Data for PDE-based Inpainting
Some recent methods for lossy signal and image compression store only a few
selected pixels and fill in the missing structures by inpainting with a partial
differential equation (PDE). Suitable operators include the Laplacian, the
biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The
quality of such approaches depends substantially on the selection of the data
that is kept. Optimising this data in the domain and codomain gives rise to
challenging mathematical problems that shall be addressed in our work.
In the 1D case, we prove results that provide insights into the difficulty of
this problem, and we give evidence that a splitting into spatial and tonal
(i.e. function value) optimisation does hardly deteriorate the results. In the
2D setting, we present generic algorithms that achieve a high reconstruction
quality even if the specified data is very sparse. To optimise the spatial
data, we use a probabilistic sparsification, followed by a nonlocal pixel
exchange that avoids getting trapped in bad local optima. After this spatial
optimisation we perform a tonal optimisation that modifies the function values
in order to reduce the global reconstruction error. For homogeneous diffusion
inpainting, this comes down to a least squares problem for which we prove that
it has a unique solution. We demonstrate that it can be found efficiently with
a gradient descent approach that is accelerated with fast explicit diffusion
(FED) cycles. Our framework allows to specify the desired density of the
inpainting mask a priori. Moreover, is more generic than other data
optimisation approaches for the sparse inpainting problem, since it can also be
extended to nonlinear inpainting operators such as EED. This is exploited to
achieve reconstructions with state-of-the-art quality.
We also give an extensive literature survey on PDE-based image compression
methods
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