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Workshop
"An interdisciplinary approach to
Textures and Natural Images Processing"
- Program -
- Abstracts -
Jean-François
Aujol - A TV-Hilbert model for image denoising
and decomposition
Abstract: In this talk, we present a general
TV-Hilbert framework for image restoration and image decomposition.
We minimize a functional of the type inf_u (|u|_TV + |f-u|_H)
We propose an automatic algorithm to get an optimal restored
image (in the SNR sens) from a noisy image. We also explain
how to design a Hilbert norm to extract specific types of textures.
We illustrate this approach with some numerical examples. |
Xavier
Descombes - Urban analysis from texture.
Abstract: We will first show that a simple
texture model allows to discrimate urban areas on middle resolution
images. Some exemple will be presented on SPOT panchormatic
images (10m resolution) and ERS images. We then will adapt the
model in case of higher spatial resolution and higher spectral
resolution. When spatial resolution increases, as for SPOT V
images, we will show that an anisotropic generalization of the
previous model is required to avoid some false alarms. Finnaly,
we will consider hyperspectral data. In this case, we will address
the problem oif dimension reduction to reduce the complexity
of the extracton problem. Some result on AVIRIS data (mmore
than 100 spectral cahnnels) will be presented. |
Agnes
Desoleux - A contrario methods for image analysis.
Abstract:
Abstract: According to Helmholtz principle, perceptual ob jects in an image can be defined as
events which have a very low probability to appear in pure noise. We will see how this principle
can be used for the detection of geometric structures in an image or for denoising.
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Jalal
Fadili - Morphological diversity, sparse overcomplete
representations and some inverse problems.
Abstract: Sparse overcomplete representations
are attracting interest in image processing theory, particularly
due to their potential to generate sparse representations of
data based on their morphological diversity. In this work, we
consider a scenario of linear inverse problems where the image
ro be recovered can be sparsely represented in an overcomplete
dictionary of sparse linear transforms. These transforms are
chosen to offer a wider range of generating atoms; allowing
more flexibility in image representation and adaptativity to
its morphological content (texture, natural parts, etc). The
linear inverse problem is formulated as the minimization of
an energy functional with a sparsity-promoting regularization
(e.g. $\ell_1$ norm of the image representation coefficients).
We will discuss theoretical aspects related to the optimization
problem, and propose some fast iterative algorithms for its
solution for which we establish convergence properties. A wide
variety of examples ranging from deconvolution to component
separation and inpainting are given to illustrate teh potential
applicability of the approach in image processing. |
Laure
Blanc-Feraud - Some applications of the $L^\infty$
norm in image processing
Abstract: Our goal in this work is to give
algorithms for minimizing generic regularizing functionals under
a $l^\infty$-constraint. We show that many classical models
using total variation can be stated under this formalism. Among
others are the Rudin-Osher-Fatemi model, the $BV-l^1$ model,
the $BV-l^\infty$ model and Y. Meyer's cartoon+texture decomposition
model. All the models we study are difficult to handle both
theoretically and numerically because of the non differentiability
of the functionals and of the domains. We propose to use, as
convergent minimization algorithm, the projected subgradient
algorithm. We give some numerical results that show the qualities
and limits of the algorithm, and we tackle the question of the
use of the total variation to treat noises of bounded amplitude. |
Yves
Fregnac - Efficient coding and spike timing precision
in V1 neurons during visual pro-
cessing of natural scenes.
Abstract:
The efficient coding hypothesis posits that our visual system is optimized for the
spatiotemporal statistical properties of our everyday environment. It is assumed that the early
visual processing carried out by the retino-thalamo-cortical pathway is to produce an efficient
representation of the incoming visual signal. Barlow and Attneave recognized the importance
of information theory in this context, and hypothesized that sensory information should be en-
coded in the most compact way, in order for our brain to most effectively utilize all available
computing resources. This principle of redundancy reduction has been shown to be equivalent
to the maximization of mutual information between the visual input and neural responses. To a
certain degree, this view is consistent with a decomposition of the visual scene into statistically
independent components.
I will review electrophysiological attempts made in my lab to reveal optimization of the neural
code for the processing of natural scenes. Cells were recorded intracellularly in the mammalian
primary visual cortex (V1). Subthreshold and spiking response patterns were compared, in the
same cell, for 4 classes of stimuli presenting spatio-temporal statistics of increasing information
content. Full field stimuli consisted of: 1) optimal drifting grating (Fourier input), 2) the same
grating animated through virtual eye-movement sequences (simulating fixation drift, microsac-
cade and tremor), 3) a natural scene animated by the same eye-movement sequence and 4) binary
dense noise. Our results show that the spike-based code, in term of noise, entropy, efficiency and
the apparent recruitment of non-linear mechanisms depend greatly on the stimulus context and
dimensionality. Noise and entropy of the spike discharge decrease with stimulus complexity,
whereas efficiency and temporal precision increase. At the lower boundary of the complexity
scale, drifting gratings evoke highly variable visual responses, the code is based on rate and a
lack of sparseness is apparent in the cortical representation. Using animated sequences of natural
images, cortical network dynamics become much more constrained, the spike timing precision
reaches the ms range and neurons carry almost independent information, with a high efficiency at
all temporal scales. At the higher boundary of the complexity scale, i.e. white noise, the cortical
network dynamics are so constrained that most neurons are kept silent. We conclude that the
cortical code is optimized for processing natural scenes and that the visual cortex operates by
removing high-order redundancies.
Support Contributed by CNRS, ANR (Natstats), ACI-NIM and the European Community
(FET- Bio-I3: 015879 (Facets)) to Y.F. Joint work with Y. Fr?egnac, P. Baudot, O. Marre and
M. Levy.
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Yann
Gousseau - Occlusion and scaling in natural images
(joint work with Francois Roueff )
Abstract:
In this talk we address the problem of the simultaneous modeling of both the
occlusion phenomenon and scaling laws, two fundamental ingredients of the structure of natural
images. Previous works (by Ruderman, Alvarez et al., Mumford et al.) have shown that the
dead leaves model from Mathematical Morphology (a superimposition of random ob jects), when
combined with scaling laws, is to a large extend coherent with the statistics of natural images.
However, such a framework imposes minimum sizes for ob jects, which prevent the modeling of
images regularity (or clutter) at any scale. We show that, under some hypotheses, it is possible
to consider limits at small scales of such models. We give some regularity properties of the
resulting ”scaling dead leaves” model in the context of Besov spaces. We then show how to use
these models to estimate the regularity of natural images by proposing a statistical estimator
for its parameters. Eventually, we conclude by showing the implications of such a modeling in a
Bayesian image denoising framework.
Reference : ”Modeling
occlusion and scaling in natural images”, with F. Roueff,
SIAM Journal of Multiscale Modeling and Simulation, to appear. |
Michael Landy
- Visual Texture: Discrimination, Pattern Identification and
Cortical Coding.
Abstract: Visual texture has been studied
psychophysically as a means of elucidating the initial coding
of spatial, visual patterns. I will review several recent
studies on texture perception and coding. In the first, we
looked at how texture may be used visually to define identifiable
objects. For texture-defined letters, we found that the channels
used to identify letters are scale-invariant, unlike the case
of luminance-defined letters. In an fMRI study, we found orientation-selective
responses to texture-defined edges in multiple cortical areas
using an adaptation paradigm. The amount of orientation-selective
adaptation increased in higher-tier areas (e.g., V3A, LOC),
unlike the case of luminance-defined edges for which the amount
of adaptation in V1 was as great as any other cortical areas
studied. I will also review studies of the visual estimation
of surface roughness in 3-d textures. We found that, despite
the availability of strong 3-d cues such as binocular disparity,
visual estimates of surface roughness were strongly influenced
by viewing conditions (the illuminant and viewing positions
relative to the surface). Finally, I will review our current
efforts at understanding visual coding of texture by comparing
discimination judgments to the wavelet statistics of texture
images.
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Stéphane
Mallat - Geometrical Grouplets
Abstract: The perception of geometrical structures
in images is the result of a complex grouping process, studied
in the 1920's by the Gestalt school, on which electro-physiology
of the the visual brain brings information. The geometry of
textures and contours provides essential parameters for the
recognition of shapes and is still not well understood. For
video sequences, geometry is the heart of movement perception.
Some geometrical perception is also present when listening
to sounds and their harmonic "movements". Behind these multiple
forms of geometries, is there some common mathematical and
algorithmic approach that could provide efficient representations
?
We will review some physiological models of simple cells
in the visual cortex in V1 and their horizontal connections.
Grouplet orthogonal bases and tight frames are constructed
with multiscale association fields between wavelet image coefficients,
that have similarites with horizontal connections between
simple cells. Applications to image super-resolution, noise
removal and texture synthesis will be shown. Link: journée
annuelle de la SMF (in french).
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Pascal
Mamassian - Three-dimensional perception from texture
and shading
Abstract: There are multiple cues that the
human visual system is using to infer the three-dimensional
(3D) structure of objects. Among these cues, texture is traditionally
taken to be informative about local surface orientation and
shading to be informative about local surface curvature. I will
present a short overview of the literature on the perception
of 3D shape from texture and shading to draw the main similarities
and differences between these cues. |
Simon
Masnou - A two-step method for texture/geometry inpainting
Abstract:
A large variety of approaches, some of them very efficient, have been proposed
in recent years for the inpainting problem, i.e. the problem of recovering
missing parts in a digital image. Yet the large-scale, unstationary geometric
structures are often poorly reconstructed. In a joint work with Frédéric Cao
and Yann Gousseau, we propose a two-step method for the restauration of both
texture and geometric information that has also the ability of recovering non
local geometric structures. I will discuss numerical and theoretical issues. |
Yves
Meyer - Geometry+texture+noise decompositions
Abstract:
A series of spectacular discoveries by David Hubel and Torsten Wiesel in
neurophysiology are paving the way to a collection of models in image processing.
In these models an image is viewed as a sum f=u+v (or f=u+v+w) between two or three
components. The first component is aimed at describing the geometry of the image
and the two other components are taking care of the texture and of the noise.
Some variational approaches are discussed.
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Jean-Michel
Morel - Texture synthesis and the technique of
abstract art
(joint work with Luis Alvarez, Bruno Galerne and Yann Gousseau)
Abstract: In this prospective talk I'll discuss,
on the technical side, the abstract art programme developed
in theory or in practice at the begining of the past century
by Cézanne, Matisse, Kandinsky, Klee and other painters.
I'll point out in examples the strong technical limitations
that painters faced when they gave up figuration and attempted
to create abstract shapes and compositions. These difficulties
led to a strong stylistic convergence, which can be interpreted
in merely technical terms. This question has taken a new aspect
thanks to the existence of computers, which permit to realize
quickly any technical idea about random shape, color and painting
technique. I'll show some examples of abstract textures made
by the very same principles at work in abstract painting. This
will revive the technical problems linked to the synthesis of
abstract images. Some explanation and images can be found at:
http://www.tsi.enst.fr/~gousseau/Algomo/
http://www2.dis.ulpgc.es/ami/demos/algomo/algomo.html |
Guy Orban
- Texture as a cue for 3D shape and material properties.
Abstract: We have investigated texture processing
in human and monkey using fMRI and single cell recordings. Neurons
in area TEs (Janssen et al Science 2000) are selective for the
direction of tilt specified by texture and disparity (Liu et
al J Neurosci 2004). In human extraction of 3D shape from texture
involves caudal ITG, LOS/V7 and parietal regions. Similar fMRI
tests in monkeys activate AIP, V4 and TEO. In human texture
judgments activate ventral cortical regions surrounding fusiform
cortex (Peuskens et al J Cogn NS 2004). Infero-temporal neurons
exhibit selectivity for materials, which in a number of cases
disappears with scrambling. |
Gabriel Peyré
- Sparse Modeling of Textures.
Abstract: In this talk I will present a statistical
model for textures that uses a sparse decomposition on a set
of local atoms learned from an exemplar. This model is described
by the variances and kurtosis of the marginals of the decomposition
of patches in the learned dictionary. A fast sampling algorithm
allows to draw a typical image from this model. The resulting
texture synthesis captures the geometric features of the original
exemplar. To speed up synthesis and generate structures of
various sizes, a multi-scale process is used. Applications
to texture synthesis, image inpainting and texture segmentation
are presented.
Gabriel Peyré, Non-negative
Sparse Decomposition for Texture Synthesis, Preprint,
sept. 2006.
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Denis
Pelli - Crowding: Perhaps texture is what we see
when object recognition fails.
Abstract: "Crowding" is a failure of object
recognition in visual perception. When a letter presented in
the peripheral visual field is surrounded by other letters,
the visual system cannot isolate it and we are unable to identify
the original letter. We see a jumble. Crowding was discovered,
clinically, more than fifty years ago, but is now taking off
as a research topic, as a way to study object recognition. I
propose that it would be very useful to define "texture" as
what we see when object recognition fails. Crowding manipulations
make it easy to turn object recognition on and off. I will show
that crowding limits reading and face recognition. I will also
show examples of situations (art & science) that explore perception
without recognized objects. |
Jean-Luc
Starck - Texture, Edges and Sparsity: The MCA
approach.
Abstract: The Morphological Component Analysis
(MCA) is a a method which allows us to separate features contained
in an image when these features present different morphological
aspects. We show that MCA can be very useful for decomposing
images into texture and piecewise smooth (cartoon) parts and
for inpainting applications. This method is extended to multichannel
data, which leads to a new approach for blind source separation,
based on the morphological diversity concept instead of the
statistical independence of the source. |
Song-Chun
Zhu - A Mathematical Model for Texture, Texton
and Primal Sketch - Visual Learning with Implicit and Explicit
Manifolds.
Abstract: In this talk, I will first review
two representation schemes for modeling textures and textons
respectively. The first is the Markov random fields (MRF) for
stochastic texture. Originated from statistical physics, an
MRF (or Gibbs, FRAME) represents a texture category as a micro-canonical
ensemble of images that satisfy certain global statistics property.
A texture is then an equivalence class that satisfies some implicit
constraint equations and is called an implicit manifold. The
second is the texton model for atomic image structures. This
model, steamed from harmonic analysis and sparse coding, represents
a texton as a set spanned by some explicit functions with a
small number of hidden variables. Thus it is called an explicit
manifold.
Then I will show that the two models lie in
two extreme regimes of the Image space. The texture is at high
entropy regime and the textons are at low entropy regime. The
two types of manifolds are the pure-atomic spaces which are
composed to create complex image patterns.
As a result of this analysis, we achieve two
interesting models. (i) A math model for the primal sketch concept,
proposed by David Marr for early vision representation, which
integrates the texture and texton models. (ii) A perceptual
scale space theory for studying the information scaling and
thus the perceptual transitions between the two types of spaces.
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