Processing Seminar (296J/3)
Fridays 4:00 pm - 5:00 pm.
Invited speakers and graduate students
give informal presentations from their research. Topics include
image analysis and computer vision techniques by partial differential
equations, wavelets, statistics, or combined approaches.
Luminita Vese and Triet Le (Mathematics Department) : firstname.lastname@example.org
Potential speakers are invited to
contact one of the organizers.
Graduate students attending all the seminar meetings
will receive a one unit credit.
SCHEDULE WINTER 2006
Friday, January 27, 2006, Time 4-5pm, Location MS 5147
Speaker: Arthur Szlam, Yale University
Title: "Anisotropic diffusions for learning and image processing"
Monday, January 30, 2006, Time 4-5pm, Location MS 5225
Speaker: Mauro Maggioni, Yale University
Title: Multiscale analysis on manifolds and graphs induced by diffusion:
constructions and applications.
Abstract: The study of diffusion operators of manifolds, graphs and "data sets" is
useful for the analysis of
the structure of the underlying space and of functions on the space. This
in turn has many and
important applications to disparate fields including partial differential
learning, dynamical and control systems, data analysis. We discuss old and
new ideas and algorithms
for multiscale analysis associated to such diffusion operators. Given a
local operator $T$ on a
manifold or a graph, with large powers of low rank, we present a general
construction for efficiently computing, representing and compressing
$T^t$. This allows the
computation, to high precision, of functions of the operator, notably the
function, in compressed form, and their fast application. The dyadic
powers of $T$ can be used to
induce a multiresolution analysis, as in classical Littlewood-Paley and
wavelet theory: we
construct, with efficient and stable algorithms, scaling functionand
wavelet bases associated to
this multiresolution analysis, togetherwith the corresponding down
sampling operators. This allows
to extend multiscale signal processing to general spaces (such as
manifolds and graphs) in a very
natural way, with correspondingefficient algorithms. We will sketch
motivating applications, which
include function approximation, denoising, and learning on data sets,
model reduction for complex
stochastic dynamical systems, multiscale analysis of Markov chains and
Markov decision processes.
Friday, February 24, 2006, Time 4-5pm, Location MS 5128
Speaker: Karen Egiazarian, Institute of Signal Processing of Tampere University of Technology, Finland.
Anisotropic Multi-Scale Estimation: Directional LPA-ICI method
Abstract: The LPA is a technique applied for a linear and nonlinear filter design
using a polynomial fit in a sliding window. The window size of this fit is
one of the key-parameters which is interpreted as a scale of adaptation and
In this form the LPA â~H~R ICI technique is a novel powerful tool for a lot
of image processing problem. In particular, in many imaging systems the
recorded observations have the physical meaning of numbers of detected
photons. The photons are counted at different spatial locations and in this
way form an image of an object. This sort scenario is typical for the
so-called photon-limited imaging including digital photo/video, positron
emission tomography, astronomy, microscopy, etc. The local maximum/quasi
likelihood based anisotropic adaptive algorithms are presented for
this problems. We show that overall the new algorithms demonstrate the
state-of-art performance and on many occasions visually and quantitatively
outperform some of the best existing methods. Based on convolution
operations it is free from artifacts typical for wavelets (short version of abstract)
Wednesday, March 15, 2006: Time 4-5pm, Room MS 6229
Speaker: Naoki Saito, Department of Mathematics, UC Davis
Title: Laplacian Eigenfunctions as a tool for image analysis on general
Abstract: In this talk, I will discuss a new method to analyze and represent
deterministic and stochastic data recorded on a domain of general shape
(even on a multiply-connected domain) by computing the eigenfunctions of
Laplacian defined over there and expanding the data into these
These eigenfunctions are in fact "modes" of the vibration of the domain
if the domain is interpreted as a "drum".
In essence, what our Laplacian eigenfunctions do for data on a general
domain is roughly equivalent to what the Fourier cosine basis functions do
data on a rectangular domain. Instead of directly solving the Laplacian
eigenvalue problem on such a domain (which can be quite complicated and
find the integral operator commuting with the Laplacian and then diagonalize
that operator. We then show that our method is better suited for small
data than the Karhunen-Loeve transform/Principal Component Analysis.
In fact, our Laplacian eigenfunctions depend only on the shape of the
domain, not the statistics (e.g., covariance) of the data.
I will show several interesting examples and will discuss some strategy
to design fast algorithms to compute such eigenfunctions.
SCHEDULE FALL 2005
Monday, October 10, 2005:
Speaker: Joachim M. Buhmann,
Institute for Computational Science, Departement Informatik, ETH Zurich.
Title: Complex Statistical Models for Image Segmentation and Object Recognition
Abstract: Image analysis has gained significantly in quality over the last
decade by complex statistical models. Grouping algorithms based on
local histograms to represent image patches have shown satisfactory
performance in image segmentation, i.e., if they are combined with
feature selection. I will discuss a nonparametric Bayesian approach to
smooth image segmentation where the algorithm determines the
properties and the number of segments using a mixture of Dirichlet
processes while simultaneously enforcing a Markov Random Field
constraint. In the second part of the talk I will discuss a structured
statistical model for object recognition which is designed in the
spirit of Geman's compositionality architecture. Feature histograms of
local image patches are extracted to form "parts" which are then
linked to combinations. Bags of combinations are then used to
categorize images. Cross-validated test errors on the Caltech 101
database yield a categorization rate of 52 percent.
Monday, October 17, 2005:
Speaker: Yonggang Shi, LONI UCLA.
Title: A Real-Time Algorithm For Level-Set-Based Curve Evolution
Abstract: The level set method is popular for the numerical implementation of
curve evolution, but its high computational cost has limited its
application in real-time problems. In this talk, we propose a novel
two-cycle algorithm for the approximation of level-set-based curve
the need of solving partial differential equations (PDEs). Our algorithm
is applicable to a broad class of speeds that can be viewed as composed of
a data dependent term and a smoothness regularization term. In our fast
algorithm, we separate the evolution of the curve according to these two
different types of speeds into two cycles, and incorporates smoothness
regularization by evolving the curve with a smoothing speed derived from a
Gaussian filtering process. The evolution of the implicitly represented
curve in our algorithm is realized with simple element switching
operations between two linked lists of grid points, leading to
significant speedups compared with PDE-based approaches. We demonstrate
the efficiency of our algorithm with image segmentation and real-time
video tracking experiments.
Monday, October 24, 2005: CCB talk at 4pm, in LONI Dive
Stephen M. Pizer, UNC Medical Image Display & Analysis Group, UNC.
Title: Statistics of the anatomic geometry of multi-object complexes via m-reps.
Both dense multi-object complexes and non-dense complexes are important in such medical areas as neuroscience and radiation treatment planning. A probabilistic point of view on anatomic geometry is important for such objectives as segmentation by posterior optimization and hypothesis testing as to differences in object complex geometry between classes. I will review why the medial representation called m-reps is particularly well suited both to statistics on individual objects and statistics on multi-object complexes and review how a generalization of mean and principal component methods to the underlying curved abstract spaces can be done. Using novel statistical techniques, which I will briefly explain, I will show by how much m-reps of single objects together with the appropriate non-linear statistics yields a requirement of smaller training samples. For multi-object complexes it is particularly important that the probabilistic algorithms be at multiple scale levels, each with its own characteristic entity, e.g., object complex, object (and interstitial region), figure, figural section, voxel; and that they provide probabilities the geometry relationships between neighboring entities. The Markov random field framework that this produces and the means of simultaneously representing probabilities on entity and inter-entity geometry will be discussed.
Monday, October 31, 2005, 4pm, MS 6229:
Speaker: Triet Le, Department of Mathematics, UCLA.
Title:Modeling oscillatory components with div(BMO) and homogeneous Besov spaces
Abstract: This talk is devoted to the decomposition of an image f
into u+v, with u a piecewise-smooth or ``cartoon''
component, and v an oscillatory component (texture or
noise), in a variational approach. In 2001, Y. Meyer
theoretically proposed weaker norms than the L^2 norm to model oscillatory
components. Following his work, we study cases where the oscillatory
component v belongs to div(BMO) or to generalized homogeneous Besov
spaces, while keeping the piecewise smooth component u of bounded
variation. Numerical results will be presented to validate the
proposed models. This is joint work with John B. Garnett and Luminita A.
Friday, November 4, 2005, 3-4pm, in MS 6229: NOTE: different day and time
Speaker: George Kamberov, CS, Stevens Institute of Technology
Title:Segmentation and Geometry of 3D Scenes from Unorganized Point Clouds
Abstract: We present a new method for defining orientation and topology (a collection
of neighborhoods), and assigning principal curvature frames, and mean and
Gauss curvatures to the points of an unorganized 3D point-cloud. The
neighborhoods are estimated by measuring implicitly the surface distance
between points. The 3D shape recovery is based on conformal geometry, works
directly on the cloud, and does not rely on the generation of polygonal or
smooth models. The implicit surface distance estimate is used to define a
metric for scoring how well an orientation and topology fits a given cloud.
Friday, November 4, 2005, 4-5pm, in MS 6229: NOTE: different day and time
Speaker: Xiao-Qun Zhang, LMAM, Universite de Bretagne Sud.
Title:Total variation based Fourier reconstruction and regularization for
Abstract:We present a simple framework for solving different ill-posed inverse
computer vision by means of constrained total variation minimizations.
We argue that drawbacks commonly attributed
to total variation algorithms (slowness and incomplete fit to the image
can be easily bypassed by performing only a few number of iterations in our
optimization process. We illustrate this approach in the context of
tomography, that comes down to inverse a Radon transform obtained by
object by straight and parallel beams of x-rays. This problem is ill-posed
because only a finite number of line integrals can be measured, resulting in
an incomplete coverage of the frequency plane and requiring, for a direct
Fourier reconstruction, frequencies interpolation from a polar to a
We introduce a new method of interpolation based on a total variation minimization constrained by the knowledge of frequency coefficients in
the polar grid, subject to a Lipschitz regularity assumption.
The experiments show that our algorithm is able to avoid Gibbs and noise
associated to the direct Fourier method, and that it outperforms classical
reconstruction methods such as filtered backprojection and
TV restoration, in terms of both PSNR and visual quality.
Monday, November 7, 2005: NO MEETING
Monday, November 14, 2005: NO MEETING.
Monday, November 21, 2005: NO MEETING
Monday, November 28, 2005:
Speaker: Simon Baker, Research Scientist,
The Robotics Institute,
Carnegie Mellon University.
Title:Model-Based Face Analysis.
A face model is a mapping from a set of parameters to an image of a face.
The most well-known face models are Active Appearance Models and 3D Morphable
Models. Computer vision applications of face models include head pose estimation
for user interfaces, gaze estimation, pose normalization for face recognition,
lip-reading, expression recognition, and face coding for low-bandwidth
video-conferencing. In all of these applications, the key task is to fit the
face model to an input image; i.e. to find the parameters of the model that
match the input image as well as possible. Applying model fitting to each image
in a video in turn results in a non-rigid face tracking algorithm.
In this talk I will describe how face model fitting, a non-linear optimization,
can be posed as an image alignment problem. Image alignment is a standard
computer vision technique, with applications to optical flow, tracking, mosaic
construction, layered scene representations, and medical image registration. I
will describe a new efficient image alignment algorithm and show how it relates
to others in a unifying framework. Applying this algorithm to faces results in
real-time 2D, 3D, and multi-view face model fitting algorithms.
I will also describe some of our recent research on face model construction,
including automatic (unsupervised) model construction, model update, and 3D
model construction from 2D images.
Monday, December 5, 2005:
Speaker: Lin He, Dept. of Mathematics, UCLA
Title: MR Image Reconstruction from Sparse Radial
Samples Using Bregman Iteration
Many applications in magnetic resonance imaging (MRI) require very short
scan time while the image reconstruction can be performed off-line. To
this end, during the scanning process it is necessary to sample the
frequency plane (or k-space) very sparsely. This usually results in image
artifacts and/or low signal to noise ratio (SNR). In this work, we develop
an iterative MR image reconstruction algorithm for severely undersampled
MR measurement data that have a radial trajectory in k-space. Our method
is based on the sparse representations of the images, which is realized by
both the gradient operation and wavelet transform. We formulate a cost
functional that includes the L1 norm of the sparse representations and a
constraint term that is imposed by the raw measurement data in k-space.
The functional is then minimized by the conjugate gradient (CG) algorithm
and Bregman iteration. In each iteration of CG, to account for the
non-Cartesian sampling grid, we take the nonuniform fast Fourier transform
(NFFT) of the reconstructed image and compare with the raw data in the
least square sense. Our experimental results achieve high image quality
with significantly less image artifacts as compared with the conventional
Monday, December 12, 2005: TBA