Image Processing Seminar (296J/3)

 

Time:

Fridays 4:00 pm - 5:00 pm.

Location:

MS 5128.

Scope:

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.

Organizers:

Luminita Vese and Triet Le (Mathematics Department) : lvese@math.ucla.edu tle@math.ucla.edu

 

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 equations, machine 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 multiresolution construction for efficiently computing, representing and compressing $T^t$. This allows the computation, to high precision, of functions of the operator, notably the associated Green's 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.
Title: 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 estimation. In this form the LPA ~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 domains
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 eigenfunctions. 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 for data on a rectangular domain. Instead of directly solving the Laplacian eigenvalue problem on such a domain (which can be quite complicated and costly), we find the integral operator commuting with the Laplacian and then diagonalize that operator. We then show that our method is better suited for small sample 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 evolution without 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
Speaker: Stephen M. Pizer, UNC Medical Image Display & Analysis Group, UNC.
Title: Statistics of the anatomic geometry of multi-object complexes via m-reps.
Abstract: 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. Vese.

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 computerized tomography
Abstract:We present a simple framework for solving different ill-posed inverse problems in 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 model) can be easily bypassed by performing only a few number of iterations in our optimization process. We illustrate this approach in the context of computerized tomography, that comes down to inverse a Radon transform obtained by illuminating an 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 Cartesian grid. 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 oscillations associated to the direct Fourier method, and that it outperforms classical reconstruction methods such as filtered backprojection and Rudin-Osher-Fatemi 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.
Abstract: 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
Abstract: 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 gridding algorithm.

Monday, December 12, 2005: TBA