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Wolfgang Baatz (Academy of Fine Arts, Vienna)  WPI Seminarroom C714  Mon, 11. Jun 07, 10:15 
Inpainting and presentation  views of the the conservatorrestorer.  
During the 20th century various concepts for conservationrestoration and in particular for presentation and retouching were postulated, according to the respective phases of development of the discipline. An overview over a series of relevant aspects, methods and problems is given with the aim of facilitating definitions forming the basis of automated virtual completion of works of art.  

Mike Kostner (Academy of Fine Arts, Vienna)  WPI Seminarroom C714  Mon, 11. Jun 07, 11:00 
Interrelation aspects between artist, tool and image  
In the last 15 years the artists working process comes more and more in the influence by computercontrolled surfaces like screens, mouses, keyboards and specialdesigned software. Most of the software and hardware was developed from classical analog image generation tools like the use of pencils or photographic methods. This main focus often clouds new capacities in the interaction between artist and computeraided methods in image editing and image generation. So the proposal is to research new aspects in interrelation between artist and tool using transdiscipline science methods.  

Arjan Kuijper (RICAM Linz)  WPI Seminarroom C714  Mon, 11. Jun 07, 11:45 
Inpainting with higher order energies  
Second order variational inpainting methods, like total variation inpainting (cf. RudinOsherFatemi), have drawbacks as in the connection of edges over large distances or the continuous propagation of level lines into the damaged domain. In an attempt to solve both the connectivity principle and the so called staircasing effect resulting from second order image diffusions, a number of third and fourth order diffusions have been suggested for image inpainting. A new approach in the class of fourth order inpainting algorithms is inpainting of binary images using the Cahn Hilliard equation proposed in BertozziEsedogluGillette. In this talk I will present some analytic and numerical results for CahnHilliard inpainting. Besides this also other variations of this higher order approach for grayvalue images will be discussed.  

Darya Apushkinskaya (Saarland University)  WPI Seminarroom C714  Mon, 11. Jun 07, 14:45 
Regularity of free boundaries in parabolic problems  
In this talk we discuss resent results on the regularity of the free boundaries in a certain type of parabolic free boundary problems. Mathematically the problem is formulated as follows. Let a function $u$ and an open set $\Omega \subset \mathbb{R}^{n+1}_+=\{(x,t): x \in \mathbb{R}^n, t \in \mathbb{R}, x_1>0\}, n \geqslant 2$ solve the following problem: $$ H(u)=\chi_{\Omega } \quad \text{in} \quad Q_1^+, \qquad u=Du=0 \quad \text{in} \quad Q_1^+ \setminus \Omega, \qquad u=0 \quad \text{on} \quad \Pi, $$ where $H=\Delta \partial_t$ is the heat operator, $\chi_{\Omega }$ denotes the characteristic function of $\Omega $, $Q_1$ is the unit cylinder in $\mathbb{R}^{n+1}$, $Q_1^+=Q_1 \cap \mathbb{R}^{n+1}_+$, $\Pi =\{(x,t): x_1=0\}$, and the first equation is understood in the weak (distributional) sense.  

Harald Grossauer (University of Innsbruck)  WPI Seminarroom C714  Mon, 11. Jun 07, 15:30 
Inpainting Algorithms for Every Purpose  
In many image acquisition processes only incomplete data is recorded for a variety of reasons, like for example defective sensors, superimposed texts or logos, or occlusions by other objects. Further, nondigitally stored image data like photographs or celluloid movies may suffer from fading, mechanical stress or simply from aging. Typical symptoms are blotches or torn out pieces, which both lead to image regions which contain no information. To restore the missing image data a multitude of inpainting algorithms has been devised in recent years. We present several inpainting algorithms, each suitable for completion of a different type of image data. Starting from the GinzburgLandau (GL) energy we derive an algorithm which can be used to inpaint levelsets. We show two possible applications: levelsetwise inpainting of images, and surface inpainting. Thereafter we show how to embed images into complex valued functions, such that GL inpainting can be directly applied to image functions, without the indirection using levelsets. The GL inpainting algorithm  like most inpainting algorithms based on variational methods or PDEs  does not handle textured images very well. Therefore we add a texture synthesis algorithm based on Markov Random Fields to supplement the missing texture information. Finally, we consider inpainting of movies. Since consecutive frames of a movie usually differ very little, one may find the image information missing in one frame in another frame nearby. To identify corresponding regions of different frames, we employ a kind of optical flow approach with a piecewise continuity constraint. If possible, the missing frame region is copied from undamaged frames, otherwise a still image inpainting is performed.  

Maria P. Gualdani (University of Texas, Austin)  WPI Seminarroom C714  Tue, 12. Jun 07, 10:00 
Diffusion type equations for price formation  
A meanfield approach to modeling in economics and finance is presented. The model consists on a system of nonlinear diffusion equation related to a freeboundary value problem. It describes the idealized situation of two groups of people, buyers and vendors, trading one good; the resulting price of the good comes from a dynamical equilibrium.  

Kangyu Ni (University of California, Los Angeles)  WPI Seminarroom C714  Tue, 12. Jun 07, 11:45 
A Texture Synthesis Approach to Elastica Inpainting  
We present a new, fully automatic technique for wire and scratch removal that works well in both textured and nontextured areas of an image. Chan, Shen and Kang introduced a technique for inpainting using an Euler's elastica energybased variational model that works well for repairing smooth areas of the image while maintaining edge detail. The technique is very slow, due to a stiff, 4th order PDE. Efros and Leung used texture synthesis techniques for inpainting and hole filling. This works well for areas of an image that contain repeating patterns. We have combined these two techniques to accelerate and constrain the solution of the 4th order PDE. Instead of a stiff minimization, we have a combinatorial optimization problem that is much quicker to solve.  

Massimo Fornasier (RICAM Linz)  WPI Seminarroom C714  Tue, 12. Jun 07, 12:15 
Sparse recovery, freediscontinuity problems and image inpainting  

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