MAIPCV2011

若手研究者のための画像処理とＣＶにおける数理的側面

ウィンタースクール
Winter Schoolfor young researcherson Mathematical Aspects of Image
Processing and Computer Vision

2011年11月24日(木)～26日(土)東北大学青葉山キャンパス
青葉記念会館
Aoba Memorial Hall, Tohoku University
24-26, November, 2011

Program
November 24 (Thu) Mathematical Aspects of Computer Graphics
10:00-12:00 Ken Anjyo (OLM Digital R&D, Japan)
Transforming 2D Image to 3D Animation – From a Practitioner’s Viewpoint
13:30-16:30 Konrad Polthier (Freie Universität Berlin, Germany)
Discrete Differential Geometry – Concepts and Applications

November 25 (Fri) Variational Methods for Computer Vision09:00-12:00 Kenji Kajiwara (Kyushu University, Japan)
Discretization of Planar Curve Motions and Discrete Integrable Systems
13:30-16:30

Ernie Esser (University of California, Irvine, USA)
Primal Dual Algorithms for Convex Optimization in Imaging Science

November 26 (Sat) Optimal Estimation for Computer Vision
09:00-12:00 Kenichi Kanatani (Okayama University, Japan)
Optimal Estimation for Computer Vision Applications
13:30-16:30

Sami Brandt (University of Copenhagen, Denmark/University of Oulu, Finland)On the Probabilistic Multi-View Geometry

Abstracts
Transforming 2D Image to 3D Animation–From a Practitioner’s Viewpoint
Ken Anjyo
Research and Development Division
OLM Digital R&D
In a digital production workplace, we often encounter the problems of how to construct andanimate a 3D scene, based only on 2D information about the scene. For example, when a single
image (photograph or drawing) is given for the scene, how we can transform it into 3D? This talkgives a brief overview of the transforming techniques used in our practice. Related research work
will also be described along with the demonstration movies.

Discrete Differential Geometry – Concepts and Applications
Konrad PolthierAG Mathematical Geometry Processing
Freie Universität Berlin
The talk introduces concepts from discrete differential geometry and applications to recent
problems in computer graphics and CAD. The topics include polyhedral surfaces, discrete
curvatures, differential forms, Hodge decomposition, manifolds and covering spaces withapplications to surfaces segmentation and parameterization, shape optimization, meshcompression and spectral modeling. Special emphasis lies on effective algorithms and industrial
applications.

Discretization of Planar Curve Motions andDiscrete Integrable Systems
Kenji Kajiwara
Institute of Mathematics for Industry
Kyushu University
It is well-known that smooth curves on the Euclidean plane admit the motion described by themodified Korteweg-de Vries (mKdV) equation, which is one of the most typical integrable systems.
In this lecture, we consider the problem of discretization of planar curve motions preserving theunderlying integrable structure. More precisely, we introduce the discrete planar curves anddiscuss their continuous and discrete motions described by the semi-discrete and discrete mKdV
equations, respectively. By applying the theory of discrete integrable systems, we constructexplicit formulas for the curve motions in terms of the tau function. We will also discuss thediscretization of space curve motions if time permits.

Primal Dual Algorithms for Convex Optimization in Imaging Science
Ernie Esser
School of Physical Sciences
University of California, Irvine
Variational models in image processing and computer vision often result in constrained
optimization problems that are difficult in the sense that they involve minimizing nonsmoothfunctions of many variables but are easy in the sense that they are convex and have separablestructure. For solving such convex minimization problems, we will discuss a class of primal dual
algorithms whose generality, simplicity and efficiency make them an essential tool. Thesealgorithms will be studied from the perspective of alternating direction methods applied toaugmented Lagrangians. In three lectures we will review some convex analysis background,discuss connections between the algorithms and show how to practically implement them forgeneral convex models with separable structure.

Optimal Estimation for Computer Vision Applications
Kenichi Kanatani
Department of Computer Science
Okayama University
In many computer vision applications, one frequently needs to estimate the parameters of theassumed model from noisy observations, for which maximum likelihood (ML) is widely regarded
as the basic principle. In this talk, I describe the general framework of ML-based optimization andsummarize assumptions and approximations associated with it. I also discuss algebraic methods
that can produce approximate solutions to be used as initial values of ML iterations and introduce
a recently established technique called ``HyperLS''. As practical applications, I discuss camera
calibration of fish-eye lens cameras and optimal 3-D similarity estimation from noisy 3-D data.

On the Probabilistic Multi-View Geometry
Sami Brandt
Machine Vision Group
University of Copenhagen/University of Oulu
Where the classic multi-view geometry is deterministic in assessing the geometric constraints andrelationships between several views, there has been recently proposed a modern, probabilistic
approach for multi-view geometry. This approach is essentially a novel direction in the branch of
integral geometry in mathematics that in the modern form studies integral transforms modeledwith the Radon or Radon-like transforms. Where the classic way in geometric computer vision is,
for instance, to take a point in an image and transfer it into another view, the probabilistic way is
to replace the point coordinates by a 2D location distribution and transfer it into another viewalong with the uncertainty distribution of the multi-view geometric entity via the geometricincidence relation. Most importantly, the resulting dual distributions make a complete
probabilistic, Bayesian treatment multilinear geometric relations possible where everything ismodeled with probability distributions. In first part of the lecture, we will start to build the intuition
with the simplest case of the point--line duality, construct the duals for epipolar lines, and discuss
the approach from the viewpoint of two view geometry. On the second part of the lecture, we willproceed to the general case where we will study the general multilinear models, construct therelated dual distributions, and demonstrate them with real examples. We will also discuss thepossible future research directions of this topic.

MAIPCV2011
Organized by : Committee of Mathematical Aspect of Image Processing andComputer Vision (MAIPCV)
Sponsored by : Graduate School of Information Sciences (GSIS), Tohoku University
Graduate School of Science, Tohoku University
Tohoku University’s Focused Research Project “Interdisciplinary Mathematics
Toward Smart Innovations (SMART)”
主催：MAIPCV 実行委員会・MAIPCV ウィンタースクール実行委員会
共催：東北大学大学院情報科学研究科・東北大学大学院理学研究科
東北大学重点戦略支援プログラム「数学をコアとするスマート・イノ
ベーション融合研究共通基盤の構築と展開 」
http://www.dais.is.tohoku.ac.jp/~smart
連絡先：maipcv@fractal.is.tohoku.ac.jp