第7回計算解剖学セミナー

概要

  • 聴講無料

プログラム

  • 講演1

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    • 講師: 大渕 竜太郎 教授(山梨大学)
    • タイトル: 3次元モデルの形状類似比較と検索
    • 要旨:形を持つ3次元モデルは,機械設計,医療,あるいは映画等のCG(コンピュータ・グラフィックス)コンテン ツ制作,などの分野で広く用いられている.本講演では,主に機械設計やCG制作などの用途を視野に,3次元 モデルを,その形の類似性で比較し検索する技術を紹介する.これらの用途では,相似変換に対する不変性に 加え,多様な形状表現(多様体メッシュ,点群,ポリゴンスープ,等)に対する不変性も要求される場合が多 い.さらに,動物等のモデルでは,姿勢変化や大域変形に対する不変性の要求もある.これらの要求を満たし つつ高精度かつ高効率の形状類似比較・検索を実現するための種々の工夫,例えば,3次元モデルをどうパラ メタ化するか,どんな形状特徴(群)を抽出するか,抽出した形状特徴(群)をどのように用いて比較・検索 するか,などについて紹介する.

  • 講演2

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    • 講師: Dr. Xavier PENNEC (INRIA, France)
    • タイトル: Statistical computing on manifolds: from Riemannian geometry to computational anatomy
    • 要旨:Computational anatomy aims at statistically analyzing and modeling the biological variability of anatomical shapes in populations of individuals. However, the anatomical features (points, lines, surfaces, transformations) that we want to study most often belong to geometric manifolds that have no canonical Euclidean structure. Hence we need to rely on more elaborated mathematical bases to design a consistent algorithmic framework. In a first part, I will detail the Riemannian structure which proves to be powerful to develop a consistent framework for simple statistics on manifolds. More interestingly, it can be extend to a complete computing framework for interpolation, filtering, diffusion and restoration of missing data on manifold-valued fields. The framework will be exemplified on real medical imaging application. For instance, the spine can be naturally modeled by the set of its articulation parameters (rigid body transformations). Likewise, when modeling the brain variability, the choice of a convenient Riemannian metric on symmetric positive defines matrices (SPD) allows extrapolating to the surface of the cerebral cortex some covariance measurements that are initially only computed on sulcal lines. Handling properly more complex features such as curves and surfaces raises the problem of infinite dimensional manifolds. We will present in the second part the approach based on currents developed by Stanley Durrleman during his PhD. This approach gives a natural linear embedding space to work with curves and surfaces. A remarkable feature is that the distance it provides turn out to be robust and does not rely on point matches. Moreover, one can easily compute the diffeomorphisms that best deform one current to another. As a consequence, it is natural to use a shape analysis model a la Grenander & Miller, which encodes the geometric variability of objects by the diffeomoprhic deformation of an anatomical template. We will show for instance how such an analysis can be used to discover which clinical variables are predictors of the right cardiac ventricle shape remodeling in repaired tetralogy of Fallot.


問い合わせ

  • 増谷佳孝 (東京大学)
    • 電話: 03-5800-8666 内37418
    • メール: masutani-utrad @ umin.ac.jp

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Last-modified: 2013-09-03 (Tue) 11:24:15 (1271d)