Model-based longitudinal analysis of dynamic multi-modal higher-dimensional data

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K11881
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61010:Perceptual information processing-related
• Research Institution: Chiba University
• Principal Investigator: Imiya Atsushi 千葉大学, 統合情報センター, 名誉教授 (10176505)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 多重解像度解析 / 多重線形主成分分析 / 縦断解析 / 四元数 / 情報圧縮 / 運動解析

Outline of Final Research Achievements

The quaternions express the three-dimensional vectors.
Using quaternions, the spatial motion field is expressed as three-dimensional tensor with quaternion elements. By applying the multi-linear principal component analysis based on the tensorial caliculus, it is possible to extract dominant motion field of the three-dimensional deformation field for longitudinal analysis of deformation of human organs, such as beating heart. This longitudinal analysis of deformation field characterise the types of deformation fields. This classification of the deformation fields will being new geometrical and information criterion for machine-based diagnosis assistance system. Furthermore, we developed a new pyramid-based image transformation for the harmonisation of the resolution of images in a sequence for the longitudinal analysis of image sequence.

Free Research Field

数理画像解析

Academic Significance and Societal Importance of the Research Achievements

本研究では, 多重線形型式の記述形式であるテンソルを利用して, 動的な高次多元高次画像の解析・認識・分類・蓄積・検索・判別を統一的に取り扱うことのできる体系を, 従来のベクトル空間におけるパターン認識において実績と蓄積のある部分空間法をテンソルに拡張した. さらに, 計測される微細構造の解析手法を, 画像理解の立場から構造を持った統計的幾何要素（テクスチャー）の解析理論の動的解析への拡張として捉え, 時間的に変動する3次元テクスチャーの特徴量解析理論を構築した.