Sliding at First-Order: Higher-Order Momentum Distributions for Discontinuous Image Registration

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE SIAM Journal on Imaging Sciences Pub Date : 2024-04-08 DOI:10.1137/23m1558665

Lili Bao, Jiahao Lu, Shihui Ying, Stefan Sommer

引用次数: 0

Abstract

SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 861-887, June 2024.
Abstract.In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a nondifferentiable kernel. This allows us to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deformation model from the viewpoint of discontinuous systems. To evaluate our approach, we conduct experiments on both artificial images and the publicly available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach in capturing plausible sliding motion.

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一阶滑动：用于不连续图像配准的高阶动量分布

SIAM 影像科学杂志》，第 17 卷第 2 期，第 861-887 页，2024 年 6 月。本文提出了一种捕捉滑动运动的可变形图像配准新方法。大变形差分公制映射（LDDMM）配准方法在表示滑动运动时面临挑战，因为它的构造会产生平滑翘曲。为了解决这个问题，我们扩展了 LDDMM，将零阶矩和一阶矩都纳入了无差别核。这使我们既能表示切换边界的不连续变形，又能表示同质区域的差分变形。我们从非连续系统的角度对所提出的变形模型进行了数学分析。为了评估我们的方法，我们在人工图像和公开的 DIR-Lab 4DCT 数据集上进行了实验。结果表明，我们的方法能有效捕捉可信的滑动运动。

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来源期刊

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.