Multiscale Representation of Deformation via Beltrami Coefficients

Lam, Ka Chun; Ng, Tsz Ching; Lui, Lok Ming

doi:10.1137/16m1056614

Cited by 9 publications

(4 citation statements)

References 28 publications

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“…3D shape analysis using quasiconformal theories have also been explored [12,13,14,15,16,17]. Besides, for deformation analysis, quasiconformal models have been proposed for multiscale analysis of deformations [18] and decomposition of deformations into normal and abnormal components [19]. [20,21] are recently proposed to study non-deterministic deformation patterns.…”

Section: Related Workmentioning

confidence: 99%

Nondeterministic Deformation Analysis Using Quasiconformal Geometry

Zhang

Lui

2022

2022 IEEE International Conference on Image Processing (ICIP)

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Deformation analysis is crucial in many applications, especially in medical image analysis. Analyzing the deformation pattern of anatomical structures provides important information for disease analysis. With degraded images or uncertainties, getting a deterministic solution of the deformation is challenging. In some cases, there may also be multiple solutions with different probabilities. As such, it is important to analyze the probability distribution of deformations, given data information with uncertainty. In this work, we propose to use computational Quasiconformal (QC) Teichmuller theories to parameterize the space of deformations. A distribution over the space of special features, called the QC features, can be computed and applied for deformation analysis. Extensive experiments are carried out on both synthetic data and real medical images, which demonstrate the efficacy of the proposed framework.

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Section: Related Workmentioning

confidence: 99%

Nondeterministic Deformation Analysis Using Quasiconformal Geometry

Zhang

Lui

2022

2022 IEEE International Conference on Image Processing (ICIP)

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“…Recently, the morphlet transform has been proposed to obtain a multi-scale representation for diffeomorphisms [14]. Wavelet tranform on the Beltrami coefficient of the deformation field has also been proposed to decompose a deformation into multiple components with various geometric scales [15]. However, to the best of our knowledge, an effective method to analyze time-dependent longitudinal deformation is still lacking.…”

Section: Previous Workmentioning

confidence: 99%

Decomposition of Longitudinal Deformations via Beltrami Descriptors

Law¹,

Lui²,

Siu³

2020

Preprint

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We present a mathematical model to decompose a longitudinal deformation into normal and abnormal components. The goal is to detect and extract subtle quivers from periodic motions in a video sequence. It has important applications in medical image analysis. To achieve this goal, we consider a representation of the longitudinal deformation, called the Beltrami descriptor, based on quasiconformal theories. The Beltrami descriptor is a complex-valued matrix. Each longitudinal deformation is associated to a Beltrami descriptor and vice versa. To decompose the longitudinal deformation, we propose to carry out the low rank and sparse decomposition of the Beltrami descriptor. The low rank component corresponds to the periodic motions, whereas the sparse part corresponds to the abnormal motions of a longitudinal deformation. Experiments have been carried out on both synthetic and real video sequences. Results demonstrate the efficacy of our proposed model to decompose a longitudinal deformation into regular and irregular components.

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“…In Finite Element Methods, multiscale analysis is widely used [11], [12], [13]. In the spectral geometry field, research works apply multiscale technology on the deformation representation [14], physics-based simulation of deformable objects [15], and surface registration [16] by analyzing the nonisometric global and local (multiscale) deformation. Moreover, for shape editing, multiscale technology also enables modeling rich facial expressions on human faces [17].…”

Section: Introductionmentioning

confidence: 99%

Multiscale Mesh Deformation Component Analysis With Attention-Based Autoencoders

Yang

Gao

Tan

et al. 2023

IEEE Trans. Visual. Comput. Graphics

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Deformation component analysis is a fundamental problem in geometry processing and shape understanding. Existing approaches mainly extract deformation components in local regions at a similar scale while deformations of real-world objects are usually distributed in a multi-scale manner. In this paper, we propose a novel method to exact multiscale deformation components automatically with a stacked attention-based autoencoder. The attention mechanism is designed to learn to softly weight multi-scale deformation components in active deformation regions, and the stacked attention-based autoencoder is learned to represent the deformation components at different scales. Quantitative and qualitative evaluations show that our method outperforms state-of-the-art methods. Furthermore, with the multiscale deformation components extracted by our method, the user can edit shapes in a coarse-to-fine fashion which facilitates effective modeling of new shapes.

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Multiscale Representation of Deformation via Beltrami Coefficients

Cited by 9 publications

References 28 publications

Nondeterministic Deformation Analysis Using Quasiconformal Geometry

Nondeterministic Deformation Analysis Using Quasiconformal Geometry

Decomposition of Longitudinal Deformations via Beltrami Descriptors

Multiscale Mesh Deformation Component Analysis With Attention-Based Autoencoders

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