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  1. We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of the input mesh surface and internal features such as the seams and junctions of medial axis, are important shape descriptors both topologically and geometrically. However, existing medial axis approximation methods fail to capture and preserve them due to the fundamentally under-sampling in the vicinity of medial features, and the difficulty to build their correct connections. In this paper we use the RPD of medial spheres and its affiliated structures to help solve these challenges. The dual structure of RPD provides the connectivity of medial spheres. The surfacic restricted power cell (RPC) of each medial sphere provides the tangential surface regions that these spheres have contact with. The connected components (CC) of surfacic RPC give us the classification of each sphere, to be on a medial sheet, a seam, or a junction. They allow us to detect insufficient sphere sampling around medial features and develop necessary conditions to preserve them. Using this RPD-based framework, we are able to construct high quality medial meshes with features preserved. Compared with existing sampling-based or voxel-based methods, our method is the first one that can preserve not only external features but also internal features of medial axes. 
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  2. Objectives

    Patients with primary muscle tension dysphonia (pMTD) commonly report paralaryngeal pain and discomfort, and extrinsic laryngeal muscle (ELM) tension and hyperfunction are commonly implicated. However, quantitative physiological metrics to study ELM movement patterns for the characterization of pMTD diagnosis and monitoring of treatment progress are lacking. The objectives of this study were to validate motion capture (MoCap) technology to study ELM kinematics, determine whether MoCap could distinguish ELM tension and hyperfunction between individuals with and without pMTD, and investigate relationships between common clinical voice metrics and ELM kinematics.


    Thirty subjects (15 with pMTD and 15 controls) were recruited for the study. Sixteen markers were placed on different anatomical landmarks on the chin and anterior neck. Movements across these regions were tracked during four voice and speech tasks using two three‐dimensional cameras. Movement displacement and variability were determined based on 16 key‐points and 53 edges.


    Intraclass correlation coefficients demonstrated high intra‐ and inter‐rater reliability (p's < 0.001). Other than greater movement displacements around the thyrohyoid space during longer phrasing (reading passage, 30‐s diadochokinetics) and more movement variability in patients with pMTD, kinematic patterns between groups were similar across the 53 edges for the four voice and speech tasks. There were also no significant correlations between ELM kinematics and standard voice metrics.


    Results demonstrate the feasibility and reliability of MoCap for the study of ELM kinematics.

    Level of Evidence

    3Laryngoscope, 133:3472–3481, 2023

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