Fitting unbranching skeletal structures to objects

Liu, Zhiyuan; Hong, Jun‐Pyo; Vicory, Jared; Damon, James; Pizer, Stephen M.

doi:10.1016/j.media.2021.102020

Cited by 16 publications

(46 citation statements)

References 18 publications

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“…This sensitivity affects m-rep correspondence among a population as two versions of the same objects can result in significantly different m-reps. Thus, (Pizer et al, 2013) relaxed the mentioned condition and defined s-rep. As described in (Liu et al, 2021)…”

Section: Skeletal Representationmentioning

confidence: 99%

“…There are different ways to fit and parameterize a ds-rep. A current implementation described in detail by (Liu et al, 2021) is available under the open-source toolbox SlicerSALT (http://salt.slicer.org). A GP-ds-rep is a tuple s GP = (p i , u i , r i ) where p i ∈ R 3 , u i ∈ S 2 and r i ∈ R + are ith spoke's tail position, direction, and length respectively where…”

Section: Gp-ds-repmentioning

confidence: 99%

“…By utilizing the inherent hierarchical structure of ds-reps, we provide a consistent definition of local frames that is independent of GCS and also avoids arbitrarily frame rotation. This can be done by introducing a leaf-shaped skeletal structure of the skeletal sheet according to the ellipsoidal design of the ds-rep applied in (Liu et al, 2021) (see Figure 5(Top)).…”

Section: Gp-ds-repmentioning

confidence: 99%

“…For GP-ds-rep fitting, (Liu et al, 2021) first deformed an object to an ellipsoid by mean curvature flow. Then by inverse mean curvature flow, warped the ellipsoid's GP-ds-rep to the target object.…”

Section: Local Framesmentioning

confidence: 99%

“…We call the members of this subset crest-midline spokes. For the model fitting, (Liu et al, 2021) deformed the ellipsoid to the object. After the deformation, the flat ellipsoid's medial axis transforms to a nonlinear surface as a 2D manifold M (i.e., topologically a 2-dimensional disk).…”

Section: Local Framesmentioning

confidence: 99%

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Statistical analysis of locally parameterized shapes

Taheri¹,

Schulz²

2021

Preprint

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The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most commonly used method and state of the art. In this work, we uncover that alignment might seriously affect the statistical analysis. For example, alignment can induce false shape differences and lead to misleading results and interpretations. We propose a novel hierarchical shape parameterization based on local coordinate systems. The local parameterized shapes are translation and rotation invariant. Thus, the inherent alignment problems from the commonly used global coordinate system for shape representation can be avoided using this parameterization. The new parameterization is also superior for shape deformation and simulation. The method's power is demonstrated on the hypothesis testing of simulated data as well as the left hippocampi of patients with Parkinson's disease and controls.

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Section: Skeletal Representationmentioning

confidence: 99%

Section: Gp-ds-repmentioning

confidence: 99%

Section: Gp-ds-repmentioning

confidence: 99%

Section: Local Framesmentioning

confidence: 99%

Section: Local Framesmentioning

confidence: 99%

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Statistical analysis of locally parameterized shapes

Taheri¹,

Schulz²

2021

Preprint

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MR‐based spatiotemporal anisotropic atrophy evaluation of hippocampus in Alzheimer's disease progression by multiscale skeletal representation

Gao,

Liu,

Deng

et al. 2023

Human Brain Mapping

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Increasing evidence has shown a higher sensitivity of Alzheimer's disease (AD) progression by local hippocampal atrophy rather than the whole volume. However, existing morphological methods based on subfield‐volume or surface in imaging studies are not capable to describe the comprehensive process of hippocampal atrophy as sensitive as histological findings. To map histological distinctive measurements onto medical magnetic resonance (MR) images, we propose a multiscale skeletal representation (m‐s‐rep) to quantify focal hippocampal atrophy during AD progression in longitudinal cohorts from the Alzheimer's Disease Neuroimaging Initiative (ADNI). The m‐s‐rep captures large‐to‐small‐scale hippocampal morphology by spoke interpolation over label projection on skeletal models. To enhance morphological correspondence within subjects, we align the longitudinal m‐s‐reps by surface‐based transformations from baseline to subsequent timepoints. Cross‐sectional and longitudinal measurements derived from m‐s‐rep are statistically analyzed to comprehensively evaluate the bilateral hippocampal atrophy. Our findings reveal that during the early AD progression, atrophy primarily affects the lateral‐medial extent of the hippocampus, with a difference of 1.8 mm in lateral‐medial width in 2 years preceding conversion (p < .001), and the medial head exhibits a maximum difference of 3.05%/year in local atrophy rate (p = .011) compared to controls. Moreover, progressive mild cognitive impairment (pMCI) exhibits more severe and widespread atrophy in the head and body compared to stable mild cognitive impairment (sMCI), with a maximum difference of 1.21 mm in thickness in the medial head 1 year preceding conversion (p = .012). In summary, our proposed method can quantitatively measure the hippocampal morphological changes on 3T MR images, potentially assisting the pre‐diagnosis and prognosis of AD.

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MRI‐based axis‐referenced morphometric model corresponding to lamellar organization for assessing hippocampal atrophy in dementia

Gao,

Ye,

Chen

et al. 2024

Human Brain Mapping

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Research on the local hippocampal atrophy for early detection of dementia has gained considerable attention. However, accurately quantifying subtle atrophy remains challenging in existing morphological methods due to the lack of consistent biological correspondence with the complex curving regions like the hippocampal head. Thereby, this article presents an innovative axis‐referenced morphometric model (ARMM) that follows the anatomical lamellar organization of the hippocampus, which capture its precise and consistent longitudinal curving trajectory. Specifically, we establish an “axis‐referenced coordinate system” based on a 7 T ex vivo hippocampal atlas following its entire curving longitudinal axis and orthogonal distributed lamellae. We then align individual hippocampi by deforming this template coordinate system to target spaces using boundary‐guided diffeomorphic transformation, while ensuring that the lamellar vectors adhere to the constraint of medial‐axis geometry. Finally, we measure local thickness and curvatures based on the coordinate system and boundary surface reconstructed from vector tips. The morphometric accuracy is evaluated by comparing reconstructed surfaces with those directly extracted from 7 T and 3 T MRI hippocampi. The results demonstrate that ARMM achieves the best performance, particularly in the curving head, surpassing the state‐of‐the‐art morphological models. Additionally, morphological measurements from ARMM exhibit higher discriminatory power in distinguishing early Alzheimer's disease from mild cognitive impairment compared to volume‐based measurements. Overall, the ARMM offers a precise morphometric assessment of hippocampal morphology on MR images, and sheds light on discovering potential image markers for neurodegeneration associated with hippocampal impairment.

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Fitting unbranching skeletal structures to objects

Cited by 16 publications

References 18 publications

Statistical analysis of locally parameterized shapes

Statistical analysis of locally parameterized shapes

MR‐based spatiotemporal anisotropic atrophy evaluation of hippocampus in Alzheimer's disease progression by multiscale skeletal representation

MRI‐based axis‐referenced morphometric model corresponding to lamellar organization for assessing hippocampal atrophy in dementia

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