Spherical Parameterization Balancing Angle and Area Distortions

Nadeem, Saad; Su, Zhaohui; Zeng, Wei; Kaufman, Arie; Gu, Xianfeng

doi:10.1109/tvcg.2016.2542073

Cited by 48 publications

(38 citation statements)

References 45 publications

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“…We first give a theoretical overview of the distortion of area in conformally mapping a genus zero Riemannian surface S to the unit sphere S 2 to motivate the pipeline in spiculation; see [10] for the relevant mathematical references. By the Theorema Egregium of Gauss, one cannot find a diffeomorphism from S with non-constant Gaussian curvature to S 2 which preserves both angles and area.…”

Section: Conformal Mappings and Area Distortionmentioning

confidence: 99%

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Interpretable Spiculation Quantification for Lung Cancer Screening

Choi

Nadeem

Riyahi

et al. 2018

Shape in Medical Imaging

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Spiculations are spikes on the surface of pulmonary nodule and are important predictors of malignancy in lung cancer. In this work, we introduced an interpretable, parameter-free technique for quantifying this critical feature using the area distortion metric from the spherical conformal (angle-preserving) parameterization. The conformal factor in the spherical mapping formulation provides a direct measure of spiculation which can be used to detect spikes and compute spike heights for geometrically-complex spiculations. The use of the area distortion metric from conformal mapping has never been exploited before in this context. Based on the area distortion metric and the spiculation height, we introduced a novel spiculation score. A combination of our spiculation measures was found to be highly correlated (Spearman's rank correlation coefficient ρ = 0.48) with the radiologist's spiculation score. These measures were also used in the radiomics framework to achieve state-ofthe-art malignancy prediction accuracy of 88.9% on a publicly available dataset. * The first two authors contributed equally to this work.

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Section: Conformal Mappings and Area Distortionmentioning

confidence: 99%

“…In the paper [10], the above program is carried out in a discrete setting with respect to a triangulated surface S = (V, E, F ), where V denotes the vertices, E the edges, and F the faces. Here, one may measure the area distortion on each triangle.…”

Section: Spiculation Quantification Pipelinementioning

confidence: 99%

Interpretable Spiculation Quantification for Lung Cancer Screening

Choi

Nadeem

Riyahi

et al. 2018

Shape in Medical Imaging

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“…Fiedler vector representation has been used in various applications including mesh processing [8], mesh parameterization [23], and shape characterization [4]. Lai et al [16] have proposed the use of Fiedler vector representation for supine and prone colon registration.…”

Section: Related Workmentioning

confidence: 99%

Corresponding Supine and Prone Colon Visualization Using Eigenfunction Analysis and Fold Modeling

Nadeem

Marino

et al. 2017

IEEE Trans. Visual. Comput. Graphics

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We present a method for registration and visualization of corresponding supine and prone virtual colonoscopy scans based on eigenfunction analysis and fold modeling. In virtual colonoscopy, CT scans are acquired with the patient in two positions, and their registration is desirable so that physicians can corroborate findings between scans. Our algorithm performs this registration efficiently through the use of Fiedler vector representation (the second eigenfunction of the Laplace-Beltrami operator). This representation is employed to first perform global registration of the two colon positions. The registration is then locally refined using the haustral folds, which are automatically segmented using the 3D level sets of the Fiedler vector. The use of Fiedler vectors and the segmented folds presents a precise way of visualizing corresponding regions across datasets and visual modalities. We present multiple methods of visualizing the results, including 2D flattened rendering and the corresponding 3D endoluminal views. The precise fold modeling is used to automatically find a suitable cut for the 2D flattening, which provides a less distorted visualization. Our approach is robust, and we demonstrate its efficiency and efficacy by showing matched views on both the 2D flattened colons and in the 3D endoluminal view. We analytically evaluate the results by measuring the distance between features on the registered colons, and we also assess our fold segmentation against 20 manually labeled datasets. We have compared our results analytically to previous methods, and have found our method to achieve superior results. We also prove the hot spots conjecture for modeling cylindrical topology using Fiedler vector representation, which allows our approach to be used for general cylindrical geometry modeling and feature extraction.

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“…The benefits of using angle and area terms were discussed in [18,24]: preserving angles reduces the shear of parameterized triangles, and preserving areas prevents features from squeezing into small regions. Nadeem et al [25] proposed parameterization algorithms that balance angle and area distortion, but using only the angle and area distortion terms may not faithfully reproduce geometric features during remeshing if original meshes are not well tessellated or contain sliver triangles. To avoid occurrence of such problems, we add an aspect radio term.…”

Section: Distortion Measurementmentioning

confidence: 99%

“…Fu et al [33] parallelized the AMIP method using OpenMP in Cþ þ and had about 150k triangles/minute, and they had 30k triangles/minute in the serialized implementation. Nadeem et al [25] proposed a divide-and-conquer method to maintain a good balance between angle and area distortion, and they achieved about 2.5K triangles/minute for balanced mapping.…”

Section: Performancementioning

confidence: 99%

Fast mapping and morphing for genus-zero meshes with cross spherical parameterization

Peng

Timalsena

2016

Computers & Graphics

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a b s t r a c tWe introduce an efficient approach to establish surface correspondences between genus-zero triangle meshes and animate a morph between them. We employ the concept of mesh simplification and refinement to progressively parameterize meshes using a novel kernel sampling algorithm. Our two-step feature alignment method optimizes the distribution of vertices in a parametric domain. A new mesh is generated after merging mesh topologies, and it represents the shapes of all input meshes and their transitions in-between. Our approach merges topological structures rather than mapping surface properties. Complex meshes with tens of thousands of vertices can be parameterized and merged in a few minutes. The advantages of our approach are demonstrated through 3D morphing applications. Comparing to existing approaches, our solution advances in performance while maintaining high-quality parameterization and morphing.Published by Elsevier Ltd.1

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Spherical Parameterization Balancing Angle and Area Distortions

Cited by 48 publications

References 45 publications

Interpretable Spiculation Quantification for Lung Cancer Screening

Interpretable Spiculation Quantification for Lung Cancer Screening

Corresponding Supine and Prone Colon Visualization Using Eigenfunction Analysis and Fold Modeling

Fast mapping and morphing for genus-zero meshes with cross spherical parameterization

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