Parametric fitting and morphometric analysis of 3D open curves based on discrete cosine transform

Zhou, Shengmin; Li, Bingjue; Nie, Huan

doi:10.1007/s00435-021-00520-w

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…These matching and classification results show that the shape-changing chain is efficient in fitting and analyzing 3D curves with a very moderate number of variables compared to other parametric methods. For example, Zhou et al employed discrete cosine transform (DCT) to analyze the same three sets of suture curves 33 . In their work, 12, 6, and 6 harmonics are employed to fit the sagittal curves, the coronal suture curves, and the lambdoid suture curves, resulting in 36, 18, and 18 coefficients to be analyzed.…”

Section: Morphometric Examples and Resultsmentioning

confidence: 99%

Shape-changing chains for morphometric analysis of 2D and 3D, open or closed outlines

Zhou

Murray

et al. 2021

Sci Rep

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Morphometrics is a multivariate technique for shape analysis widely employed in biological, medical, and paleoanthropological applications. Commonly used morphometric methods require analyzing a huge amount of variables for problems involving a large number of specimens or complex shapes. Moreover, the analysis results are sometimes difficult to interpret and assess. This paper presents a methodology to synthesize a shape-changing chain for 2D or 3D curve fitting and to employ the chain parameters in stepwise discriminant analysis (DA). The shape-changing chain is comprised of three types of segments, including rigid segments that have fixed length and shape, scalable segments with a fixed shape, and extendible segments with constant curvature and torsion. Three examples are presented, including 2D mandible profiles of fossil hominin, 2D leaf outlines, and 3D suture curves on infant skulls. The results demonstrate that the shape-changing chain has several advantages over common morphometric methods. Specifically, it can be applied to a wide range of 2D or 3D profiles, including open or closed curves, and smooth or serrated curves. Additionally, the segmentation of profiles is a flexible and automatic protocol that can consider both biological and geometric features, the number of variables obtained from the fitting results for statistical analysis is modest, and the chain parameters that characterize the profiles can have physical meaning.

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Section: Morphometric Examples and Resultsmentioning

confidence: 99%

Shape-changing chains for morphometric analysis of 2D and 3D, open or closed outlines

Zhou

Murray

et al. 2021

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this way, any closed shape in 2D can be described. This popular method [34] has been applied to biological shapes in animals [35][36][37][38] and plants [39][40][41][42][43] and has been extended to open shapes in 3D by means of the discrete cosine transform [44].…”

Section: B 2d Shapes: Planar Curvesmentioning

confidence: 99%

A constructive theory of shape

García-Morales

2021

Preprint

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We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter κ ∈ (0, ∞). The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a variety of examples: (chaotic) time series, plane curves, space filling curves and knots. In particular, we construct an infinite family of fractal curves whose shape approaches the one of Hilbert's curve in the limit κ → 0, yielding, for κ finite, fractal space-filling curves with nonlinear contours.

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Surface Representation and Morphometric Analysis Based on Discrete Cosine Transform

Zhou

Nie

2022

Evol Biol

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Parametric fitting and morphometric analysis of 3D open curves based on discrete cosine transform

Cited by 4 publications

References 27 publications

Shape-changing chains for morphometric analysis of 2D and 3D, open or closed outlines

Shape-changing chains for morphometric analysis of 2D and 3D, open or closed outlines

A constructive theory of shape

Surface Representation and Morphometric Analysis Based on Discrete Cosine Transform

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