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An advanced shape-fitting algorithm applied to quadrupedal mammals: improving volumetric mass estimates.

Brassey CA, Gardiner JD - R Soc Open Sci (2015)

Bottom Line: We fit α-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations.Our optimal model is characterized by a high correlation coefficient and mean square error (r (2)=0.975, m.s.e.=0.025).We consider α-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Life Sciences , University of Manchester , Manchester M13 9PL, UK.

ABSTRACT
Body mass is a fundamental physical property of an individual and has enormous bearing upon ecology and physiology. Generating reliable estimates for body mass is therefore a necessary step in many palaeontological studies. Whilst early reconstructions of mass in extinct species relied upon isolated skeletal elements, volumetric techniques are increasingly applied to fossils when skeletal completeness allows. We apply a new 'alpha shapes' (α-shapes) algorithm to volumetric mass estimation in quadrupedal mammals. α-shapes are defined by: (i) the underlying skeletal structure to which they are fitted; and (ii) the value α, determining the refinement of fit. For a given skeleton, a range of α-shapes may be fitted around the individual, spanning from very coarse to very fine. We fit α-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations. Our optimal model is characterized by a high correlation coefficient and mean square error (r (2)=0.975, m.s.e.=0.025). When applied to the woolly mammoth (Mammuthus primigenius) and giant ground sloth (Megatherium americanum), we reconstruct masses of 3635 and 3706 kg, respectively. We consider α-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.

No MeSH data available.


Related in: MedlinePlus

A ‘family’ of α-shapes for a given two-dimensional dataset. (a) The special case ‘convex hull’ α-shape calculated when α is infinite; (b−d) α-shapes calculated as the radius α decreases relative to the point spacing of the dataset; (e) original ‘solid’ geometric shape upon which point cloud (a−d) was derived. The suite of α-shapes ranges from ‘crude’ to ‘fine’ representations of the two-dimensional dataset.
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RSOS150302F1: A ‘family’ of α-shapes for a given two-dimensional dataset. (a) The special case ‘convex hull’ α-shape calculated when α is infinite; (b−d) α-shapes calculated as the radius α decreases relative to the point spacing of the dataset; (e) original ‘solid’ geometric shape upon which point cloud (a−d) was derived. The suite of α-shapes ranges from ‘crude’ to ‘fine’ representations of the two-dimensional dataset.

Mentions: Recently, a mass-estimation technique has been put forward which combines aspects of three-dimensional volumetric modelling and traditional linear bivariate predictive equations, by using ‘convex hulls’. A convex hull can intuitively be thought of as a shrink-wrap polytope around a given set of points, such that no points exist outside of the shape (figure 1a). Sellers et al. [26] apply convex hull fits to segmented three-dimensional models of modern quadrupedal mammal skeletons in order to determine a value for minimum convex hull volume (Cvol) of the animal as defined by the bony limits of its skeleton. Cvol can subsequently be used as the independent variable in a predictive equation with body mass. It must be emphasized that convex hulling as applied here and by Sellers et al. [26] to articulated skeletons does not seek to recreate the original fleshed-out form of the animal and should not be confused with other digital sculpting techniques. Rather Cvol is simply used an alternative metric of skeleton size (analogous to using femur circumference or molar height) to be incorporated into a bivariate predictive equation and is of uncertain use in the calculation of COM and segment inertial properties from skeletons (although see [27] for application of convex hulls to fleshed out anthropometric datasets).Figure 1.


An advanced shape-fitting algorithm applied to quadrupedal mammals: improving volumetric mass estimates.

Brassey CA, Gardiner JD - R Soc Open Sci (2015)

A ‘family’ of α-shapes for a given two-dimensional dataset. (a) The special case ‘convex hull’ α-shape calculated when α is infinite; (b−d) α-shapes calculated as the radius α decreases relative to the point spacing of the dataset; (e) original ‘solid’ geometric shape upon which point cloud (a−d) was derived. The suite of α-shapes ranges from ‘crude’ to ‘fine’ representations of the two-dimensional dataset.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4555864&req=5

RSOS150302F1: A ‘family’ of α-shapes for a given two-dimensional dataset. (a) The special case ‘convex hull’ α-shape calculated when α is infinite; (b−d) α-shapes calculated as the radius α decreases relative to the point spacing of the dataset; (e) original ‘solid’ geometric shape upon which point cloud (a−d) was derived. The suite of α-shapes ranges from ‘crude’ to ‘fine’ representations of the two-dimensional dataset.
Mentions: Recently, a mass-estimation technique has been put forward which combines aspects of three-dimensional volumetric modelling and traditional linear bivariate predictive equations, by using ‘convex hulls’. A convex hull can intuitively be thought of as a shrink-wrap polytope around a given set of points, such that no points exist outside of the shape (figure 1a). Sellers et al. [26] apply convex hull fits to segmented three-dimensional models of modern quadrupedal mammal skeletons in order to determine a value for minimum convex hull volume (Cvol) of the animal as defined by the bony limits of its skeleton. Cvol can subsequently be used as the independent variable in a predictive equation with body mass. It must be emphasized that convex hulling as applied here and by Sellers et al. [26] to articulated skeletons does not seek to recreate the original fleshed-out form of the animal and should not be confused with other digital sculpting techniques. Rather Cvol is simply used an alternative metric of skeleton size (analogous to using femur circumference or molar height) to be incorporated into a bivariate predictive equation and is of uncertain use in the calculation of COM and segment inertial properties from skeletons (although see [27] for application of convex hulls to fleshed out anthropometric datasets).Figure 1.

Bottom Line: We fit α-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations.Our optimal model is characterized by a high correlation coefficient and mean square error (r (2)=0.975, m.s.e.=0.025).We consider α-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Life Sciences , University of Manchester , Manchester M13 9PL, UK.

ABSTRACT
Body mass is a fundamental physical property of an individual and has enormous bearing upon ecology and physiology. Generating reliable estimates for body mass is therefore a necessary step in many palaeontological studies. Whilst early reconstructions of mass in extinct species relied upon isolated skeletal elements, volumetric techniques are increasingly applied to fossils when skeletal completeness allows. We apply a new 'alpha shapes' (α-shapes) algorithm to volumetric mass estimation in quadrupedal mammals. α-shapes are defined by: (i) the underlying skeletal structure to which they are fitted; and (ii) the value α, determining the refinement of fit. For a given skeleton, a range of α-shapes may be fitted around the individual, spanning from very coarse to very fine. We fit α-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations. Our optimal model is characterized by a high correlation coefficient and mean square error (r (2)=0.975, m.s.e.=0.025). When applied to the woolly mammoth (Mammuthus primigenius) and giant ground sloth (Megatherium americanum), we reconstruct masses of 3635 and 3706 kg, respectively. We consider α-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.

No MeSH data available.


Related in: MedlinePlus