Fourier analysis of size and shape changes in the Japanese skull

ABSTRACT Hybrid event beds are the deposits from sediment gravity flows that change their rheological behavior through their passage, entraining muddy sediments and damping turbulence. Muddy facies of hybrid event beds are often associated with abundant mud clasts which show a wide variety of size and shape. The variation of clast occurrence in hybrid event beds is expected to preserve the information of entrainment and transport processes of muddy sediments in submarine density currents. However, previous analyses of hybrid event beds have focused on describing the overall clast occurrence rather than the statistical size and shape analyses because traditional shape parameters are incapable of characterizing the complex shape of mud clasts. Here, a new quantitative grain-shape analysis of mud clasts is conducted and allows visualization of the spatial variation of clast size and shape, which suggests the wide variety of origin and transport systems of entrained mud clasts. This new method revises the traditional elliptic Fourier analysis, substituting Fourier power spectra (FPS) for traditional elliptic Fourier descriptors to overcome the mirror-wise shape problem. Further, principal-component analysis is shown to capture significant shape attributes more effectively than traditional shape parameters. The proposed method is applied to mud clasts in sediment-gravity-flow deposits in the lower Pleistocene Otadai Formation, central Japan. Results imply that there are distinctive shape and size differences of mud clasts that are strongly associated with depositional facies rather than the distance from the source. The clasts have a higher angularity than other facies in the debrite intervals in hybrid event beds. It is also shown that clasts in sandy, structureless facies have different characteristics in shapes based on elongation and convexity compared to laminated facies. Comparison between different shape-analysis methods demonstrates that none of the traditional methods are able to visualize these trends as effectively as the method presented herein. These results highlight the importance of the quantitative shape analysis of sediment grains and the effectiveness of FPS-based elliptic Fourier analysis.

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Visualization of Individual Growth-Related Craniofacial Changes Based on Cephalometric Landmark Data: A Pilot Study

The Cleft Palate-Craniofacial Journal ◽

10.1597/1545-1569_2002_039_0341_voigrc_2.0.co_2 ◽

2002 ◽

Vol 39 (3) ◽

pp. 341-352 ◽

Cited By ~ 1

Author(s):

Christopher J. Lux ◽

Jens Starke ◽

Jan Rübel ◽

Angelika Stellzig ◽

Gerda Komposch

Keyword(s):

Dynamic Behavior ◽

Growth Process ◽

Shape Change ◽

Individual Growth ◽

Craniofacial Skeleton ◽

Size And Shape ◽

Lateral Cephalograms ◽

Landmark Data ◽

The Individual ◽

Shape Changes

Objective: An approach based on Euclidean distances between cephalometric landmarks is presented (1) to visualize and localize the individual shape changes of the complex craniofacial skeleton during growth and (2) to depict the individual dynamic behavior of developmental size and shape changes. Patients and Method: Growth-related craniofacial changes were investigated exemplarily for two male orthodontically untreated subjects from the Belfast Growth Study on the basis of lateral cephalograms at 7, 9, 11, 13, and 15 years. The interlandmark distances among seven skeletal cephalometric landmarks served as a database for the study. A modified Karhunen-Loèvedecomposition based on orthogonal modes and time-dependent scalar amplitudes was used to describe the growth process. The individual shape changes of the various craniofacial regions were visualized by allocation of colors to the respective distances, and overdrawn representations were reconstructed by means of multidimensional scaling. Results and Conclusions: This visualization technique allows anatomical regions to be characterized with respect to reduced or strengthened growth, compared with pure size changes. The clinically relevant mechanisms of craniofacial changes are visualized (e.g., shifts in the anteroposterior or vertical dimensions of the jaws in relation to cranial base and structural imbalances during development). In addition, overdrawing the effects of shape change on the skeletal structures gives a more readily comprehensible impression of the growth process. Taking account of the methodical limitations of this approach (e.g., the restrictions concerning the number of landmarks), the clinician may take advantage of this technique in orthodontic or surgical diagnostics to gain additional insight into the individual complex size and shape changes during development along with their dynamic behavior.

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Fourier analysis applied to Stephanomys (Rodentia, Muridae) molars: nonprogressive evolutionary pattern in a gradual lineage

Paleobiology ◽

10.1017/s0094837300016201 ◽

1996 ◽

Vol 22 (2) ◽

pp. 255-265 ◽

Cited By ~ 73

Author(s):

Sabrina Renaud ◽

Jacques Michaux ◽

Jean-Jacques Jaeger ◽

Jean-Christophe Auffray

Keyword(s):

Fourier Coefficients ◽

Size Variation ◽

Evolutionary Pattern ◽

Size And Shape ◽

Mechanical Constraints ◽

Phylogenetic Studies ◽

Single Structure ◽

Lower Molar ◽

Shape Changes ◽

Elliptic Fourier Transform

Size and shape are analyzed for Pliocene lineages of the rodent genus Stephanomys Schaub 1938. Previous phylogenetic studies were based mainly on size variation and descriptive comparisons, without any attempt to quantify shape changes. Hence, on the basis of regular size increase, Stephanomys has been considered a prime example of phyletic gradualism. In order to quantify morphological variation within the lineage, a method for analyzing complex outlines, the elliptic Fourier transform, was applied to tooth contour (upper and lower first molars). It was then possible to compare evolution in size, estimated by tooth area, as well as evolution of shape, represented by Fourier coefficients.While size seems to change gradually through time, morphology gives a rather discontinuous evolutionary pattern for both the upper and lower molar. Such a discrepancy between the evolution of size and shape of a single structure suggests that different genetic determinisms and mechanical constraints may act on size and shape. Hence it may be misleading to infer generalized evolutionary processes from either size or shape alone.

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