What is Morphometrics?#

Morphometrics provides quantitative representation of morphological traits by extracting shape information as geometric invariants. It offers mathematical tools for modeling morphological properties, bridging the gap between raw digitized data and biologically meaningful phenotypic values.

Form and Shape#

In geometric morphometrics, form and shape have precise mathematical definitions:

  • Form: Geometric properties invariant to translation and rotation

  • Shape: Geometric properties invariant to translation, rotation, and scaling

This distinction is fundamental in geometric morphometrics: shape analysis removes size information, allowing comparison of organisms regardless of their absolute dimensions.

Approaches in Morphometrics#

ktch implements two major approaches to morphometric analysis:

Landmark-based Morphometrics#

Landmark-based methods model morphological properties as sets of corresponding points among specimens. Shape is extracted via Generalized Procrustes Analysis (GPA), which removes position, size, and orientation.

Key characteristics:

  • Requires identification of corresponding points across specimens

  • Suitable for structures with clearly identifiable anatomical features

  • Captures local shape information at specific points

Applications:

  • Grass phytoliths

  • Leaf shape analysis

  • Flower morphology

  • Skeletal morphology

See also

Landmark-based Morphometrics for details on Procrustes methods

Harmonic-based Morphometrics#

Harmonic-based methods describe shape using mathematical functions that capture the outline or surface geometry without requiring point-to-point correspondence between specimens.

Elliptic Fourier Analysis (EFA): Models closed outlines by approximating x and y coordinates as Fourier series, quantifying shapes through normalized Fourier coefficients.

Spherical Harmonic Analysis: Models closed 3D surfaces using spherical harmonic functions.

Applications:

  • Seed morphology

  • Leaf outlines

  • Petal shapes

  • Fruit shapes

See also

Harmonic-based Morphometrics for details on harmonic methods

Choosing an Approach#

Consideration

Landmark-based

Harmonic-based

Data type

Discrete corresponding points

Continuous outlines/surfaces

Homology

Requires explicit point correspondence

No explicit point correspondence required

Automation

Partially manual

Highly automatic

Use landmark-based methods when:

  • Clear, identifiable anatomical points exist

  • Biological homology between points is established

Use harmonic-based methods when:

  • No clear landmarks are available

  • The outline or surface itself is the feature of interest

The scikit-learn Compatible Workflow#

ktch follows the scikit-learn API design:

from ktch.landmark import GeneralizedProcrustesAnalysis
from ktch.harmonic import EllipticFourierAnalysis
from sklearn.decomposition import PCA

# Landmark workflow
gpa = GeneralizedProcrustesAnalysis()
shapes = gpa.fit_transform(landmarks)

# Harmonic workflow
efa = EllipticFourierAnalysis(n_harmonics=20)
coefficients = efa.fit_transform(outlines)

# Combine with PCA
pca = PCA(n_components=3)
scores = pca.fit_transform(shapes)  # or coefficients

See also

Use with scikit-learn Pipeline for practical examples

References#

  • Noshita, K. (2022). Model-based phenotyping for plant morphometrics. Breeding Science, 72(1), 3-13.