Size and shape computation from your digitisation data.



Data for characterisation are always RAW COORDINATES, except if “OTHER” has been selected

If “OTHER” has been selected, data are linear measurements between anatomical landmarks.

Remark: “raw coordinates” are the coordinates as saved after a digitisation session by XYOM.


For each individual, characterisation analyses provide:

    • centroid size (CS), if from landmarks (LM),
    • perimeter (PER) or square root area (ARE), if from pseudolandmarks (outlines)
    • “log-size” if data are “OTHER” (linear measurements between LM)
    • Orthogonal Projections (ORP) of aligned specimens, if from landmarks,
    • Normalized Elliptic Fourier coefficients (NEF). if from pseudolandmarks (outlines)
    • Log-Shape-Ratios (LSR) if data are linear measurements between anatomical points (traditional morphometrics). See: Mosimann JE (1970) Size allometry: size and shape variables with characterizations of the lognormal and generalized gamma distributions. J Am Stat Assoc 65:930–945.

If Input = raw coordinates of anatomical LANDMARKS (LM)


If Input = raw coordinates of LM + SL (semilandmarks)


  • GPA (Generalized Procrustes Analysis)
  • PCA (Principal component analysis) using (automatically) as input the rotated specimens after orthogonal projection (ORP)
  • DA (Discriminant analysis) using (automatically) as input the principal components (PC) of the ORP.


  • Reports 
  • Graphics
    • GPA Cuantile boxes for centroid size
    • Raw, Translated, Scaled, and Rotated landmarks
    • Mean objects (rotated landmarks averaged by groups)
    • PCA, DA Factor map of the two first multivariate variables.
  • Files (from folder …_ANALYSES_landmarks_SUBDIVISION_…)
    • Raw coordinates of landmarks (landmarks.txt)
    • Centroid size (…- CS.txt)
    • Rotated (or aligned) specimens (… – ROTATED.txt)
    • Orthogonal Projection of aligned specimens (… – ORP.txt)
    • Principal components of ORP (… – PC.txt)
    • Euclidean distances between PCs (… – ED.txt)
    • Discriminant analysis of PC, discriminant factors (… – DF.txt)
    • Mahalanobis distances (… – Mahalanobis distances – .txt)


If Input = raw coordinates of pseudoLANDMARKS (outlines)


  • EFA (Elliptic Fourier analysis), which generates two important outputs for subsequent analyses:
    • (1) … – EST_OUTL.txt, the estimated coordinates after EFA 
    • (2) …- the Normalized Elliptic Fourier coefficients (… – NEF.txt). 
  • GPA, which is automatically applied on  … – EST_OUTL.txt for graphical outputs
  • PCA, automatically using as input the … – NEF.txt data 
  • DA, automatically using as input the principal components of NEF (… – PCs.txt).


  • Reports
  • Graphics:
    • Graphical comparison of outlines, using estimated outlines (…_EST_OUTL.txt)
      • Usual graphics after GPA
      • Especially: Mean objects (rotated landmarks averaged by groups)
    • EFA (…_PER.txt): Quantile boxes for perimeter
    • EFA (…PC.txt on NEF)PCA, DA: Factor map of the two first PC.
    • EFA (…DF.txt from …PC.txt): Factor map of the two first DF.
  • Files  (from folder: _ANALYSES_outlines_SUBDIVISION_…)
    • Coordinates of pseudolandmarks (outlines.txt)
    • Perimeter (… – PER.txt)
    • Square Root area (… – ARE.txt)
    • Estimated coordinates after EFA (… – EST_OUTL.txt)
    • (Centroid sizes)
    • (ROTATED)
    • (ORP)
    • Normalized Elliptic Fourier Coefficients (… – NEF.txt)
    • Principal components (of NEF) (… – PCs.txt)
    • Euclidean distances between principal components (… – ED.txt)

If Input = linear measurements between landmarks (traditional morphometrics)


  • Log transformation -> log-data = log(1+ data)
  • log-size of specimen x -> average of log-transformed characters describing x
  • log-shape-ratios (LSR) -> centered log-data 
  • PC of logShape Ratios <- last PC = 0 removed.


  • Files
    • shape variables (PCs of LSR))
    • global size estimate (log-size)