Fig 1.
Deformed surface mesh of Gorilla gorilla with landmarks.
The virtually deformed cranium used as reference for the comparisons of retrodermation methods in frontal (A), superior (B), right lateral (C) and ventral view (D).
Fig 2.
Visualization of asymmetric noise with a standard deviation of 2 mm. Red: original placement; green: displaced coordinates.
Fig 3.
The pattern of deformation in Saccopastore 1 (SCP1).
Frontal (A), basal (C), posterior (B) and superior (D) views of the fossil cranium; the red dashed line represents the mid-sagittal plane as defined by the points: supra-glabellar, bregma, lambda. The external outline of a coronal plane corresponding to the biporionic width (E), subdivided in 41 evenly-spaced points. The left set of the external outline is mirrored to emphasize the difference between the two parietal profiles (F).
Fig 4.
Original surface mesh of SCP1 with landmarks.
The landmark sets before (red) and after (cyan) the retrodeformation procedure shown in frontal and posterior views.
Fig 5.
Removal of asymmetric noise in the semi-landmarks.
Placement of semi-landmark sets before (cyan) and after sliding (red) on the cranium of SCP1 in frontal and posterior views.
Fig 6.
The surface mesh of SCP1 warped to the new (semi-) landmark positions.
Fig 7.
Visualization of the per-vertex displacement between original and retrodeformed mesh of SCP1.
The mesh distance expressed in millimeters (mm) ranging from 0 (blue) to 3.0 (red).
Fig 8.
Visualization of the retrodeformation error using our proposed method in the Gorilla case study.
The heat-map shows the surface to surface distance between the retrodeformed and the original Gorilla cranium.
Fig 9.
Relation between number of semi-landmarks and recovery of anatomical information (Gorilla case study).
In the plot are reported the number of semilandmark per side (x axis) used at each iteration and the respective amount of vertex displacement (y axis) after the retrodeformation procedure.
Fig 10.
Effect of asymmetric noise on retrodeformation error (Gorilla case study).
Using 200 semi-landmarks, this figure shows the effect of noise in regard to mean and maximum per-vertex error. Blue solid dots: mean error of our proposed regularized method; Mean (solid circles and left y axis) and maximum (open circles and right y axis) error of proposed regularized method (blue) and unregularized retrodeformation (red).
Table 1.
Euclidean distances (mm) acquired before and after the retrodeformation procedure between selected paired bilateral landmarks placed on SCP1.