# A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape

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## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Samples

#### Ape Crania

#### 2.2. Methods

#### 2.2.1. Three Semilandmarking Approaches

#### Generation of the Template

#### Semilandmarking Approaches

- (a)
- Sliding TPS

- (b)
- Rigid registration

- (c)
- Non-rigid registration

#### 2.2.2. Comparison of Three Semilandmarking Approaches

#### The Locations of Semilandmarks

#### Comparisons of Mean Landmark and Semilandmark Configurations

#### Procrustes Distances among Specimens Obtained Using Different Semilandmarking Approaches and Densities

- (a)
- The effect of different semilandmarking approaches

- (b)
- The effect of different densities of semilandmarks

#### PCA and Allometry

## 3. Results

#### 3.1. The Locations of Semilandmarks

#### 3.2. Differences among Mean Landmark and Semilandmark Locations

#### 3.3. Comparison of Centroid Sizes and Procrustes Distance Matrices

#### 3.4. PCA and Allometry

## 4. Discussion

#### 4.1. Significance and Implications of Findings

#### 4.2. Limitations and Future Work

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**800 semilandmarks generated by sliding TPS (black points), LS&ICP (amber points), and TPS&NICP (magenta points) approaches on the mean surface generated by sliding TPS.

**Figure 3.**The average differences in location (mm) between 800 semilandmarks generated by different approaches. (

**a**) Differences between sliding TPS and TPS&NICP approaches. (

**b**) Differences between sliding TPS and LS&ICP approaches. Differences between TPS&NICP and LS&ICP approaches are not shown because they are very similar to those in (

**b**).

**Figure 4.**Comparisons of centroid sizes estimated by different semilandmarking approaches. (

**a**) Sliding TPS vs. LS&ICP. (

**b**) Sliding TPS vs. TPS&NICP.

**Figure 5.**Comparison of the vector of Procrustes distances from the mean between semilandmarking approaches. (

**a**) Sliding TPS vs. LS&ICP. (

**b**) Sliding TPS vs. TPS&NICP.

**Figure 6.**Vectors of Procrustes distances between each individual and the mean computed for each semilandmarking approach using different densities of semilandmarks. Cyan points represent Procrustes distances between every specimen and the Procrustes mean shape and red points represent the average value of the Procrustes distance vector.

**Figure 7.**Visualization of superimposed scatterplots of PC1 and PC2 from analyses of 20 ape crania using landmarks and semilandmarks from sliding TPS, LS&ICP, and TPS&NICP approaches with varying densities. The horizontal axis represents PC1 and the vertical, PC2. Cross: Pongo abeli. Circle: Gorilla. Rectangle: Pan troglodytes; Triangle. Hylobates lar. Amber: Sliding TPS. Blue: TPS&NICP. Magenta: LS&ICP.

diff. mm | 50 | 100 | 200 | 400 | 800 | |||||
---|---|---|---|---|---|---|---|---|---|---|

dev | % | dev | % | dev | % | dev | % | dev | % | |

[0.0–1.0) | 0.56 | 52.00 | 0.64 | 46.00 | 0.70 | 35.50 | 0.68 | 30.25 | 0.70 | 33.75 |

[1.0–2.5) | 1.34 | 48.00 | 1.44 | 54.00 | 1.47 | 64.00 | 1.49 | 69.50 | 1.50 | 66.13 |

[2.5–5.0) | - | - | - | - | 2.99 | 0.5 | 2.57 | 0.25 | 2.73 | 0.12 |

$\ge $5.00 | - | - | - | - | - | - | - | - | - | - |

Total | 0.94 | 100.00 | 1.08 | 100.00 | 1.21 | 100.00 | 1.25 | 100.00 | 1.23 | 100.00 |

diff. mm | 50 | 100 | 200 | 400 | 800 | |||||
---|---|---|---|---|---|---|---|---|---|---|

dev | % | dev | % | dev | % | dev | % | dev | % | |

[0.0–1.0) | - | - | - | - | - | - | - | - | - | - |

[1.0–2.5) | - | - | - | - | - | - | - | - | - | - |

[2.5–5.0) | 4.93 | 2.00 | 4.54 | 4.00 | 4.58 | 5.50 | 4.82 | 1.25 | 4.80 | 1.38 |

$\ge $5.00 | 9.04 | 98.00 | 9.89 | 96.00 | 10.41 | 94.50 | 11.05 | 98.75 | 11.52 | 98.62 |

Total | 8.96 | 100.00 | 9.68 | 100.00 | 10.09 | 100.00 | 10.97 | 100.00 | 11.37 | 100.00 |

**Table 3.**Procrustes distance (permutation test p < 0.05 *) between mean landmark and semilandmark configurations derived at varying densities.

50 | 100 | 200 | 400 | 800 | |
---|---|---|---|---|---|

Sliding TPS LS&ICP | 0.0419 | 0.0532 | 0.0554 * | 0.0582 * | 0.0581 * |

Sliding TPS TPS&NICP | 0.0051 | 0.0061 | 0.0072 | 0.0067 | 0.0072 |

LS&ICP TPS&NICP | 0.0419 | 0.0534 | 0.0556 * | 0.0589 * | 0.0591 * |

**Table 4.**Pearson correlations (all p < 0.01, except

^{#}, p < 0.05, * = n.s., parametric test) among the vectors of Procrustes distances between each ape cranium and the mean and Mantel tests among Procrustes distance matrices.

50 | 100 | 200 | 400 | 800 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | |

Sliding TPS LS&ICP | 0.7630 | 0.8024 | 0.6789 | 0.7403 | 0.5954 | 0.6711 | 0.5066 ^{#} | 0.5993 | 0.4185 * | 0.5241 |

Sliding TPS TPS&NICP | 0.9988 | 0.9986 | 0.9962 | 0.9970 | 0.9959 | 0.9961 | 0.9951 | 0.9947 | 0.9948 | 0.9944 |

LS&ICP TPS&NICP | 0.7540 | 0.7929 | 0.6643 | 0.7268 | 0.5806 | 0.6561 | 0.4739 ^{#} | 0.5761 | 0.3881 * | 0.5050 |

**Table 5.**Pearson correlations (all p < 0.001, parametric test) among vectors of Procrustes distances between each individual and the mean and Mantel tests comparing Procrustes distance matrices between each density of semilandmarking and the maximum density.

50 | 100 | 200 | 400 | |||||
---|---|---|---|---|---|---|---|---|

Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | |

Sliding TPS | 0.9770 | 0.9752 | 0.9907 | 0.9899 | 0.9945 | 0.9945 | 0.9991 | 0.9990 |

LS&ICP | 0.8931 | 0.9123 | 0.9324 | 0.9453 | 0.9688 | 0.9752 | 0.9918 | 0.9931 |

TPS&NICP | 0.9849 | 0.9833 | 0.9943 | 0.9937 | 0.9973 | 0.9974 | 0.9993 | 0.9994 |

**Table 6.**Pearson and Mantel correlations (all p < 0.01, except

^{#}, p < 0.05) between vectors and matrices of Procrustes distances from each semilandmarking approach and density and those from the landmarks alone.

50 | 100 | 200 | 400 | 800 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | Pearson | Mantel | |

Sliding TPS | 0.9619 | 0.9579 | 0.9460 | 0.9401 | 0.9303 | 0.9244 | 0.9160 | 0.9079 | 0.9105 | 0.8995 |

LS&ICP | 0.7424 | 0.7951 | 0.6627 | 0.7532 | 0.6081 | 0.7153 | 0.5413 ^{#} | 0.6742 | 0.4916 ^{#} | 0.6402 |

TPS&NICP | 0.9602 | 0.9551 | 0.9473 | 0.9391 | 0.9350 | 0.9241 | 0.9260 | 0.9135 | 0.9221 | 0.9076 |

**Table 7.**Comparison of Pearson correlations (all p < 0.01, except

^{#}, p < 0.05, * = n.s.) of PC1 and PC2 between sliding TPS and TPS&NICP.

50 | 100 | 200 | 400 | 800 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | |

Sliding TPS LS&ICP | 0.9400 | 0.9387 | 0.8981 | 0.8119 | 0.8561 | 0.6647 | 0.8163 | 0.4961 ^{#} | 0.7666 | 0.3334 * |

Sliding TPS TPS&NICP | 0.9993 | 0.9989 | 0.9983 | 0.9992 | 0.9978 | 0.9985 | 0.9974 | 0.9977 | 0.9972 | 0.9967 |

LS&ICP TPS&NICP | 0.9357 | 0.9264 | 0.8919 | 0.8030 | 0.8443 | 0.6610 | 0.7988 | 0.4749 ^{#} | 0.7498 | 0.3291 * |

**Table 8.**Pearson correlations (all p < 0.01, except

^{#}, p < 0.05, * = n.s.) among PC scores from each semilandmarking density and from the landmarks alone.

50 | 100 | 200 | 400 | 800 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | |

Sliding TPS | 0.9487 | 0.8634 | 0.9238 | 0.8435 | 0.9104 | 0.8188 | 0.9021 | 0.8155 | 0.8963 | 0.8077 |

LS&ICP | 0.9399 | 0.7606 | 0.9329 | 0.6427 | 0.9291 | 0.5515 ^{#} | 0.9228 | 0.4363 * | 0.9116 | 0.3325 * |

TPS&NICP | 0.9430 | 0.8732 | 0.9186 | 0.8434 | 0.8999 | 0.8020 | 0.8880 | 0.8108 | 0.8833 | 0.8012 |

**Table 9.**Pearson correlations (all p < 0.01, parametric test) among PC scores from each semilandmarking density and the maximum density.

50 | 100 | 200 | 400 | |||||
---|---|---|---|---|---|---|---|---|

PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | PC1 | PC2 | |

Sliding TPS | 0.9888 | 0.9769 | 0.9971 | 0.9900 | 0.9987 | 0.9963 | 0.9996 | 0.9984 |

LS&ICP | 0.9512 | 0.6821 | 0.9692 | 0.8368 | 0.9837 | 0.9268 | 0.9942 | 0.9838 |

TPS&NICP | 0.9876 | 0.9765 | 0.9962 | 0.9908 | 0.9989 | 0.9965 | 0.9998 | 0.9993 |

**Table 10.**The angles (°) between allometric vectors (permutation test p < 0.05 *) derived at varying densities.

50 | 100 | 200 | 400 | 800 | |
---|---|---|---|---|---|

Sliding TPS LS&ICP | 65.19 * | 75.25 * | 82.38 * | 86.50 * | 90.25 * |

Sliding TPS TPS&NICP | 6.52 | 7.67 | 8.68 | 8.97 | 8.73 |

LS&ICP TPS&NICP | 65.83 * | 75.68 * | 82.82 * | 86.19 * | 90.16 * |

**Table 11.**Procrustes distances between the predicted landmark and semilandmark configurations from sliding TPS and TPS&NICP corresponding to the maximum (Max) and minimum (Min) centroid sizes.

50 | 100 | 200 | 400 | 800 | |
---|---|---|---|---|---|

Max | 0.0095 | 0.0113 | 0.0122 | 0.0124 | 0.0134 |

Min | 0.0168 | 0.0189 | 0.0211 | 0.0214 | 0.0202 |

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**MDPI and ACS Style**

Shui, W.; Profico, A.; O’Higgins, P. A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape. *Animals* **2023**, *13*, 1179.
https://doi.org/10.3390/ani13071179

**AMA Style**

Shui W, Profico A, O’Higgins P. A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape. *Animals*. 2023; 13(7):1179.
https://doi.org/10.3390/ani13071179

**Chicago/Turabian Style**

Shui, Wuyang, Antonio Profico, and Paul O’Higgins. 2023. "A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape" *Animals* 13, no. 7: 1179.
https://doi.org/10.3390/ani13071179