Authors: J. Coelho, S. Ammer

library(ggplot2)
library(Momocs) # package for outline and curve analysis
This is Momocs 1.1.0

Attaching package: ‘Momocs’

The following object is masked from ‘package:stats’:

filter

The following object is masked from ‘package:base’:

table
setwd("/Users/del/ACADEMY/WIP/HumerusProject/Photos_final/") # location of my data
rawLPF <- import_tps(tps.path = "LPF/LPF.TPS", curves = T) # read data Left, Posterior, Females
rawLPM <- import_tps(tps.path = "LPM/LPM.TPS", curves = T) # read data Left, Posterior, Males

## Rebuild dataset

For some reason, I can’t use Momocs::Out() directly on my imported TPS. Tried many ways, always obtaining different errors. I thought this might be because the p of coordinates is not consistent. So I resample them. In my understanding coo_sample() works well for open curves, while I preferred coo_interpolate() for my closed outlines, since they had very inconsistent p.

# Rebuild datasets
# For females
for (i in seq_along(rawLPF$cur)){ # open (curves) rawLPF$cur[[i]][[1]] <- coo_sample(rawLPF$cur[[i]][[1]], n = 16) # closed (outlines) rawLPF$cur[[i]][[2]] <- coo_interpolate(rawLPF$cur[[i]][[2]], n = 24) # keep the IDs names(rawLPF$cur)[[i]] <- names(rawLPF$cur)[[i]] } ## For males for (i in seq_along(rawLPM$cur)){
# open (curves)
rawLPM$cur[[i]][[1]] <- coo_sample(rawLPM$cur[[i]][[1]], n = 16)
# closed (outlines)
rawLPM$cur[[i]][[2]] <- coo_interpolate(rawLPM$cur[[i]][[2]], n = 24)
# keep the IDs
names(rawLPM$cur)[[i]] <- names(rawLPM$cur)[[i]]
}

## Spliting data

I tried to work with my curves together but for some reason, I also got errors trying to Out() these. So first I will split my open curve (TE: Throclear Extension) from my closed outlines (OF: Olecranon Fossa), but combine my males and females datasets to see the differences among these groups.

TE.f <- list()
for (i in seq_along(rawLPF$cur)){ TE.f[[i]] <- rawLPF$cur[[i]][[1]]
names(TE.f)[[i]] <- names(rawLPF$cur)[[i]] } TE.m <- list() for (i in seq_along(rawLPM$cur)){
TE.m[[i]] <- rawLPM$cur[[i]][[1]] names(TE.m)[[i]] <- names(rawLPM$cur)[[i]]
}
Sex <- rep("Female", length(TE.f))
TE.f <- Out(TE.f, fac = as.data.frame(Sex))
Sex <- rep("Male", length(TE.m))
TE.m <- Out(TE.m, fac = as.data.frame(Sex))
TE <- combine(TE.f, TE.m)
###
OF.f <- list()
for (i in seq_along(rawLPF$cur)){ OF.f[[i]] <- rawLPF$cur[[i]][[2]]
names(OF.f)[[i]] <- names(rawLPF$cur)[[i]] } OF.m <- list() for (i in seq_along(rawLPM$cur)){
OF.m[[i]] <- rawLPM$cur[[i]][[2]] names(OF.m)[[i]] <- names(rawLPM$cur)[[i]]
}
Sex <- rep("Female", length(OF.f))
OF.f <- Out(OF.f, fac = as.data.frame(Sex))
Sex <- rep("Male", length(OF.m))
OF.m <- Out(OF.m, fac = as.data.frame(Sex))
OF <- combine(OF.f, OF.m)

## Procrustes and Rotation

My pics were (anatomically) upside-down. So I use the very useful coo_rotate() by Pi radians (180º). I have done some landmarks-based analysis before were Procrustes was a mandatory step. I am not sure if it is with open curves and closed outlines, however I am also doing a superimposition step here.

TE.aligned <- TE %>% coo_rotate(.,theta = pi) %>% fgProcrustes() %>% Opn()
OF.aligned <- OF %>% coo_rotate(.,theta = pi) %>% fgProcrustes() %>% coo_close()

# Throclear Extension

MANOVA_PW(TE.pca, 1)

PC axes 1 to 2 were retained
$stars.tab Female Male Female .$summary (see also \$manovas)
Df  Pillai approx F num Df den Df Pr(>F)
Female - Male  1 0.03713    2.854      2    148 0.0608

# Olecranon Fossa

OF.lda <- LDA(OF.pca, 1)

0.99 total variance
7 PC retained
---
title: "Distal Humeri Shape Analysis Notebook"
output:
  word_document: default
  html_notebook: default
  html_document: default
---

*Authors:* J. Coelho, S. Ammer

```{r importing data, cache=TRUE}
library(ggplot2)
library(Momocs) # package for outline and curve analysis
setwd("/Users/del/ACADEMY/WIP/HumerusProject/Photos_final/") # location of my data

rawLPF <- import_tps(tps.path = "LPF/LPF.TPS", curves = T) # read data Left, Posterior, Females
rawLPM <- import_tps(tps.path = "LPM/LPM.TPS", curves = T) # read data Left, Posterior, Males

```

## Rebuild dataset

For some reason, I can't use `Momocs::Out()` directly on my imported TPS. Tried many ways, always obtaining different errors. I thought this might be because the **p** of coordinates is not consistent. So I resample them. In my understanding `coo_sample()` works well for open curves, while I preferred `coo_interpolate()` for my closed outlines, since they had very inconsistent **p**.

```{r rebuild, cache=TRUE}
# Rebuild datasets
# For females

for	(i in seq_along(rawLPF$cur)){
	# open (curves)
	rawLPF$cur[[i]][[1]] <- coo_sample(rawLPF$cur[[i]][[1]], n = 16)
	# closed (outlines)
	rawLPF$cur[[i]][[2]] <- coo_interpolate(rawLPF$cur[[i]][[2]], n = 24)
	# keep the IDs
	names(rawLPF$cur)[[i]] <- names(rawLPF$cur)[[i]]
}

## For males

for	(i in seq_along(rawLPM$cur)){
	# open (curves)
	rawLPM$cur[[i]][[1]] <- coo_sample(rawLPM$cur[[i]][[1]], n = 16)
	# closed (outlines)
	rawLPM$cur[[i]][[2]] <- coo_interpolate(rawLPM$cur[[i]][[2]], n = 24)
	# keep the IDs
	names(rawLPM$cur)[[i]] <- names(rawLPM$cur)[[i]]
}

```

## Spliting data

I tried to work with my curves together but for some reason, I also got errors trying to `Out()` these. So first I will split my open curve (TE: Throclear Extension) from my closed outlines (OF: Olecranon Fossa), but combine my males and females datasets to see the differences among these groups.

```{r split, cache=TRUE}

TE.f <- list()
for	(i in seq_along(rawLPF$cur)){
	TE.f[[i]] <- rawLPF$cur[[i]][[1]]
	names(TE.f)[[i]] <- names(rawLPF$cur)[[i]]
}

TE.m <- list()
for	(i in seq_along(rawLPM$cur)){
	TE.m[[i]] <- rawLPM$cur[[i]][[1]]
	names(TE.m)[[i]] <- names(rawLPM$cur)[[i]]
}

Sex <- rep("Female", length(TE.f))
TE.f <- Out(TE.f, fac = as.data.frame(Sex))
Sex <- rep("Male", length(TE.m))
TE.m <- Out(TE.m, fac = as.data.frame(Sex))
TE <- combine(TE.f, TE.m)

###

OF.f <- list()
for	(i in seq_along(rawLPF$cur)){
	OF.f[[i]] <- rawLPF$cur[[i]][[2]]
	names(OF.f)[[i]] <- names(rawLPF$cur)[[i]]
}

OF.m <- list()
for	(i in seq_along(rawLPM$cur)){
	OF.m[[i]] <- rawLPM$cur[[i]][[2]]
	names(OF.m)[[i]] <- names(rawLPM$cur)[[i]]
}

Sex <- rep("Female", length(OF.f))
OF.f <- Out(OF.f, fac = as.data.frame(Sex))
Sex <- rep("Male", length(OF.m))
OF.m <- Out(OF.m, fac = as.data.frame(Sex))
OF <- combine(OF.f, OF.m)


```

## Procrustes and Rotation

My pics were (anatomically) upside-down. So I use the very useful `coo_rotate()` by Pi radians (180º). I have done some landmarks-based analysis before were Procrustes was a mandatory step. I am not sure if it is with open curves and closed outlines, however I am also doing a superimposition step here.

```{r Procrustes, cache=TRUE}
TE.aligned <- TE %>% coo_rotate(.,theta = pi) %>% fgProcrustes() %>% Opn()
OF.aligned <- OF %>% coo_rotate(.,theta = pi) %>% fgProcrustes() %>% coo_close()
```

# Throclear Extension

```{r TE plotting, cache=TRUE, fig.width=12}

TE.aligned %>% stack(., title = "Trochlear Extension (H. sapiens)", fac = "Sex")
ftimes <- rep('red', length(grep('Female', TE.aligned$fac$Sex)))
mtimes <- rep('blue', length(grep('Male', TE.aligned$fac$Sex)))
panel(TE.aligned, borders = c(ftimes, mtimes), names = substr(names(TE.aligned), 7, 9))

TE.aligned %>% npoly() %>% PCA() %>% plot(.,"Sex") # I need to read about this
TE.aligned %>% opoly() %>% PCA() %>% plot(.,"Sex") # read about this
TE.aligned %>% dfourier() %>% PCA() %>% plot(.,"Sex") # strange results; might not be proper method for this dataset.

TE.n <- npoly(TE.aligned, nb.pts = 16, degree = 5)
TE.pca <- PCA(TE.n)
TE.pca %>% as_df() %>% ggplot() +
	aes(x = PC1, y = PC2, col = Sex) + coord_equal() + 
	geom_point() + geom_density2d() + theme_light()

# mean shape:
TE.n %>% mshapes() %>% coo_plot()
# mean shape per group:
TE.ms <- mshapes(TE.n, 1)
TE_female <- TE.ms$shp$Female %T>% coo_plot(border = "red")
TE_male <- TE.ms$shp$Male %T>% coo_draw(border = "blue")
legend("topright", lwd = 1, col = c("red", "blue"), legend = c("Female", "Male"), cex = 0.8)
title(main = "Throclear Extension - Mean shapes")

# TPS plots
coo_arrows(TE_female, TE_male); title("Deformations")
tps_grid(TE_female, TE_male)
tps_arr(TE_female, TE_male)
tps_iso(TE_female, TE_male)

# Manova analysis

MANOVA(TE.pca, 1)
MANOVA_PW(TE.pca, 1)

# LDA / CVA analysis

TE.lda <- LDA(TE.pca, 1)
TE.lda
plot(TE.lda)
plot_CV(TE.lda)
plot_CV2(TE.lda)

```

# Olecranon Fossa

```{r OF plotting, cache=TRUE, fig.width=12}

OF.aligned %>% stack(.,title = "Olecranon Fossa (H. sapiens)", fac = "Sex")
OF.aligned %>% panel(., fac = "Sex", names = substr(names(OF.aligned), 7, 9))

OF.aligned %>% efourier(norm=TRUE) %>% PCA() %>% plot(.,"Sex")

OF.ef <- efourier(OF.aligned, nb.h = 6)
OF.pca <- PCA(OF.ef)
OF.pca %>% as_df() %>% ggplot() +
	aes(x = PC1, y = PC2, col = Sex) + coord_equal() + 
	geom_point() + geom_density2d() + theme_light()

# mean shape:
OF.ef %>% mshapes() %>% coo_plot()
# mean shape per group:
OF.ms <- mshapes(OF.ef, 1)
OF_female <- OF.ms$shp$Female %T>% coo_plot(border = "red")
OF_male <- OF.ms$shp$Male %T>% coo_draw(border = "blue")
legend("topright", lwd = 1, col = c("red", "blue"), legend = c("Female", "Male"), cex = 0.8)
title(main = "Olecranon Fossa - Mean shapes")

# TPS plots
coo_arrows(OF_female, OF_male); title("Deformations")
tps_grid(OF_female, OF_male)
tps_arr(OF_female, OF_male)
tps_iso(OF_female, OF_male, grid = TRUE)

# MANOVA analysis

MANOVA(OF.pca, 1)
MANOVA_PW(OF.pca, 1)

# LDA / CVA analysis

OF.lda <- LDA(OF.pca, 1)
OF.lda
plot(OF.lda)
plot_CV(OF.lda)
plot_CV2(OF.lda)



```

