Load libraries

library (jpeg)
library(OpenImageR) 
library(EBImage)

Use of Graphics

num=17
files=list.files("C:/Users/dkbs0/OneDrive/Desktop/Data 605/Week 4/jpg", pattern="\\.jpg")[1:num]

View Shoes Function

height=1200; width=2500;scale=20
plot_jpeg = function(path, add=FALSE)
{ jpg = readJPEG(path, native=T) # read the file
  res = dim(jpg)[2:1] # get the resolution, [x, y]
  if (!add) # initialize an empty plot area if add==FALSE
    plot(1,1,xlim=c(1,res[1]),ylim=c(1,res[2]),asp=1,type='n',xaxs='i',yaxs='i',xaxt='n',yaxt='n',xlab='',ylab='',bty='n')
  rasterImage(jpg,1,1,res[1],res[2])
}

Load the Data into an Array

im=array(rep(0,length(files)*height/scale*width/scale*3), dim=c(length(files), height/scale, width/scale,3))

for (i in 1:17){
  temp=resize(readJPEG(paste0("C:/Users/dkbs0/OneDrive/Desktop/Data 605/Week 4/jpg/", files[i])),height/scale, width/scale)
  im[i,,,]=array(temp,dim=c(1, height/scale, width/scale,3))}

Vectorize

flat=matrix(0, 17, prod(dim(im))) 
for (i in 1:17) {
  newim <- readJPEG(paste0("C:/Users/dkbs0/OneDrive/Desktop/Data 605/Week 4/jpg/", files[i]))
  r=as.vector(im[i,,,1]); g=as.vector(im[i,,,2]);b=as.vector(im[i,,,3])
  flat[i,] <- t(c(r, g, b))
}
shoes=as.data.frame(t(flat))

Actual Plots

Old Shoes

par(mfrow=c(3,3))
par(mai=c(.3,.3,.3,.3))
for (i in 1:17){  #plot the first images only
plot_jpeg(writeJPEG(im[i,,,]))
}

Eigencomponents from Correlation Structure

scaled=scale(shoes, center = TRUE, scale = TRUE)
mean.shoe=attr(scaled, "scaled:center") #saving for classification
std.shoe=attr(scaled, "scaled:scale")  #saving for classification...later

Calculate Covariance (Correlation)

Sigma_=cor(scaled)

Get the Eigencomponents

myeigen=eigen(Sigma_)
cumsum(myeigen$values) / sum(myeigen$values)
##  [1] 0.6928202 0.7940449 0.8451073 0.8723847 0.8913841 0.9076338 0.9216282
##  [8] 0.9336889 0.9433872 0.9524455 0.9609037 0.9688907 0.9765235 0.9832209
## [15] 0.9894033 0.9953587 1.0000000

Eigenshoes

scaling=diag(myeigen$values[1:5]^(-1/2)) / (sqrt(nrow(scaled)-1))
eigenshoes=scaled%*%myeigen$vectors[,1:5]%*%scaling
par(mfrow=c(2,3))
imageShow(array(eigenshoes[,1], c(60,125,3)))

#imageShow(array(eigenshoes[,2], c(60,125,3)))
#imageShow(array(eigenshoes[,3], c(60,125,3)))
#imageShow(array(eigenshoes[,4], c(60,125,3)))
#imageShow(array(eigenshoes[,5], c(60,125,3)))

Generate Principal Components

Transform the images.

Generate Variables

height=1200
width=2500
scale=20
newdata=im
dim(newdata)=c(length(files),height*width*3/scale^2)
mypca=princomp(t(as.matrix(newdata)), scores=TRUE, cor=TRUE)

Eigenshoes

Generate Eigenshoes.

mypca2=t(mypca$scores)
dim(mypca2)=c(length(files),height/scale,width/scale,3)
par(mfrow=c(5,5))
par(mai=c(.001,.001,.001,.001))
for (i in 1:17){#plot the first 25 Eigenshoes only
plot_jpeg(writeJPEG(mypca2[i,,,], bg="white"))  #complete without reduction
}

Capture

a=round(mypca$sdev[1:17]^2/ sum(mypca$sdev^2),3)
cumsum(a)
##  Comp.1  Comp.2  Comp.3  Comp.4  Comp.5  Comp.6  Comp.7  Comp.8  Comp.9 Comp.10 
##   0.693   0.794   0.845   0.872   0.891   0.907   0.921   0.933   0.943   0.952 
## Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17 
##   0.960   0.968   0.976   0.983   0.989   0.995   1.000

New Data Set

x = t(t(eigenshoes)%*%scaled)