KGyatso_assignment4

## 
## Attaching package: 'EBImage'

## The following objects are masked from 'package:OpenImageR':
## 
##     readImage, writeImage

Preparing the dataset

We are given data containing of 17 images of shoes of 1200X2500 dimension each. We will first load the data in a variables.

num <- length(list.files("/Users/karmagyatso/Documents/cunySps/data605/wk-4/jpg/"))
files_dir <- "/Users/karmagyatso/Documents/cunySps/data605/wk-4/jpg/"
file_images <- list.files(path = files_dir, pattern = "\\.jpg")[1:num]
#saves the images as file list

Read One Shoe and follows

First, we are reading the image and storing in the shoe_jpg variable. Then, creating a empty data matrix

Using loop to fill the empty matrix data with RGB vectors

shoe_jpg = readJPEG(paste0(files_dir, file_images[1]))
data = matrix(0, num, prod(dim(shoe_jpg)))


for (i in 1:num){
  im <- readJPEG(paste0(files_dir, file_images[i]))
  r  <- as.vector(im[,,2])
  g  <- as.vector(im[,,3])
  b  <- as.vector(im[,,1])
  data[i,]= t(c(r,g,b))
  }

Create a dataframe with the transpose of the data matrix.

shoes_df = as.data.frame(t(data))

Eigen Related Math

scaled_shoes = scale(shoes_df, center = TRUE, scale = TRUE)

Sigma_ <- cov(scaled_shoes)

eig          <- eigen(Sigma_)
eigenvalues  <- eig$values
eigenvectors <- eig$vectors

Check Our Variance

We will look at the variance to determine the threshold for variability.

cum_var = cumsum(eigenvalues) / sum(eigenvalues)
cum_var

##  [1] 0.6833138 0.7824740 0.8353528 0.8629270 0.8825040 0.8996099 0.9144723
##  [8] 0.9271856 0.9374462 0.9472860 0.9561859 0.9647964 0.9732571 0.9804242
## [15] 0.9874038 0.9941511 1.0000000

thres    <- min(which(cum_var > .80))
thres

## [1] 3

A graphical representation of how fast we can achieve the result.

plot(1:num, y = cum_var, type = "b")

length(cum_var)

## [1] 17

Eigenshoes

We’re creating a diagonal matrix based on the number of threshold components (in our case 3) before scaling it. This is our scaling matrix. We then multiply our original scaled dataframe by our first three eigenvectors followed by that diagonal matrix.

scaling_shoes = diag(eigenvalues[1:thres]^(-1/2)) / (sqrt(nrow(scaled_shoes)-1))
eigen_shoes = scaled_shoes%*%eigenvectors[,1:thres]%*%scaling_shoes
eigenimage <- array(eigen_shoes[,3], dim(shoe_jpg))

imageShow(eigenimage)

view SHow 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

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

for (i in 1:num){
  temp=resize(readJPEG(paste0(files_dir, file_images[i])),height/scale, width/scale)
  image_array[i,,,]=array(temp,dim=c(1, height/scale, width/scale,3))
  }

Vectorize

We create a empty matrix Flat and populated all the images into the arraywith RBG vector

flat=matrix(0, 17, prod(dim(image_array))) 
for (i in 1:num) {
  newim <- readJPEG(paste0(files_dir, file_images[i]))
  r=as.vector(image_array[i,,,1]); g=as.vector(image_array[i,,,2]);b=as.vector(image_array[i,,,3])
  flat[i,] <- t(c(r, g, b))
}
shoes=as.data.frame(t(flat))

Actual Plots

Using the par() to divide the frame into desired grid. using mai to determine the margin size specified in inches in the format c(bottom, left, top, right).

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

Conclusion

Eigenimages refer to a group of eigenvectors that have the ability to identify images through a process called dimensionality reduction. This involves transforming images into separate red, green, and blue vectors which are then arranged in a matrix. The covariance matrix is then calculated, and from this, the eigenimages are generated.

Given that images of shoes can have a large number of pixels, processing them computationally can be quite inefficient. To address this, the matrices are reduced to lower dimensions in an attempt to represent the set of images more efficiently.

Reference:

“Chat.openai.com.” ChatGPT, https://chat.openai.com/chat/4cdade1c-0280-476b-be4f-29affab5a6ca

Herrero, Diego. “Face Recognition Using Eigenfaces.” RPubs, 26 Oct. 2019, https://rpubs.com/dherrero12/543854.