Dan Shen

Project 1: Image Filtering and Hybrid Images

Cat and Dog Hybrid Image.

This project is about hybrid Images via the usage of a high frequency image and a low frequency image. This is done so by applying a filter over a frame or a subsection of the original image for each pixel in the image. Here is an example of a hybrid image.

Code and Algorithm Discussion

Before I can even start my algorithm, I need to first define some variables that i'll be using throughout the entire code. Specifically, they are row_count and col_count, and they are used to define the number of rows and columns in the filter. By themselves, they don't serve much purpose, but they are used to calculate vertical_padding and horizontal_padding. Since the filter has been assumed to always be an 'm x n' filter, where m and n are both odd numbers, we can calculate the actual padding by dividing the number of rows and columns by two, taking the mathematical floor of them both, and allocate those values to vertical_padding and horizontal_padding, respectively.

% Variables
row_count = size(filter,1);
col_count = size(filter,2);
vertical_padding = floor(row_count/2); %number of rows
horizontal_padding = floor(col_count/2); %number of columns

After defining those values, I need to create two more images. One of them is the padded_image, where I use Matlab's padarray method to create a padded version of my original image to allow for the filter's dimensions. Specifically, I used the symmetric option since that caused the padding to affect the convolution of the padded image the least. Other options, such as padding the image with 0's, would leave a shadow towards the edges of the image due to the dot-product taking in those values as part of the convolution algorithm. The second image that I created was a new image, that mocked the dimensions of the original image, regardless of it being grayscale (1-dimension) or color (3-dimensions). I also padded it with 0's as an initialized value, which would ultimately get replaced later on in the convolution algorithm.

% Image Setup
padded_image = padarray(image,[vertical_padding,horizontal_padding],'symmetric'); %creates a symmetrically padded array
new_image = zeros(size(image)); %creates an array filled with zeroes of the same size

Below is the core of my algorithm. There are three for-loops to allow the three dimensions of a color image: height, width, and the three rgb color channels. However, grayscale also works with the same code due to the fact that the color channel for-loop is dependent on the size of length(size(image)), which tells you how many color channels there are. One thing to note is that even though I am using the padded array, I am indexing across the unpadded, or the original image. This means that I'm indexing and making all of my calculations relative to the center of each frame. I thought that the code would be cleaner in the end,specifically when i have to calculate the coordinates of the new image's corresponding pixel and place a value in there. Next, I define the frame in which the dot-product would be performed on. This fram would match the size of the filter. After that, I calculate the dot-product of the two submatrices, and allocate that value to the cell at the same coodinates of the original image. I do this for every pixel in the image.

%Convolution Algorithm
for row = ((vertical_padding + 1):(vertical_padding + size(image,1)))
    for col = ((horizontal_padding + 1):(horizontal_padding + size(image,2)))
        for color_layer = 1:length(size(image))
            frame = padded_image(row - vertical_padding: row + vertical_padding,
                                 col - horizontal_padding: col + horizontal_padding,
                                 color_layer);
            dot_product = frame .* filter(:,:);
            blurred_value = sum(dot_product(:));
            new_image(row - vertical_padding ,col - horizontal_padding,color_layer) = blurred_value;
        end
    end
end

Application of Different Filters

Original Image Identity Filter Small Blur with a Box Filter Large Blur

Sobel Filter High Pass Filter (Laplacian Filter) High Pass "Filter" Alternative

Hybrid Image Generation

Original Cat Image Original Dog Image

High Frequencies Image Low Frequencies Filter Hybrid Image of Varying Sizes

Original Einstein Image Original Marilyn Image

High Frequencies Image Low Frequencies Filter Hybrid Image of Varying Sizes