Pulkit Sachdeva

Example of a hybrid image

Image Filtering

In order to filter an image, we take the filter and the image as the input. The first step that we need to do is to identify if the image is a colored image or not. We do this by checking the size of the image matrix.

if size(image,3) == 3
    red = image(:,:,1);
    green = image(:,:,2);
    blue = image(:,:,3);
    output2 = cat(3,myfilter(red,filter),myfilter(green,filter),myfilter(blue,filter));
else
    output2=myfilter(image,filter);

We then use our filter function to apply the filter. The first step in doing that is to pad the image. To do this, we look at the size of the filter matrix, and based on that decide how much padding is needed.

pad_rows = size(filter,1)-1;
pad_cols = size(filter,2)-1;
new_image = zeros(size(image,1) + pad_rows,size(image,2)+pad_cols);

The next step is to add padding to the image. I ran a for loop to do this. The code basically copies values from the image matrix to the new image matrix after adjusting for the padding.

m=pad_rows/2;
n=pad_cols/2;
for i=1:size(image,1)
  for j=1:size(image,2)
    new_image(i+m,j+n)=image(i,j);
  end
end

After this, we iterate over the original image, and for each pixel, apply the filter formula to perform the filter operation. We basically go to each pixel, and then each point iterate on the filter pixels to apply the filter operation, and then sum up the individual values from these operations to get the new value for each cell.

for i=1:size(image,1)
  for j=1:size(image,2)
    sum=0;
    for x=(-1*m):m
      for y=(-1*n):n
        sum=sum+(new_image(i+x+m,j+y+n)*filter(x+m+1 ,y+n+1));
      end
    end
    output(i,j)=sum;
  end
end

This output matrix is the result of the function

Hybrid Images

Hybrid images involve taking two images and combining them. In order to combine them, we remove high frequencies from one image and low frequencies from the other image. In order to do this, we used the formulas described in the SIGGRAPH 2006 paper. One image is filtered with a low pass filter to remove the high frequencies.

low_frequencies = my_imfilter(image1,filter);

From the other image, we remove the low frequencies by subtracting a low pass filtered version of this image from the original image

high_frequencies = image2 - my_imfilter(image2,filter);

We then combine high frequencies and low frequencies

hybrid_image = low_frequencies + high_frequencies;

Results

Intermediate Images