Xi Wu-GTID: 902849967

Fig.1. Example of a hybrid image made up of one image of cat and the other image of dog.

1.Filtering

1.1. Pad with Zeros

Linear filtering operators involves weighted combinations of pixels in small neighborhoods, which means if the filter is desired to be centered on pixels at the image boundary, parts of the filter should be out of bounds. In order to solve this problem, various padding methods have been developed. The one that will be introduced here is padding with zeros. In other words, pixels outside the source image are set to zeros.

In this part, my_imfilter_Zero.m, DotProduct.m and proj1_test_filtering_Zero.m will be used. As shown from the following codes, the width and height of both image and filter are supposed to be acquired first in order to get the padding size. For zero padding, left zeros array and top zeros array are created which equal to right zeros array and down zeros array, respectively. Then, the new image with padding comes into being.

The core codes in my_imfilter_Zero.m and DotProduct.m are as below:

    %% The width and height of both image and filter
    [ImageWidth]=size(image,2);
    [ImageHeight]=size(image,1);
    [FilterWidth]=size(filter,2);
    [FilterHeight]=size(filter,1);
    
    %% Pad with Zeros
    PadLeft = zeros((FilterWidth-1)/2,ImageHeight)';
    PadUp = zeros(ImageWidth+(FilterWidth-1),(FilterHeight-1)/2)';
    
    %% Filtering
    for channel = 1:1:size(image,3)
        ImageColor = squeeze(image(:,:,channel));
        ImageNew(:,:,channel) = DotProduct(ImageWidth,ImageHeight,FilterWidth,FilterHeight,ImageColor,filter,PadLeft,PadUp);
    end
    

    %% Dot Product
    ImageNewR=zeros(ImageWidth,ImageHeight)';
    
    for WCordinate=1:1:ImageWidth
        for HCordinate=1:1:ImageHeight
            EachF=PadComplete(HCordinate:(FilterHeight-1)+HCordinate,WCordinate:(FilterWidth-1)+WCordinate);
            ImageNewR(HCordinate,WCordinate)=sum(sum(EachF.*filter));
        end
    end
    

The core idea of filtering is to get the filtered image's each pixel by calculating the sum of the dot product of the neighboring matrix of each pixel in the padding image and the filter which is accomplished in DotProduct.m. In order to let the code work for both color image and grayscale image, I write a for loop to determine whether to do the dot product for just once or three times for each R, G, B channel.

Then simply using proj1_test_filtering_Zero.m, we can get the images after using identify filter, small blur box filter, large blur filter, oriented filter as well as two different high pass filters-one using Discrete Laplacian and the other simply subtracting low frequency content.

The original images and the results of filtered image are displayed as follows:

Fig.2. Original marilyn image and Filtered marilyn image using the method of zero padding

Fig.3. Original dog image and Filtered dog image using the method of zero padding

1.2. Mirror the Image Boundary

The other method used in this project is mirroring the image boundary which means reflecting pixels across the image edge.

In this session, my_imfilter_Mirror.m, DotProduct_Mirror.m and proj1_test_filtering_Mirror.m will be used to realize the filtering function. The methods of obtaining the size of image and filter, doing dot product and making it work for both color and grayscale images are similar. The only difference is to replace zero components with the boundary components of the image. I still tried to use the padding method utilized in the first session at first but it is a little complicated thus, I choose to use the padarray(A, PADSIZE, 'symmetric') function which reduces much code. The code for this is shown as follows:

    %% Filtering
    for channel = 1:1:size(image,3)
        ImageColor=squeeze(image(:,:,channel));
        PadComplete=padarray(ImageColor,[(FilterHeight-1)/2,(FilterWidth-1)/2],'symmetric');
        ImageNew(:,:,channel)=DotProduct_Mirror(ImageWidth,ImageHeight,FilterWidth,FilterHeight,PadComplete,filter);
    end
    

The results of using various filters are shown as below:

Fig.4. Filtered marilyn image using the method of mirror padding

Fig.5. Filtered dog image using the method of mirror padding