Computer Vision Project

The goal of this project is to make an image filter processing function and use it to create hybrid images by combining two different images by applying low and high frequency filters respectively on each image and adding them together. If this hybrid image is viewed up close, the high frequency image is visible. However, as you move further away, the low frequency image gets clearer. An example of such a picture can be seen to the right. From up close, the cat is prominent but as you move further away the dog becomes more prevalent. The function I coded works with both greyscale and color images. However it only works on filters with odd sized dimensions to avoid ambiguity in selecting the center (most dominant) pixel.

Algorithms

Building the Filter

Pad the image with a black border to be able to apply the filter even on the edges of the picture.


padded_image = zeros(height, width);

for i = 1:image_height
    for j = 1:image_width
        padded_image(i + middle_height - 1, j + middle_width - 1) = image(i, j, k);
    end
end

Build a function to apply the filter to a pixel appropriately.


function filtered = filter_func(i, j)
    start_height = i - middle_height;
    start_width = j - middle_width;

    filtered = 0;

    for x = 1:filter_height
        for y = 1:filter_width
            filtered = filtered + padded_image(x + start_height, y + start_width)*filter(x, y);
        end
    end
end

Pass each pixel of the image into this function.


for i = 1:image_height
    for j = 1:image_width
        output(i, j, k) = filter_func(i + middle_height - 1, j + middle_width - 1);
    end
end

You can see this function at work with various filters


Original Image	Blur Image	Large Blur Image

Identity Image	Laplacian Image	Sobel Image

Creating the Hybrid Image

Create a Gaussian filter with an appropriate cutoff frequency (based on the images to be blended).


cutoff_frequency = 7;

filter = fspecial('Gaussian', cutoff_frequency*4+1, cutoff_frequency);

Apply the filter on the image you want only the low frequencies of. The Gaussian filter will blur out all the high frequencies.
```
low_frequencies = my_imfilter(image1, filter);
		
```

Apply the filter on the second image. However, since you want only the high frequencies of this image, subtract the filtered image from the original image to remove all the low frequencies and only be left with the high frequencies.
```
high_frequencies = image2 - my_imfilter(image2, filter);
		
```

Add these two processed imaged together to get a hybrid image.
```
hybrid_image = low_frequencies + high_frequencies;
		
```

Effect of Cutoff Frequency

Different cutoff frequencies were tried and applied to each set of images in order to get the best possible hybrid image. The results displayed here are the outcomes of this experiment. The cutoff frequencies tried for each set of images were based on guesses made by following intuition. As the cutoff frequency is increased, the low frequency image gets blurrier and as the cutoff frequency is decreased, the high frequency image gets sharper.

Experimenting with cutoff frequencies on Marilyn and Einstein: