Computer Vision Project

Project 1: Image Filtering and Hybrid Images

Author: Mitchell Manguno (mmanguno3)

Table of Contents
Synopsis
Image Filtering
Hybrid Images

Synopsis

For this project, an image filtering function was written and then used to produce "hybrid images" of pairs of images. Hybrid images are defined here in a paper by Oliva, Torralba, and Schyns. Essentially, two images are taken into consideration. One is filtered such that all that remains are the low frequency componenets of the image; the other, only high frequency components remain. When blended, this images appear differently at varying viewing distances.

I will now explain in detail the image filtering function, and present the result of using this function to create hybrid images.

Image Filtering

The algorithm used for the function closely follows the classical definition of filtering: given a image f and a filter g, the output image h is defined as:

h[m, n] = Σ_{k, l} g[k, l] f[m+k, n+l]

Each element of h is the inner product of the filter and the region upon which the filter is situated. With this consideration, the function can be made a bit simpler to reason about, and can utilize some of MATLAB's functions (which are faster to run than using for-loops, due to their implementation in FORTRAN).

// Calculate the appropriate amount to pad
extra_rows = floor(num_rows(filter) / 2);
extra_cols = floor(num_cols(filter) / 2);

// Pad the image symmetrically by the extra rows and columns
padded = pad_image_symmetrically(image, extra_rows, extra_cols;

for m from 1 ... num_rows(image)
    for n from 1 ... num_cols(image)
        // Get the region of the padded image to filter
        region = padded[m ... num_rows(filter) + m, n ... num_cols(filter) + n]
        // The value of the output at [m, n] is the inner product of the
        // filter and the region
        output[m, n] = filter · region

The above code was implemented in MATLAB, and run to produce the results seen below.

It's worth noting two things about the design of this algorithm:

It uses as few for-loops as it reasonably can, without butchering readability. This is because MATLAB's language-level constructs are slow, but the matrix operations that are in its standard library are very fast (by virtue of their implementation in FORTRAN).
The image is being padded symmetrically, rather than with zeros or in some other manner. This is done to preserve nearby pixel information without introducing undue noise in a sensible way.

Here are some of the results of the filtering algorithm on a picture, with different filters applied.


fig. 1 identity filter	fig. 2 blur filter	fig. 3 large blur filter

fig. 4 high pass filter	fig. 5 laplacian filter	fig. 6 sobel filter

As you can see, the filters appear to work well on the images, and no strange discolorations occur around the edges of the images since a symmetrical padding strategy was used.