Homework 3: Image Arithmetic, Geometric Operations

Chris Smemoe , Computer Science 450


Table of Contents

1. Combining Several Noisy Images

2. Rotating an Image


1. Combining Several Noisy Images

How I combined several images:

I combined several images by taking the images, adding their together into a new image, and dividing each pixel in the new image by the number of combined images. Here is the source code.

Why does this work?

This works because averaging several images with random noise at different locations in an image produces a final image with very little noise. The signal-to-noise power ratio is increased by a factor of the number of images at all points in the image.

How many images is enough?

Just a few images may be enough to make a pretty good final image from noisy images, or it may take several images to combine into a high-quality final image.

How can I tell?

The signal-to-noise ratio of the final image is a function of the number of images and the signal-to-noise ratio of the original image. If you have several noisy images and combine them, the result will be fairly good. But if you have several good images and combine them, the result will be even better.

Final Results:

Here are two of the original images, and the final image after averaging all the images.

Image 1:

Image 2:

Final Image:

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2. Rotating an Image

How I Rotated an Image:

I rotated the image by finding the center of the image, stepping through the pixels in the final image, and finding x and y on the original image from the pixel locations on the second image using the rotation equation given on the web page with a negative rotation angle. I used bilinear interpolation to determine the pixel value at each (x, y) location on the original image. The final source code is here.

Results from rotating the image in 15-degree increments:

When rotating the image in 15-degree increments, you lose some resolution on the image (the image gets fuzzy) because of the backward mapping algorithm used. Here are the final images from rotating the image in 15-degree increments:

Image 1:

 

Image 2:

 

Image 3:

 

Image 4:

 

Image 5:

 

Image 6:

 

Image 7:

 

Image 8:

 

Results from rotating the image directly by 120 degrees:

Here is the result from rotating the image directly by 120 degrees:

 

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smemoe@byu.edu
Date last modified: 9/29/1999