Lab Homework $10$

Background

Every image that you see on a computer is composed of many pixels and each pixel has a numerical value that represents the color$/$grayscale of that individual pixel. This means that images are, at the basic level, numerical arrays that are processed in a special way to display an image. It also means that we can apply simple models to modify numerical pixel values to change the appearance of an image. This is the basis behind image processing. Image processing is a necessity for machine learning, artificial intelligence, pattern recognition, and many other engineering related fields. While it may seem complex, the mathematical principles of image processing are rather simple.

One method of image processing is done using kernels. A kernel is a matrix that is multiplied by a set of pixel values, the resulting matrix is summed up$,$ and the sum replaces the central pixel. Suppose we have an image $($in gray scale$)$ that is represented by the following matrix of pixel values:

$[(2$&$2$&$5$&$6$@$6$&$10$&$7$&$5$@$9$&$35$&$18$&$0$@$5$&$6$&$2$&$6)]$

There are many kernel matrix possibilities, but suppose we want to apply a kernel matrix that looks like:

$[(1$&$0$&$0$@$0$&$1$&$0$@$0$&$0$&$1)]$Lab Homework $10$

Background

Every image that you see on a computer is composed of many pixels and each pixel has a numerical value that represents the color$/$grayscale of that individual pixel. This means that images are, at the basic level, numerical arrays that are processed in a special way to display an image. It also means that we can apply simple models to modify numerical pixel values to change the appearance of an image. This is the basis behind image processing. Image processing is a necessity for machine learning, artificial intelligence, pattern recognition, and many other engineering related fields. While it may seem complex, the mathematical principles of image processing are rather simple.

One method of image processing is done using kernels. A kernel is a matrix that is multiplied by a set of pixel values, the resulting matrix is summed up$,$ and the sum replaces the central pixel. Suppose we have an image $($in gray scale$)$ that is represented by the following matrix of pixel values:

$[(2$&$2$&$5$&$6$@$6$&$10$&$7$&$5$@$9$&$35$&$18$&$0$@$5$&$6$&$2$&$6)]$

There are many kernel matrix possibilities, but suppose we want to apply a kernel matrix that looks like:

$[(1$&$0$&$0$@$0$&$1$&$0$@$0$&$0$&$1)]$