Lecture - Image Processing

Any transformation of an image that starts with the original image and ends with an altered version that concerns pixel value and position can generically be called an operation. Basically, operations can be divided into transformations that change the array of the image pixels but not their value, and consequently transformations that change the values themselves. In certain cases both types are present, for example when an image is shifted along one image axis by a non-integer number of pixels. In this case, new pixel values need to be calculated when the old coordinate system is mapped onto the new one.

Now, that we have seen how basic pixel manipulation works we want to apply certain transformations to the entire array of pixels, i.e. the image itself. Simple transformations such as geometric processes like translation or rotation can be expressed relatively easily by translating pixel positions. 

More complex processes like the change of scaling of the pixel value from linear to logarithmic or the subtraction of two images can also be performed pixel-wise. However, an image can also be understood as a matrix that can be altered by another matrix, called the operator, or kernel. In section 5 "Linear/Non-linear Filters" we will see that this formulation allows for the easy usage of operators or filters, that smooth, sharpen, contrast, or gray scale the image by convolving the operator matrix with the original image. 

For this part of the lecture basic knowledge of matrix algebra is assumed.