• (Section 4.2) In this section, we discuss mathematical representations both for the information contained in an image and for the ways in which images are stored and manipulated in a digital machine.

• (Section 4.3) In this section, we introduce a way of thinking about images – as surfaces with varying height – which we will find to be a powerful way to describe both the properties of images as well as operations on those images.

• 2D images: The familiar 2D image is the brightness image, also called luminance image. These include photographs; the things you are used to calling “images” or “pictures.” These might be color or grayscale. (Be careful with the words “black and white,” as that might be interpreted as “binary”). A shadow is a 2D binary image. We usually denote the brightness at a point < x, y > as f (x, y). Note: x and y could be either real numbers or integers. In the integer case, we are referring to discrete points in a sampled image. These points are called “pixels,” short for “picture elements.” In the case of real numbers we are usually thinking of the image as a function.