GPT: What is image 

In computer vision, an image is often represented as a function that maps a set of coordinates to pixel values. This function is typically referred to as the image function or image signal.

To understand this concept better, let's break it down. An image is composed of pixels, which are the smallest elements that make up the image. Each pixel has a specific location in the image, which can be represented by its coordinates (x, y) in a 2D plane.

The image function takes these coordinates as input and returns the corresponding pixel value. The pixel value represents the intensity or color of the pixel at that location. For grayscale images, the pixel value is usually a single value ranging from 0 to 255, where 0 represents black and 255 represents white. For color images, the pixel value is typically a combination of three values representing the intensities of red, green, and blue channels.

By treating an image as a function, we can perform various operations on it using mathematical techniques. For example, we can apply filters or transformations to the image function to enhance certain features or extract useful information.

Section 2- What is an image?

Def: Every image that we see in this world is nothing, but an array of numbers with various value ranges depending on the colorspaces we are using. For example, for RGB colorspace, each change value has a range of 0–255, whereas the hue channel in the HSV channel has a range of 0–180 [2].

Def: A visual representation of a real-life entity, such as a person or any object, in two-dimensional form is known as an image. Essentially, an image is a compilation of pixels arranged in various color spaces.

Concepts:

So here's an image of an old and I think now expired comedian who's, therefore, cannot sue me. That's Phyllis Diller, by the way, in case you remember. And by the way, we're going to start with black and white because black and white just makes everything easier because it's just a single channel. We, we'll do color on and off, but pretty much everything we do for black and white do, you do for color, hold for black and white, and, and it's just easier. So when I show this to you, you actually think of it as a picture or something to look at. But

what actually is, is a function. In fact, we can just call it a function of I of x y, all right, where the I has something to do with the image intensity. So, if I think of this as a function, then I can just plop this as a surface and MATLAB makes this incredibly easy. And if I did, it would look something like this. Okay? Now this is the exact same function, but instead of showing you as a picture where, you know, sort of straight on, and by the way, the way MATLAB does it it's really cool, the, the higher the thing is it also makes it brighter, so you can see. So if you take a look at like the, the, the checkers pattern on that awful shirt she was wearing, right, so the bright spots are here, and the dark spots are down there. Okay, that function is the same function as the image that I was showing you before. Computer vision and especially image processing, we'll be talking mostly about the image processing side of computer vision today and the next few are about taking these functions and computing something from them. Often, we're just going to computer another image-like function, so images in, images out. And sometimes, we'll be getting some sorts of information. So here's a very simple example. Suppose I took that previous function, and I just smoothed it. All right, so now you see, I have the same surface I had before, but it's now, you know, it blends smoother, and the peaks and the valleys of that shirt are, are much smoother. They're not as steep as they were before. Okay. So that’s the function. Now, of course, I can show that to you as an image again. What’s that going to look like? Well, you’ve probably figured this out because you’re all so smart. It’s just going to be a blurry version of that image, okay. And I’m showing it here side by side with the blurred function, oh, sorry, the smooth function, right? Because there is this direct analogy between what we call blurring in the image and smoothing of that function. It's exactly the same thing. 

Functions of function -smoothing the function

References

2- Computer Vision Tutorial Series M1C1

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