The + sign in the figure is shown using 9 pixels in a 3 ×3 grid. The color levels are given to t

The + sign in the figure is shown using 9 pixels in a 3 ×3...

The $+$ sign in the figure is shown using 9 pixels in a $3 \times 3$ grid. The color levels are given to the right of the figure. Each color is represented by a specific number: $0,1,2,$ or $3 .$Use this information to solve Exercises $51-52$. a. Find a matrix that represents a digital photograph of the $+$ sign. b. Adjust the contrast by changing the black to dark gray and the light gray to white. Use matrix addition to accomplish this. c.Adjust the contrast by changing the black to light gray and the light gray to dark gray. Use matrix addition to accomplish this.

The $+$ sign in the figure is shown using 9 pixels in a $3 \times 3$ grid. The color levels are given to the right of the figure. Each color is represented by a specific number: $0,1,2,$ or $3 .$Use this information to solve Exercises $51-52$.
a. Find a matrix that represents a digital photograph of the $+$ sign.
b. Adjust the contrast by changing the black to dark gray and the light gray to white. Use matrix addition to accomplish this.
c.Adjust the contrast by changing the black to light gray and the light gray to dark gray. Use matrix addition to accomplish this.

Key Concepts

Contrast Adjustment

Contrast adjustment in digital images involves enhancing or reducing the difference between the dark and light regions. This is often achieved by shifting the pixel intensity values so that the image exhibits a greater or lesser range of tones, thereby altering the overall visual dynamics.

Digital Image Representation

This concept involves representing a digital image as a matrix where each element corresponds to the intensity or color value of a pixel. It allows the image to be manipulated using mathematical operations by treating the image as an array of numerical values.

Matrix Operations in Image Processing

Matrix operations, such as addition and subtraction, are fundamental in image processing. They are used to perform uniform adjustments across the entire image, enabling modifications like brightness, contrast, and filtering by applying a constant transformation to each pixel value.

Transcript

00:03 So we're given a three by three plus sign picture where each block on that three by three grid is a color.

00:15 White is zero, light gray is one, dark gray is two, and black is three.

00:20 Those are maybe you might say the intensity or something.

00:22 And our first task is to make a matrix that represents those colors for that plus sign picture.

00:29 So in the upper left hand corner we have light gray, so that's a one.

00:33 Right next to it we have black, so that's a three.

00:37 And next to that, we have another light gray.

00:39 That's the one.

00:40 In the second row, it's all black, so we're going to have three, three, and three.

00:46 And then in the bottom row, we have, again, light gray, then black, and light gray.

00:52 So there's our matrix representing that plus sign.

00:56 Now our next task is to take that and using matrix addition, create a, a, a contrast changed matrix.

01:08 So our new contrast is going to have black become gray.

01:12 So everywhere we have a three, we want it to become, let's see, i think we want it dark gray.

01:21 We have black to become dark gray.

01:22 So the threes have to become twos.

01:25 And we want light gray to become white.

01:27 So we want the ones to become zero.

01:29 So in this case, basically, we want each pixel to be one color lighter.

01:34 So if we add a matrix of all negative ones, we will end up with everything shifted.

01:43 So we'll have this big three by three matrix of negative ones, and then we can add them together to get our resultant contrast adjusted matrix.

01:54 So one minus one is zero.

01:57 Three minus one is two...

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