Digital Images

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Objective

SWBAT understand how matrices are used in computer graphics.

Big Idea

Digital photos can be easily altered on your cell phone, but what's the math behind it?

Launch

5 minutes

Note: Today is a half day with an abbreviated class period, so we will be looking at just a little about digital images and their connection to matrices. In this video I talk about why I like this lesson so much. 

Most of my students have Instagram or know what it is. The app has transformed photo sharing by taking a user's photograph and applying artistic filters to enhance its aesthetics. But how can the software so easily modify your photograph? I start the class by asking my students this question and showing them this image. Then I will have them to discuss with their table groups. We will share out with the entire class. Some students will correctly hypothesize that it has something to do with matrices since that is what unit we are in. 

 

Explore

15 minutes

This worksheet is an investigation of how digital images are manipulated using computers. Students are introduced to the concept of a pixel and how a corresponding matrix can be used to represent many pixels.

For questions a) through d) students are to investigate how the matrix can be changed to make the image lighter, darker, more contrasting, or more clear. At this point in the unit we have looked at matrix addition, subtraction, and multiplication, so students must choose which operation will produce the indicated change. I find that students have an easier time with questions a) and b) than the remaining two. Some students don't know what it means for an image to have more contrast, so you may have to explain to them that it makes the light shades lighter and the dark shades darker. 

The back of the worksheet gives students some actual practice with analyzing an image using these values to represent the darkness of each pixel. Although we are doing math, students sometimes comment that it doesn't feel very "math-y." This is a good opportunity to talk about how the applications of matrices can be far-reaching and go beyond the traditional topics we associate with mathematics.

Summarize

5 minutes

For the last few minutes of class, I will go back to the image of the Instagram filter that students saw at the beginning of class and discuss what changes are made.

Since we are working in color, it adds a new layer of complexity to the problem. Some students may know that a printer used magenta, cyan, and yellow ink to print all colors. Teachers may know that a standard television had pixels that were red, green, or blue to create all colors. For this specific image, students may understand that the hue has changed because one color component has changed more than the others.