| GK-12
Sensors!
Portable Module
Title: Matrices and Digital Pictures
Author: Anthony Puckett
Discipline: Math (Algebra II, Precalculus, or Calculus)
Introduction
This module is a lecture demonstrating
an application of matrices that students should easily relate to.
Computers store pictures digitally. A computer talks and thinks in
numbers; therefore pictures must be translated into numbers. A digital
picture is represented by a matrix. Indices (i.e.
row and column identifiers) represent the locations of matrical elements,
each of which represents a color as defined by a color map.
The first lesson introduces the physics behind turning pictures into
matrices. The second lesson demonstrates how scalar multiplication
can be used to alter pictures and introduces some other operations
to manipulate matrices. The text of this module is meant to be
an aid in the presentation of the slides, and not necessarily a handout
for the students.
Objective
The objective of this module is to show
students a practical application of matrices and matrix operations
to which they can relate. Students will encouter the concept of the
electromagnetic spectrum, and sensor devices such as the charge-coupled
device. The usefulness of colors to represent data is also stressed.
Associated Maine Learning Results
MATHEMATICS
C. Data Analysis and Statistics
I. Discrete Mathematics
K. Mathematical Communication
Required Equipment
- Laptop or PC with MS PowerPoint and LCD projector or
Overhead projector and Slides of PowerPoint presentation
- PC CCD Camera
- MATLAB (optional with the Laptop or PC)
- Digital video camera (optional)
Procedure
Lesson 1: Introduction to Digital Pictures
Associated PowerPoint Presentation: Matrices
and Digital Pictures: Part I - Matrix Representation of Digital Pictures
Lecture (Word format): Matrices
and Pictures--Lesson 1: Introduction to Digital Pictures
Lesson 2: Matrix Operations with Digital Pictures
Associated PowerPoint Presentation: Matrices
and Digital Pictures: Part II- Matrix Operations with Digital Pictures
Lecture (Word format): Matrices
and Pictures--Lesson 2: Matrix Operations with Digital Pictures
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