16-311 Homework 1

Learning Objectives

1. Recall simple linear algebra.
2. Manipulate an imamge to identify key objects.

Background

Linear algebra refers to the study of vectors and linear functions. Linear algebra come up all the time in robotics from computer vision to manipulation. It is helpful to have a solid understanding of vectors and matrices for robotics. In this homework, we touch on orthogonal matrices, inverses and transposes. Further reading can be found here: Orthogonal Matrix, Transpose and Inverse.

We have learned a little bit about ways to think about and identify items from arrays of numbers. This homework builds off of some of the principles we covered in class.

One of the first techniques we discussed was thresholdiing. This enables us to take colored or grayscale image and reduce it down to a black-and-white thresholded version where each pixel is either a 0 or a 1. In order to create this result, we choose a pixel value (or perhaps a value for each of the colored channels in a pixel) and set all the pixels with a lower value than this threshold value to 0 (black if we assume lower numbers are closer to black) and all pixels with a higher value than this threshold value to 1.

In order to pick this threhold value, we can use a histogram to visualize the distribution of pixel values. Here we see a simple example of a 9-pixel image and the accompanying histogram.

Example image and corresponding histogram.

Based on this histogram, we may decide to threshold at 2, so any pixels greater than or eaqual to 2 are set to the high value. And any pixels less than 2 are set to 0.

Example image thresholded at 2.

Alternatively, we may see the lighter pixels as still valuable portions of the colored space and decide to threshold at 1, instead of 2.

Example image thresholded at 1.

Homework Requirements

The specifications for the assignment are presented in the following document.

2018 Homework 1 Handout

Extensions