## Homework 3 16-311 Introduction to Robotics Prof. Howie Choset

### Due by 3:30 PM on Tuesday, Jan 30

• (65%) Individual:

• (35%) Individual:
1. Assume we have a digital image I (2D, discrete) representing a 3D scene. Let's choose some particular pixel P (not on an edge or corner). This pixel might be corrupted with noise, so we want to take an average of P and its neighbors and use that value instead of P's stored value.
Formally, we want: , where and N is the total number of pixels in the neighborhood (including P).
1. Come up with a 3x3 mask (corresponding to an 8-connected neighborhood) that implements the average operator.
2. Now perform this procedure (multiply pixel's neighborhood by mask and add) for each pixel in the image. What popular image processing operator have we just applied?
3. Have we lost information? Can you recreate the original image from the "mean image" we've just generated? If so, how? If not, why not?
4. Above, we weighted the actual pixel's contribution just as much as its neighbors' contributions. However, the neighbors might have different values not because of noise, but because they are actually storing information for a different region in 3D space. Propose a different 3x3 mask that performs a weighted average, with larger weight on the actual pixel (i.e., the pixel we want to replace). Recall that the weights in a weighted average must sum to one.

2. On the surface of Mars, Pathfinder identifies a Martian with its stereographic vision system (Figure 2).

The Martian's face is 50 pixels to the left of the center of the display in the left camera, and 40 pixels to the left of the centerline in the right camera.

The resolution of the camera display is 72 pixels per inch. The cameras are 12.5 inches apart, and have a focal length of half an inch.

How far is the Martian from Pathfinder?

Figure 2

Turn in:
• Put your lab results and the answers to the above questions on a web page in HTML format.

• Email Nick Armstrong with:
• The URL of your web page