CIS 580, Machine Perception, Fall 2023
Homework 2W (Writing)
Due: Thursday October 12, 2023, 11:59pm ET
Version of 2023/09/22, 04:14GMT
Instructions
• This is an individual homework and worth 100 points.
• You must submit your solutions on Gradescope, the entry code is VBGNPG. We
recommend that you use LATEX, but we will accept scanned solutions as well.
• Start early! Please post your questions on Ed Discussion or come to office hours!
Submission
• Please separately submit your solutions on Gradescope.
1
Questions
Problem 1 (20 pts.) The image of the rectangle-shaped facade of a building has
two vanishing points, one at (−b, 0) corresponding to horizontal lines and one at (0, h)
corresponding to the vertical lines. Find the transformation that will map the facade
to a rectangle. Assume that the origin (0,0) and the point (1, 1) remain fixed.
Problem 2 (20 pts.) The following diagram represents an aerial photograph of a
straight road on flat ground. At A there is
a sign ‘Junction 1 km’, at B asign ‘Junction
km’, and C is the road junction. Also, a
police patrol car is at X,and a bridge is at
Y .The distances marked on the left of the
diagram are measured in cm from the photograph. Calculate the actual distances (in
km) of the patrol car and the bridge from
the junction.
Problem 3 (20 pts) For this question you
will need to read the article “How to Detect
Faked Photos” (Farid). Is the following
reflection painting perspectively correct?
To answer this question you can draw lines
on top of the image and use them for your
argument. The original image can be found
here.
Problem 4 (20 pts.) In the following image, the points A, B, C, D are collinear.
Point V is the vanishing point for line AB. For the world points we know that AwBw =
BwCw = CwDw = 4. Given the distances AB = 3, CD = 2, compute (i) The distance
BC
(ii) The distance DV .
Problem 5 (20pts) In the lecture, we have talked about how seeing two lighthouses
(two points) under a fixed angle does not tell us where we are on the sea. However if we
had a compass giving us the North we might localize ourselves. Assume that the two
lighthouses are at points (0,0) and (a,0) and are seen at bearings β and α with respect
to the North, respectively. Find your coordinates (x,y) as a function of a, α and β.