Do the following two problems as a group.

Consider the following two images. The purpose of this homework is to develop software that can distinguish blurry photographs of objects that may appear similar. You can write the programs using any programming language that you want.

1. (100 points)
   Write a program to determine the object properties for each airplane:
   1. the area;
   2. the coordinates of the centroid of the object;
   3. the length of the perimeter;
   4. a measure of the objects compactness;
   5. the mean distance from the centroid to the shape boundary and its standard deviation.
2. (100 points)
   Write a computer program to implement an artificial neural network to approximate the following function.
   f(x₁,x₂,x₃) = 1 if any two of the three input variables are 1 and the other is zero and
   f(x₁,x₂,x₃) = 0 otherwise.
   Assume that the inputs can only be 1 or zero. Using the back propagation method for training the network is recommended, but not required.

   Networks to make other predictions are acceptable with prior permission from the instructor. Possibilities include predicting the outcome of sporting events, predicting the weather, etc. A program to automatically download a summary of professional football scores can be found here. You may have to ask the instructor for more details regarding this program.