Assignment #8

Due: Fr. Nov. 14th (TWO week assignment)
Score: 10 points(!)

The programs must be sent to the TA as MATLAB-scripts.

Check the CDF-algorithm (Centroid Distance Fourier)!

A very easy way to get a first impression of a shape comparison measure is to compare two shapes A and B, where B is a distorted version of A.
A useful similarity measure is expected to show less similarity the more B is distorted.
You have to program this test for the CDF-algorithm, using the shape given below.

How to:

Compute the boundary polygon of the donkey (you hopefully saved your function for this!).
Write a function that subsamples the boundary to N equally distant (with respect to the runlength) boundary vertices
Have a look at these new shapes, using sampling rates from 200 vertices down to 5 vertices (=196 versions of the donkey)
This visual inspection gives you a feeling, at which sampling rate the shape gets 'really' distorted or even unrecognizable. The picture below gives you an impression of the boundary curve using 90,70,50,30,10 sample points:
Write a function that creates the CDF-representation of a boundary-polygon:
- Create the centroid distance representation (a 1 dimensional vector)
- Get the Fourier-Spectrum (the AMPLITUDES of the fourier coefficients)
  use the following lines (precondition: cd = centroidDistance) to create the fourier spectrum FS:
  fourier=abs(fft(cd));
  lng=floor(length(fourier)/2);
  FS=fourier(2:lng) ./ fourier(1); % normalize
Write a program that creates the CDF representation of all 196 donkey versions.
Compare the CDF representation of all 196 versions to the one having the highest sampling rate (200 vertices)
- compare two spectra by the euclidean distance (each spectrum is a vector)
- since the vectors might have different lengths, fill the shorter one with zeros (at the end, of course !)
Your result is a vector showing the similarity of the 196 versions. Plot this result and analyse the behavior of the CDF-algorithm, comparing the plot to your visual impression !

Have fun !