1. In the previous assignment, you designed a Bayes classifier assuming the following 2D
In this assignment, we will assume that you do not know the true parameters of the
Gaussian distributions and that you need to estimate them from the training data using
the Maximum Likelihood (ML) approach.
a. Using the same 10,000 samples from the previous assignment, estimate the
parameters of each distribution using ML and classify all 10,000 samples assuming
P (ω1) = P (ω2); then, count the number of misclassified samples and compare your
results to those obtained in assignment 1.
b. Repeat experiment (1.a) using 1/10 of the samples (randomly chosen) to estimate
the parameters of each distribution using ML and classify all 10,000 samples
assuming P (ω1) = P (ω2); then, count the number of misclassified samples and
compare your results to those obtained in experiment (1.a).
2. Repeat problem 1 assuming the following 2D Gaussian distributions:
3. As we have discussed in class, face detection using skin color is a popular approach.
While color images are typically in RGB format, most techniques transform RGB to a
different color space (e.g., chromatic, HSV, etc.). This is because RGB values are more
sensitive to changes of brightness due to illumination changes.
a. Implement the skin-color methodology outlined in Section 3.1 of [Yang96 “A
Real-time Face Tracker”] which uses the chromatic color space. To build the skin
color model, use Training_1.ppm (and ref1.ppm), shown in Figure 1, which are
available from the course’s webpage. To test your method, use Training_3.ppm
(and ref3.ppm) and Training_6.ppm (and ref6.ppm), which are also available
from the course’s webpage. To quantitatively evaluate the performance of your
method, generate ROC plots (i.e., false positives (FP) vs false negatives (FN)) by
varying the skin-color threshold. A FP would be a non-face pixel which was
classified as skin-color while a FN would be a face pixel which was classified as
non-skin color. To compute the FPs and FNs for each test image, use the
corresponding reference images.
b. Repeat (3.a) using the YCbCr color space In the YCbCr color space, the
luminance information is contained in Y component; and, the chrominance
information is in Cb and Cr. Therefore, Y should not be used in building the skin
color model. The RGB components can be converted to the YCbCr components
using the following transformation:
Y = 0.299R + 0.587G + 0.114B
Cb = -0.169R – 0.332G + 0.500B
Cr = 0.500R – 0.419G – 0.081B
Figure 1. Training_1.ppm and ref1.ppm images.
For comparison purposes, plot the ROC curves in the same graph.
Note: Irfanview is a nice tool for image display/manipulation. Sample code to read/write
color images in PPM format is provided on my CS 302 webpage:
Information on the PPM image file format can be found here:
PROJECT REPORT SUBMISSION REQUIREMENTS
1. Cover Page. The cover page should contain Project title, Project number, Course
number, Student’s name, Date due, and Date handed in.
2. Technical discussion. This section should include the techniques used and the principal
equations (if any) implemented.
3. Discussion of results. A discussion of results should include major findings in terms of
the project objectives, and make clear reference to any figures generated.
4. Division of work: Include a statement that describes how the work was divided between
the two group members.
5. Program listings. Includes listings of all programs written by the student. Standard
routines and other material obtained from other sources should be acknowledged by
name, but their listings should not be included.
You need to turn in a printed copy of your report (i.e., items 1-4), in the beginning of the class on
the due date. Program listings (i.e., item 5) should be emailed to the instructor, as a zip file,
before class on the due date. Each group should submit one report only.