CMSC 426 Homework 6 Due May 4 Spring 05
1. (25 points) Suppose we are trying to distinguish cats from dogs and the only
measurement we have is the weight of the animal. Let the prior probabilities
for the animal being a cat or a dog be P(CAT) = 0.3, P(DOG) = 0.7
and let the class conditional density functions for (integer-valued) weight
given class be uniformly distributed as follows:
–P(Weight|CAT) is uniform on [20, 39]
–P(Weight|DOG) is uniform on [30,59].
Explain how Bayes’ rule can be used to classify an unknown animal having
weight 35 pounds given the prior and conditional probabilities defined above.
2. (60 points) A geometric transform is a vector function T that maps the pixel
(x, y) to a new position (x0, y0). T is defined by its two components
x0 = Tx(x, y) y0 = Ty(x, y)
Geometric transformations of images are usually implemented in two steps.
First for a point (x0, y0) we find from the inverse transform T−1 the
corresponding point (x, y). Second, since x and y are not integers, we need to
estimate the brightness value at (x, y) by interpolation (from neighboring
integer points).
Explain why you think the transforms are implemented in this way.
Develop programs for the following geometric transforms:
(a) Rotation
(b) Change of scale
(c) Affine transform calculated from three pairs of corresponding points.
Recall an affine transform is defined as
x0 = a0 + a1x + a2y y0 = b0 + b1x + b2y
For each of the above transforms, implement the following two brightness
interpolation approaches:
• Nearest-neighbor interpolation
• Bi-linear interpolation (from four neighboring points).
Run your algorithms on a picture of your choice. Print the code. Print your
results for
(a) Scaling by a factor 3
(b) An affine transform with points A = (1, 0),B = (−1, 0),C = (0,p3)
mapping to points A0 =(1.9, 0),B0 = (−0.5, 0),C0 = (0, 1) using bi-linear
interpolation.
