COSC$6343$
Pattern$Recognition$
Department$of$Computer$Science$
University$of$Houston$
Assignment$$1:$Probabilistic$Image$Segmentation$
Due:$3/3/08!
The goal of this assignment is to apply statistical decision theory for the purpose of segmenting
an image into two components, foreground and background. Specifically, the goal of this
assignment is to segment the “cheetah” image into two components, the cheetah (foreground)
and the grass (background).
1.) Any descriptor that we could use to describe the observation space would be a function of the
image intensity. For the image in this case, a good descriptor would be a measure of texture
in the image. We will consider a simple texture measure based on the discrete cosine
transform (DCT). We will assume our observation space to be comprised of 8x8 image
blocks, i.e. we view each image as a collection of 8×8 blocks. For each block we compute the
discrete cosine transform (function dct2 on MATLAB) and obtain an array of 8×8 frequency
coefficients. For computational ease, we can convert the 2D array of coefficient into a 1D
vector comprising of 64 coefficients. The file ‘CoefficientPattern.txt’ provides the position
of each coefficient in the 8x8 array. Further, the file ‘TrainingSamplesPart1.mat’ contains
features for each class computed from a similar image. The features for the classes are stored
in two separate matrices, ‘TrainsampleDCT_BG’ and ‘TrainsampleDCT_FG’ for
background and foreground respectively.
The next step is to estimate the class conditional densities. To make this task easier, we are
going to reduce the feature vector to a single scalar. To do so, compute the position of the
coefficient with the 2nd largest energy value (absolute value) in the vector. This will serve as
our observation x. Given the training samples, build a histogram of these indexes to obtain
