Dynamic Programming: Image Comparison

[oNeUpKid88]

Greetings,

I'm hoping to attain assistance with the following assignment:

Design an algorithm (using pseudocode) that takes in as an input, two 2-D int arrays that are assumed to be 2 black-and-white images: initialImage x, whose dimensions are IxJ, and finalImage y, whose dimensions are IxK. The algorithm will compare x to the y, row-by-row, as defined below. Your algorithm will employ a dynamic programming scheme to compare X to Y identifying the minimal difference between each row.

Because you are working with black-and-white images only, you should assume that each image is a 2-D int array consisting of 2 possible values: 0 or 1, where 0 represents black and 1 represents white. Thus, this 2-D grid of 0 and 1 values comprise a 2-D black-and-white image. Each row of this image is then simply a 1-D int array filled with either 0s or 1s. Therefore, you must define how you will measure the difference between the strings of 0s and 1s in each row.

Remember that you will do the comparison one row in the images at a time.

First, compare X1,* to Y1,*. (Here X1,* is the first row in image X and Y1,* is the first row in image Y ). Next, compare X2 to Y2... Each one of these comparisons will require the construction of a D (distance) matrix.

In the following example, the first row of X is X1,*, and the first row of Y is Y1,* = 00110.

D[j,k] = min { d[j - 1, k - 1], if x_i,_j = = y or d[j - 1, j - 1] + 1 , if x_i,_j!=y line 1
d[ j - 1,k] + 1, account for x_i,_j is not in y_i* line 2
d[j, k - 1] + 1, Account for y_i,_k is not in x_i* line 3

Use the following recurrence relation to develop your pseudocode:

D[j,k] = min { d[j - 1, k - 1], if x_i,_j = = y or d[j - 1, j - 1] + 1 , if x_i,_j!=y line 1
d[ j - 1,k] + 1, account for x_i,_j is not in y_i* line 2
d[j, k - 1] + 1, Account for y_i,_k is not in x_i* line 3


After the D matrix is completed, the minimum number in the bottom row is the minimal mismatch for this row. You will assign this value to the variable minVali. This number tells how different row X1,* is from row Y1,* . You will then repeat this comparison for all rows i and aggregate the difference when complete into variable totalDifference = Σi minVali.

As a result, the algorithm will compare the total difference to a threshold value called thresh. If total value is above the threshold, the images are declared different, otherwise they are declared to be similar images. You can assume that the thresh variable is supplied as an input to your algorithm.