Faith Quist

16-311 Homework 3

1.       Digital Images

a.       My 3x3 mask that implements the average operator b.      I used this mask on a picture of a bagpiper. The results are shown below.  Figure 1: Piper original                                             Figure 2: Piper blurred

c.       This operation loses information in two ways. First, unless the picture is extended, the mask would cut off the pixels around the border, creating a smaller image. Furthermore, since every pixel becomes the average of the pixels around it, it is impossible to deduce what the previous values were. Although you know what the pixels in the mask would have to add up to, you do not know how that sum was divided among those pixels.

d.      Weighted mask. I chose this weight because it more than doubles the amount that the central pixel contributes, but the neighbors are not made totally insignificant. 2.       Convolution

a.       Convolution is commutative, as shown by the following pictures. The horizontal mask is . The vertical mask is     Figure 3: From left to right: image*horizontal, image*vertical, image*horizontal*vertical, image*vertical*horizontal

3. Martian Vision Lab

·         Thresholding was done using a value that minimized the variance of the two resulting groups.

·         Contrasting was achieved by giving pixels with an original value (z) a new value corresponding to the range maximum times the cumulative distribution function of the histogram at z. ·         The histograms show values ranging from 0 to 255. The maximum bin of each histogram has a column height equal to the histogram’s height.

 Original Thresholding Contrasting Histogram            