Image Processing Final Exam 2014 SOLUTION

INTRODUCTION TO IMAGE PROCESSING P ROCESSING Fall 2014, Final Exam Student Name:................................ Name:.................................................. ................................. ...............

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PROBLEM 15 - 15 points

Consider an image with a histogram as in Figure 1a. The intensity transformation depicted in Figure 1b is applied to this image. Sketch the histogram of the processed image.

Figure 1a

SOLUTION

The resulting histogram:

Figure 1b

PROBLEM 2 – 10 points

Which operation should be applied to the image in Figure 2a to obtain the image in Figure 2b? Why?

Figure 2a

Figure 2b

SOLUTION Histogram equalization can be applied to the image in Figure 2a to obtain the image in Figure 2b. Histogram equalization spreads the gray levels across a wide range from black to white.

PROBLEM 3 – 10 points

Consider an image with histogram depicted in Figure 3 a. What operation should be applied to this image to obtain an image with histogram in F igure 3b? Why?

Figure 3a

Figure 3b

SOLUTION Histogram equalization is applied to the image obtain an image with the histogram in Figure 3b. Histogram equalization spreads the gray levels across a wide range from black to white.

PROBLEM 4 – 10 points

Consider a pair of input (Figure 4a) and output (Figure 4b) images of a certain procedure. Which operations are most likely involved in this procedure? Why?

Figure 4a

Figure 4b

SOLUTION A median filter is applied to the image in Figure 4a to eliminate the salt & pepper noise. Then an edge detection algorithm is applied to obtain the edge m agnitude map in Figure 4b.

PROBLEM 5 – 10 points

Figure 5a

Figure 5b

Which of the following filters is applied to the image in Figure 5a to obtain the image in Figure 5b? Why?

SOLUTION The resulting image in Figure 5b is a “blurred” version of the original image in Figure 5a. This effect  can be

obtained by the average filter in (a).

PROBLEM 6 – 15 points

Consider the following image:

(a) Increase the size of this image from 2x2 to 4x4 by copying each pixel into a 2x2 block. (b) Apply an averaging filter of size 3x3 t o the resulting image. Use replication for border pixels.

SOLUTION (a)

(b)

PROBLEM 7 – 10 points

Show that the Sobel mask can be implemented by one pass of differencing mask of the image, followed by a smoothing mask of the form

SOLUTION

1[2] 1

along the columns.

−1 0 1

 along the rows

PROBLEM 8 – 20 points

Segment the image shown below using the split and merge procedure. Let Q(R) = TRUE if all pixels in region R have the same intensity (e.g. homogeneous region). Show the quadtree corresponding to your segmentation.

SOLUTION