CS 659 Image Processing
Sample Midterm Exam (Closed Book, 90 minutes)
Covering Lectures 1~6. There are 5 questions. Each is 20 points.
- (20 points)
(a) Let a grayscale image be the size 100-by-200 with 256 gray levels. How many bits in
memory are required to store this grayscale image without adding the overhead?
(b) Let a color image be the size 100-by-200. How many bits in memory are required to store
this color image without adding the overhead?
(c) If we reduce the image size by a half in both row and column. What fraction in the memory
size can we reduce?
Answer:
(a) 1002008=160,000 bits
(b) 1002008*3=480,000 bits
(c) or 0.25 - (20 points) Let an image f of 4-by-4 and a mask g of 2-by-2 as follows. Calculate the
convolution f * g and correlation f ° g. Note the origin is located at lower-left corner. - (20 points)
(a) Let an image of 2-by-2 as follows. Perform image negative on this image. What is the
resulting image? - 33
- 255
(b) Let an image of 2-by-2 as follows. Perform bit-plane slicing on this image. What are the eight
images on each bit-plane, B0, B1, B2, B3, B4, B5, B6, and B7, from Least Significant Bit (LSB)
B0 to Most Significant Bit (MSB) B7? - 33
- 255
Answer:
(a) We use 255 to subtract each pixel. - 222
- 0
(b) We represent each pixel into 8-bit as:
3=00000011,
33=00100001
170=10101010
255=11111111
Therefore, - (20 points)
Let a binary image be f and a template be g as follows. Perform image matching using the
equation: Note that is correlation and
is the complement. What is the
resulting image?
1 - (20 points) Explain the image equalization and image specification. Briefly describe both
procedures to achieve their goals.
Answer:
In histogram equalization we are trying to maximize the image contrast by applying a gray level
transform which tries to flatten the resulting histogram. It turns out that the gray level transform
that we are seeking is simply a scaled version of the original image’s cumulative histogram. That
is, the graylevel transform T is given by T[i] = (G-1)c(i), where G is the number of gray levels
and c(i) is the normalized cumulative histogram of the original image.
r: the gray levels to be enhanced.
Assume r continuous in [0,1]
s=T(r)
a) T(r) single-valued, monotonically increasing
b) 0<=T(r)<=1
When we want to specify a non-flat resulting histogram, we can use the following steps (called
image specification): - Specify the desired histogram g(z)
- Obtain the transform which would equalize the specified histogram, Tg, and its inverse
Tg-1 - Get the transform which would histogram equalize the original image, s=T[i]
- Apply the inverse transform Tg-1
on the equalized image, that is z=Tg-1
WX：codehelp