Digital Image Processing (DIP)

CSC 532 Test 12 March 2017

Name ______

Instructions

You may use your computer, Excel, and any tools that you have personally developed for performing Fourier transforms or conducting digital signal processing (DSP) operations.

Problems

Digital Image Processing (DIP)

1. Given a monochrome image, describe the histogram equalization algorithm for enhancing the contrast in the image?
   
2. For a color image, how would you improve contrast? What differences arise in using the histogram equalization algorithm with an RGB versus an HSB/V representation?
   
3. For a color image stored in RGB format, assume that you need its negative representation. How would you determine the values for, and create the pixels to represent, the negative image?
   
4. Suppose that you have a gray-scale image stored in an RGB format and need to identify, mark or enhance the boundary contours (sometimes called edges).
5. Define the x- and y-direction Sobel masks, Gx and Gy, respectively.
   
6. How are Gx and Gy used to identify boundary contour pixels?
   
7. If there are Sobel masks of other orientations, provide examples and describe what image features those masks would be used to identify.
   
8. Suppose you are given an image, Im, and a pixel P=Im(h, k), which is located in column h and row k of Im. Further, suppose r1>0 and r2>0 are given, with r1<r2. Let A be the annulus of pixels that are within r2 pixels of P but more than r1 pixels of P. How would you rotate the annulus A counter-clockwise through an angle Θ around P?
   
9. What would be the visual effects of applying the convolution mask:

(Interior pixels are those that are not in the first or last row or column of an image.)

One-Dimensional Digital Signal Processing (DSP): Fourier Methods and Applications

For these DSP problems, consider the data in the file(s) linked to the course web site. The signal was sampled at a rate of 44,100 samples per second and there are 512 samples.

1. Use fast convolution to construct and apply a six-point, smoothing filter for the data in file “noisysignal.txt”. For reference, a plot of the 512 samples of the noisy signal appears in Fig. 1.
   
   
2. What are the values of the convolution smoothing filter and how many nonzero values does the smoothing filter employ?
   
3. On a single graph, plot and label the original signal data and the smoothed signal data.
   
4. Use an FFT and whatever additional processing is necessary to estimate the power spectral density (PSD) of the filtered signal derived from “noisysignal.txt”.
5. Use a bar graph to plot the PSD estimate.
   
6. Identify and report the center frequencies of the two bins containing the most power.
   

1. What DTMF tone does the data in the “noisysignal.txt” file represent? For reference, the DTMF tone assignments a given in Table 1.
   

1. Assume that the pulse and echo (signal) data given in the file “rangetest.txt”, arise from an airport radar system. Use fast correlation to locate the point at which the pulse is best correlated with the echo, and in turn, estimate the distance to the reflector (in this case, possibly a plane). The signal, again a noisy signal, is illustrated in Fig. 2.
   
   Assume that:
2. The return consists of a single sample window with 1024 samples that were taken at a 500 MHz sampling rate; i.e., the signal samples are taken every 2 nanoseconds (a nanosecond is 10-9 seconds);
3. The receiver is turned off for 20 microseconds (a microsecond is 10-6 seconds) after the pulse is transmitted;
4. To allow the receiver to stabilize, the return signal measurements were taken from the eleventh sampling window after the receiver begins listening again (thus 20 microseconds + the time required for 10 sampling windows elapses before the sample given as data was taken); and
5. Electromagnetic waves travel at approximately 3 x 108 meters per second in air.

Plot the results of the computation of the fast correlation of the signal and the pulse.

How many time steps of delay elapse before the pulse is best correlated with the signal?

What is the distance to the primary reflector?

1. Suppose that one had samples , and computed X = FFT(x) using these samples.
   What is X(0)=______?
2. Use pseudo-code to describe an algorithm for using a one-dimensional Fourier transform to implement a two-dimensional Fourier transform.