[SOLVED] ME6406 Assignment #1

All programs should be written using MATLAB. Solutions must be consolidated into a single pdf file (including all results and an explanation of results) and a zip file (including all m-files used for the results). Solutions must be submitted electronically through Canvas.  Late solutions will be penalized at 10% deduction from the homework score, and will NOT be accepted 24 hours after due date.

1. Pin-hole optics

Consider a dark edge projected through a pinhole. Show that

=A = 1 cos−1 s    s   Rs 2 

−     1−

 O           R R          

                              

where−R s R  ; s is the displacement of the pinhole center from

the edge; δO is the pin hole projection area; and δA is portion of δO in  the dark area. Plot ρ as a function of s/R.   ^{Fig. 1}

2. Histogram equalization

Figure 2 shows an 8-bit gray-scale image of an eye-retina.

Fig. 2 eyeball.png

• Perform a histogram equalization of the sub-region shown in image matrix; give your results by completing Table 1. Show the histogram equalized results of sub-region matrix.

Table 1

• Perform histogram equalization on an image by writing a Matlab script for the following:
  1. Read in and display the image ‘eyeball.png’.
  2. Compare by displaying the original and processed images and their histograms.

Suggested Matlab functions:  imshow, imhist or hist, histeq

3. Filtering masks

(a) Show the value of a 5×5 Gaussian filter with  equal to 2 pixels.

Sobel operator

• Use a 3×3 Sobel operator to calculate the magnitude and direction of the gradient at pixel (X, Y)=(4, 5) in Fig. 2. Indicate the direction of the gradient on the pixel. (Note: Sobel operator is coordinate dependent. Be sure to use consistent coordinate systems on the sub-regions.)
• Write a Matlab script to compute the gradient of an image. For illustration, use the Sobel operator on the image “IC_pin.png” shown Fig. 3(a). Display the gradient images (G_x, G_y, G). Suggested Matlab functions: edge.m

Gaussian operator and Difference of Gaussian (DOG):

• Use an m×m Gaussian filter mask with different (=1, 2 and 5) to smooth the noisy image shown in Fig. 3(b). Compare the effect of _ on the smoothed image. Suggested Matlab functions: imfilter.m.

 Notes: ‘Smoothing effects are more prominent as sigma increases. Mask size increases as sigma increases.

• Perform DoG operation (with =1 and =2) on Fig. 3(c) and show the processed image.

(a) ‘IC_pin.png’                  (b) ‘salt_and_pepper_checker.png’                      (c) ‘checker.png’

Fig. 3

4. Low-level information processing

• Read in and convert the image (Fig. 4) into a gray-scale image. Binarize the image using three different thresholds; the “best or preferred” value, and an over-estimate and under-estimate values. (Use image histogram to help pick the threshold values).
• Obtain the area and centroid of the two objects (nut and shelf) in the image with an appropriate threshold.

Suggested Matlab functions: rgb2gray.m, im2bw.m, bwlabel.m, regionprops.m

Figure 4 ‘nut_and_shell.png’

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