Homework

There are several components to this homework as listed below:

a. Assuming a distance of 16 mm between the center of the lens and the retina along the visual axis, what is the height of the retinal image while observing a 20 m flag from 75 meters? Please show your calculations. (You can do this calculation in Octave)

b. Find/create an 8-bit grey scale image no larger than 256x256. Using Octave, resize the image to 1.5x, 2.0x and 3.0x its original size. For each of the 3 resizes apply nearest neighbor, bilinear and bicubic interpolation. Display and compare the original and the interpolated images.  Discuss your results including the strengths and limitations you found using each of the 3 different interpolation algorithms.

c. Create or findan image of your favorite letter or number. The image should be binary (pixels are 1 or 0) and be at least 64x64 in size. Using Octave, perform a single translation of +5 units in x and -8 units in y.  Be sure to wrap as oppose to crop your image.  Also, perform rotations (on the original non-translated image) of 30, 45, 90 and 135 degrees. Also, perform a vertical shear of .27 on your original image. Select the interpolation algorithm that yields the best results (in your opinion) for each of the affine transformations. You should plot the original image along with each of the transformations in separate Octave figures.

d. Find/create an 8-bit grey scale image at least 64x64 in dimensions. Using Octave, perform negative, log and gamma intensity transformations. You should select constants of your choice for the log and gamma transformations. For the gamma transformations, select 3 different gamma values that demonstrate different image transformation results. Display the original image and each of the intensity transformations in Octave plots. Discuss the results of your transformations including the obvious changes to the original images and the similarities and differences you observed between the transformations.

e. Using Octave, implement the spatial filtering equations for correlation (equation 3.4-1) and convolution (equation 3.4-2) found on pages 148-149 in the Gonzalez textbook.  Using your implementations, perform a correlation and convolution on the following 2-D image and 3x3 filter. Display the original images and the correlation and convolution of each. Demonstrate that performing a correlation on the 180-degree rotated filter results are equal to the convolution.

myimage = [0, 0, 0, 0, 0, 0, 0, 0;

                      0, 1, 1, 1, 1, 1, 1, 0;

                      0, 0, 0, 1, 1, 0, 0, 0;

                      0, 0, 0, 1, 1, 0, 0, 0;

                      0, 0, 0, 1, 1, 0, 0, 0;

                      0, 0, 0, 1, 1, 0, 0, 0;

                      0, 0, 0, 1, 1, 0, 0, 0;

                      0, 0, 0, 0, 0, 0, 0, 0];

myfilter =[2,1,2;

                  3,2,3;

                   2,3,2];

f. Find/create a binary image at least 64x64 in dimensions. Using Octave's existing functions, perform  Average, Gaussian and Laplacian filters on the image. Display the original image and each of the filtered images in Octave plots. Discuss and compare your results.

g. Using Octave, generate 3 different small rectangles with varying x and y dimensions (for example 1x9, 3x9 and 4x2), binary image and pad each to 32x32 dimension. Perform a 2-D FFT on each and plot the Magnitude of each. Experiment with translating and rotating the images and continue to calculate the Magnitude of the 2-D FFTs. Compare the original and translated and rotated images. Describe your results being sure to discuss the spacing between the zero crossing as a function of rectangle size and the impact of translation and rotation on the Spectrum.