CENG391 - Introduction to Image Understanding - Homework 2 - Solved

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         Exercise 1           2D Image Filtering
a. Write a new member function Image::filter  2d that takes an odd integer n, and an n × n single-precision floating point matrix K. The function should return a new image that is of size

(w() − n + 1) × (h() − n + 1)

and filtered by the kernel K.

Hint: If n is even you may take n as the largest odd number smaller than n. Make sure to clamp the filter results to the range [0,255]. The size of the output is smaller so that you do not need to worry about the image borders.

         Exercise 2          Image Derivatives
a. Write a new member function Image::deriv x that takes computes

                                                                                                                                              −1     0    1

            the image derivative in the x direction using a filter of the form −2    0     2.

                                                                                                                                                 −1     0    1

The results should be returned in a newly allocated array of type short which can store negative values.

b. Write a new member function Image::deriv y that takes computes
 
−1 −2

      the image derivative in the y direction using a filter of the form  0                                                                          0

                                                                                                                                             1                                                                                                                                             2

The results should be returned in a newly allocated array of type short which can store negative values.
 .
1

         Exercise 3           Geometric Transforms
a.     Write a new member function Image::warp  affine that takes a twoby-two transform matrix A and a two-by-one translation vector t, and an Image pointer out. After the function call finishes the image pointed by out should contain the result of applying the affine transform

x 

with nearest neighbor sampling.

b.    Add an option to perform bilinear sampling to the function Image::warp affine.

Hint: You must not change the size of the image out. Assume that the matrix and vector entries are stored in the double-precision floating point format and the matrix is stored in the column major order (Its entries are stored in memory in the order [a11,a21,a12,a22]).