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
- 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.
- Write a new member function Image::deriv y that takes computes
−1 −2 −1the image derivative in the y direction using a filter of the form 0 0 0 . 121
The results should be returned in a newly allocated array of type short which can store negative values.
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Exercise 3 Geometric Transforms
a. Write a new member function Image::warp affine that takes a two- by-two transform matrix A and a two-by-one translation vector t, and an Image pointer out. After the function call finishes the im- age pointed by out should contain the result of applying the affine transform
′ a11 a12 t1 x=Ax+t=a a x+t
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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]).
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