/Image_Processing_2

Image Filtering with Gaussian (Blurring), Taking Image Derivatives, Geometric Transforms (Rotation)

Primary LanguageC++

Exercise 1 Image Filtering with a Gaussian Filter

a. Write a new member functionImage::smoothxthat takes a single-
precision floating point numbersigmaand convolves the image in the
x direction with a Gaussian filter with the corresponding standard de-
viation. Assume that the filter coefficients are zero after two standard
deviations.

b. Write a new member functionImage::smoothythat performs the
same operation in the y direction.

c. Write a new member functionImage::smooththat performs Gaussian
smoothing both in the x and y directions with standard deviations
sigmaxandsigmay.

Hint:To compute the filter first compute the filter length in one direction, sayl. The filter length should be 2∗l+ 1 since the Gaussian is symmetric. Fill in coefficient values by sampling the Gaussian form

exp ^( (− 0.5) * (x^2) / (σ^2) )

by assuming the filter center is atx= 0. Then normalize the filter such that the elements sum up to 1. Note that, we did not need the normalization factor 1/√2πσ^2 since we normalize the filter coefficients at the end.

Exercise 2 Image Derivatives

a. Write a new member functionImage::derivxthat takes computes
the image derivative in the x direction using a filter of the form

[-1 0 1

-2 0 2

-1 0 1 ]

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

b. Write a new member functionImage::derivythat takes computes
the image derivative in the y direction using a filter of the form

[-1 -2 -1

0 0 0

1 2 1 ]

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

Exercise 3 Geometric Transforms

a. Write a new member functionImage::rotate that takes a single-
precision floating point numberθand anImagepointerout. After
the function call finishes the image pointed byoutshould contain the
result of applying the rotation

x′=Rθx= [ cosθ −sinθ ; sinθ cosθ ]

with nearest neighbor sampling.

b. Add an option to perform bilinear sampling to the functionImage::rotate.
c. Add an option to perform the rotation around the image center.

Hint:You must not change the size of the imageout.