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174 3 Image processing

Ex 3.11: Sharpening, blur, and noise removal Implement some softening, sharpening, and
non-linear diffusion (selective sharpening or noise removal) filters, such as Gaussian, median,
and bilateral (Section 3.3.1), as discussed in Section 3.4.4.
Take blurry or noisy images (shooting in low light is a good way to get both) and try to
improve their appearance and legibility.
Ex 3.12: Steerable filters Implement Freeman and Adelson’s (1991) steerable filter algo-
rithm. The input should be a grayscale or color image and the output should be a multi-banded
image consisting of G 0 ◦ and G 90 ◦ . The coefficients for the filters can be found in the paper
1 1
by Freeman and Adelson (1991).
Test the various order filters on a number of images of your choice and see if you can
reliably find corner and intersection features. These filters will be quite useful later to detect
elongated structures, such as lines (Section 4.3).

Ex 3.13: Distance transform Implement some (raster-scan) algorithms for city block and
Euclidean distance transforms. Can you do it without peeking at the literature (Danielsson
1980; Borgefors 1986)? If so, what problems did you come across and resolve?
Later on, you can use the distance functions you compute to perform feathering during
image stitching (Section 9.3.2).

Ex 3.14: Connected components Implement one of the connected component algorithms
from Section 3.3.4 or Section 2.3 from Haralick and Shapiro’s book (1992) and discuss its
computational complexity.

• Threshold or quantize an image to obtain a variety of input labels and then compute the
area statistics for the regions that you find.

• Use the connected components that you have found to track or match regions in differ-
ent images or video frames.

Ex 3.15: Fourier transform Prove the properties of the Fourier transform listed in Ta-
ble 3.1 and derive the formulas for the Fourier transforms listed in Tables 3.2 and 3.3. These
exercises are very useful if you want to become comfortable working with Fourier transforms,
which is a very useful skill when analyzing and designing the behavior and efficiency of many
computer vision algorithms.

Ex 3.16: Wiener filtering Estimate the frequency spectrum of your personal photo collec-
tion and use it to perform Wiener filtering on a few images with varying degrees of noise.
1. Collect a few hundred of your images by re-scaling them to fit within a 512 × 512
window and cropping them.
2. Take their Fourier transforms, throw away the phase information, and average together
all of the spectra.

3. Pick two of your favorite images and add varying amounts of Gaussian noise, σ n ∈
{1, 2, 5, 10, 20} gray levels.

4. For each combination of image and noise, determine by eye which width of a Gaussian
blurring filter σ s gives the best denoised result. You will have to make a subjective
decision between sharpness and noise.