Description
1. Develop a strategy for storing an image given over a hexagonal tessellation into a 2D array (I.e. by
describing the position of each cell using indices i,j).Then show how to:
a. Compute Euclidian distances
b. Determine 6-adjacency
given only the indices (in the new data structure) of 2 arbitrary pixels. You may assume each side
length of a hexagonal cell is a units.
2. Consider the connected component (cc) labeling algorithm involving single pass of an operator propagating labels and keeping equivalences.
a b c
d p
where p is the pixel under consideration. Explain in the form of a table what happens in the algorithm
for all possible states (There are 32 possible states for the 5 binary variables). Also give an example on
a simple image.
3. Determine the value of |P|²/A (perimeter squared, divided by area) for a regular polygon having N
sides and show that it is always greater than the value of |P|²/A that corresponds to a circle.
4. a) Consider two points that are d units apart from each other at the same vertical level. If we use a
(horizontal) line shaped structuring element to make these points connected to each other, what is the
minimum length of the line (in terms of d) which is used as a closing operator? Justify your answer as
clearly as possible.
b) Consider four points located at the corners of a square of side length d. If we use a disk shaped
structuring element to make these points connected to each other, what is the minimum radius of the
disk (in terms of d) which is used as a closing operator? Justify your answer as clearly as possible.
5. Find the parameters of a forward affine transformation that rotates the input image by 45 degrees
clockwise around image center (NR/2,NC/2) and alters the aspect ratio of the rotated image from 4:3 to
16:9 (width:height).
6. Write a computer program that reads a pgm format image file and applies gamma correction to the
input image using a gamma value specified at the command line. You
can simply modify the file example1.c which is part of SGimproV1.2b.zip. Submit c code attached to
the rest of your solutions.
Note:vcorrected=(
vuncorrected
vmax )
γ
. vmaxand vmax is the maximum gray value in the image.
