## Description

## Question1: Color Theory – 10 points

One of uses of chromaticity diagrams is to find the gamut of colors given the primaries. It

can also be used to find dominant and complementary colors –

Dominant color of a given color D (or dominant wavelength in a color D) is defined as the

spectral color which can be mixed with white light in order to reproduce the desired D

color.

Complementary colors are those which when mixed in some proportion create the

color white. Using these definitions and the understanding of the chromaticity diagram that

you have, answer the following.

• In the image alongside find

the dominant wavelength of

color D. Show this

wavelength. (2 points)

• Do all colors have a

dominant wavelength?

Explain your reasoning. (3

points)

• Find the color which is

complimentary to the color

C. Show this color (2

points)

• What colors in RGB color space map to the equiluminous point E

upon projection into the chromaticity space. (3 points)

## Question 2: Color Theory (10 points)

• The chromaticity diagram in (x, y) represents the normalized color matching

functions X, Y and Z. Prove that (2 points)

Z = [ (1-x-y)/y ] Y

Here you are tasked with mapping the gamut of a printer to that of a color CRT

monitor. Assume that gamuts are not the same, that is, there are colors in the printer’s

gamut that do not appear in the monitor’s gamut and vice versa. So in order to print a

color seen on the monitor you choose the nearest color in the gamut of the printer.

## Answer the following questions

• Discuss (giving reasons) whether this algorithm will work effectively? (2 points)

• You have two images – a cartoon image with constant color tones and a real image

with varying color tones? Which image will this algorithm perform better – give

reasons. (2 points)

• Can you suggest improvements rather than just choosing the nearest color? (4

points)

Entropy Coding – 20 points

Consider a communication system that gives out only two symbols X and Y. Assume that

the parameterization followed by the probabilities are P(X) = x2

and P(Y) = (1-x

2

).

• Write down the entropy function and plot it as a function of x.(1 + 3 points)

• From your plot, for what value of x does the Entropy become a minimum? At what

values of x is the Entropy a maximum? .(2 points)

• Although the plot visually gives you the value of x for which the entropy in

maximum, can you now mathematically find out the value(s) for which the entropy

is a maximum? (6 points)

• Can you do the same for the minimum, that is can you find mathematically prove

the value(s) of x for which the entropy is a minimum? (8 points)

Generic Compression – (20 points)

The following sequence of real numbers has been obtained sampling a signal:

5.8, 6.2, 6.2, 7.2, 7.3, 7.3, 6.5, 6.8, 6.8, 6.8, 5.5, 5.0, 5.2, 5.2, 5.8, 6.2, 6.2, 6.2, 5.9, 6.3, 5.2, 4.2, 2.8,

2.8, 2.3, 2.9, 1.8, 2.5, 2.5, 3.3, 4.1, 4.9

This signal is then quantized using the interval [0,8] and dividing it into 32 uniformly distributed

levels.

• What does the quantized sequence look like? For ease of computation, assume that you

placed the level 0 at 0.25, the level 1 at 0.5P, level 2 at 0.75, level 3 at 1.0 and so on. This

should simplify your calculations. Round off any fractional value to the nearest integral

levels (4 points)

• How many bits do you need to transmit the entire signal? (2 points)

• If you need to encode the quantized output using DPCM. Compute the successive

differences between the values – what is the maximum and minimum value for the

difference? Assuming that this is your range (ie, ignore first value), how many bits are

required to encode the sequence now? (4 points)

• What is the compression ratio you have achieved (ignoring first value)? (1 point)

• Instead of transmitting the differences, you use Huffman coded values for the differences.

How many bits do you need now to encode the sequence? Show all your work and how you

arrived at the final answer (5+3 points)

• What is the compression ratio you have achieved now (ignoring first value)? (2 points)

## Programming Part (140 points)

This assignment will help you gain a practical understanding of analyzing color channels

especially as it pertains to image segmentation. Image segmentation is a challenging task in

the field of image processing and computer vision. In order to obtain an accurate

segmentation performance, user interaction is always used in practical image-segmentation

applications.

Here you will implement one such application where the image pixels need to

be segmented based on two threshold values in the HSV color space, using the hue values

as thresholds. All the pixels falling between these two hue thresholds will be displayed in

the original color in the output image, whereas all the other pixels outside the threshold will

be displayed in gray.

You will be given input images in the usual rgb format. You are free to use extend the

display code sample given of assignment 1 to implement this project or you may write your

own in any language of your choice (no scripting languages such as MATLAB or python

please!).

Recall that the HSV color space (Hue, Saturation and Value) describes Hue as a number

between 0 and 360, 0 being closer to red

The input to your program will take three parameters where

• The first parameter is the name of the image, which will be provided in an 8 bit per

channel RGB format (Total 24 bits per pixel). You may assume that all images will

be of the same size for this assignment of size 512 x 512

• The second parameter will be a number between 0-360. This will provide the first

hue threshold h1 for deciding your segmentation boundary.

• The third parameter will be a number between 0-360. This will provide the second

hue threshold h2 for deciding your segmentation boundary. This number will be

greater than the previous number.

To invoke your program we will compile it and run it at the command line as

YourProgram.exe C:/myDir/myImage.rgb h1 h2

where h1 and h2 are the parameters as described above. To run your program you will need

to convert your rgb values Example inputs are shown below and this should give you a fair

idea about what your input parameters do and how your program will be tested.

1. YourProgram.exe roses_image1.rgb 0 359

The left image is your input and the right image is the produced output. Here the thresholds

h1 and h2 scan through all colors 0 to 359, so the output will be same as the input.

2. YourProgram.exe roses_image1.rgb 320 359

The left image is your input and the right image is the produced output. Here the thresholds

h1 and h2 scan through 320 to 359 which is the red part of the HSV space.

Correspondingly the output is shown below.

input.

3. YourProgram.exe roses_image1.rgb 60 120

The left image is your input and the right image is the produced output. Here the thresholds

h1 and h2 scan through 160 to 120 which falls in the green spectrum of the HSV space.

Correspondingly the output is shown below.

Now for the details – You will need to convert your image from an RGB representation to

a HSV representation. Unlike other color space conversions, there is no matrix to linearly

convert to the HSV color space. The HSV color space is represented as a cylindrical

coordinate system with H varying from 0 (near violet/blue) to 360 (red), where as H and V

both vary from 0 to 1. You can read about the color conversion here:

https://en.wikipedia.org/wiki/HSL_and_HSV

https://www.cs.rit.edu/~ncs/color/

Once in the HSV space, you can appropriately use the thresholds h1 and h2 to perform the

assignment.

### What should you submit?

• Your source code files, and your project file or makefile, if any – all combined into

a zip archive with your name on the archive. Please do not submit any binaries or

images. We will compile your program and execute our tests accordingly.

• If you need to include a readme.txt file with any special instructions on compilation,

that is fine too.