1. This assignment consists of three questions for 20 Marks. Answer all of them.
2. The marks are given alongside the questions.
3. You may use any source on the Internet but should give the reference in your assignment.
4. If you use any AI Tool, make sure you include, in the assignment, the prompt given by you. However, remember that you are being very bad to the environment! You can power 100 high-end apartments in Hyderabad for a month with the power AI tools consume in one hour.

1. (8 Marks) Use the book, Digital Image Processing, to find the equations for converting RGB to L*a*b* space and vice-versa. Write a Python module or C functions on your own to implement the conversions. Hint: You may want to use the openCV library in both Python and C languages.
   Use your code to find the pair-wise distances between the colours: C1 = (64, 192, 96), C2 = (168, 255, 128) and C3 = (64, 66, 96) in RGB and L*a*b* spaces. Which distances appear to match your perception of the three colours?
2. (4 Marks) Consider the colour C = (0, 32, 128). Convert it into C^hsv using Python colorsys/openCV libraries. Multiply the intensity value by 1.5 and then convert the colour back into RGB space. Multiply the original C in RGB space by 1.5. In other words, multiply each component by 1.5. Are the two colours the same? Explain your answers.
3. (8 Marks) Download the Colour Matching Matrix in csv format. This contains the CIE colour matching functions from 400 nm to 700 nm in 5 nm intervals (i.e. 61 rows and 3 columns).
   Using the data, write programs for two functions: to create a spectrum as follows create_gauss_spectrum(center, bandwidth, energy) The parameter center is the wavelength, expressed in nanometres between 400 and 700nm, bandwidth is the width of the spectrum and energy is the total area under the spectrum. The spectrum is a gaussian function centred at the wavelength with its standard deviation given by the bandwidth divided by 6. The gaussian function is defined as $$\mbox{gauss}(x, m, w, A) = \frac{A}{\sqrt{2\pi}w}e^{-\frac{(x-m)^2}{2w^2}}~~~ \mbox{(Corrected,}~`-'~\mbox{missing in exponent earlier)}$$ In this equation, \(m = \mbox{center}, w = \frac{\mbox{bandwidth}}{6}, A = \mbox{energy}\).
   Important: Remember to write the function such that the spectrum is also in steps of 5 nm from 400 nm to 700 nm.
   The second function is to convert a spectrum into a colour spect2rgb(spect) where spect is the input spectrum and the return value from the function is an RGB triplet. If you are using a C program, use extra parameter(s) to get the return value as it is not easy to return an array.
   You also need the XYZ to RGB conversion matrix (3x3). Download or copy the XYZ to sRGB matrix for D65 illuminants from any source on the WWW.
   Use your functions to create three gaussian spectra with different sets of parameters and convert them into RGB colours. Are the colours what you expect? Explain briefly.

Chapter 6: Colour Image Processing
Sections covered

• Basics of Full Color Image Processing
• Color Transformations
• Color Image Smoothing and Sharpening

Link for Vector Image Processing (also available as Item IV in the Syllabus section).
Also, Material from class