Please attempt all the questions. The questions are open$-$ended and there is no correct or wrong

answer. Try to work these problems to the best of your ability using the concepts discussed in the

course. Specify any assumptions that you make and provide justification for it$.$ Support your answers

with calculations. Use of MATLAB is expected.

$$Beauty$$ and the Pandemic

A recent report from McKinsey & Company presents a detailed analysis of the affect of Covid$-19$

pandemic on the beauty industry. One of the upcoming startup is facing similar challenges and

during its recent board meeting its top management decides to engage a consultant to help them get

out of this crisis. In this context, their technical head Ms$.$ Laxmi Sundar approaches YOU for a

solution.

After detailed discussion with Ms$.$ Sundar, YOU suggest her to revamp their organisation$$s website.

The overall idea is that the website should be such that it not only entice the direct users of beauty

products but also the indirect users. For instance, the website must facilitate any person, irrespective

of their gender, to buy beauty products for their loved one. Ms$.$ Sundar is intrigued by your solution

and asks how is it going to be implemented. YOU tell her that a $$virtual try$-$on$$ application can

be designed wherein the visitor $($of the website$)$ uploads a photograph of the face of the person and

the application suggests a suitable make$-$up for a particular occasion. Ms$.$ Sundar says that since

their organisation is a start$-$up they have only $5$ products to choose from and that they design their

products only for a standard make$-$up$.$ YOU further add that the implentation of $$virtual try$-$on$$ will

be much easier in this case. Basically, YOU say, the user selects the skin tone $($deep$,$ medium, fair$),$ its

undertone $($warm$,$ neutral, cool$)$ and uploads a photograph of the person. The application does some

background calculations and gives the match percentage for each of the five products, under standard

lighting conditions. Ms$.$ Sundar likes your idea and asks you to implement it$.$

Question

Some details of the skin undertone, skin tone etc. can be found here.

$1.$ Based on the discussion above, please answer the following. Elucidate each part by a working $(50)$

example.

$($a$)$ What strategy would you use to map the skin$-$tone and skin$-$undertone to the $5$ products

named, P$1,...,$ P$5?$

$($b$)$ How will you define the standard lighting conditions?

$($c$)$ Assuming that the user uploads a clear photograph of the person$$s face, how will you modify

it for standard lighting conditions.

$($d$)$ How will you incorporate the information provided by the user, regarding skin tone or undertone, to calculate the percentage match for the products, P$1,...,$ P$5?$

$($e$)$ Assuming that the user chooses one of the products, how will you alter the photograph to

reflect the person$$s image when this product is used.