But researchers here also try out new ideas. Looking to build a new system for searching with images instead of words, a team in Bangalore turned to Watson to index 600,000 photos from the world’s top fashion shows and Bollywood movies. Last spring, a major Indian fashion house, Falguni Shane Peacock, tried the tool, which helps designers avoid direct copies or even do a riff on an old look, and generated new patterns for three dresses.

“It has the capability of doing research in a couple of seconds that would take a long time,” Shane Peacock, who runs the Mumbai firm with his wife, said in an interview.

IBM even has a Bangalore “garage” full of app designers who build corporate iPhone and iPad apps to simplify tasks like helping airline agents rebook passengers, bankers make loans and doctors update patient files.

During a recent visit, Ramya Karyampudi, a user experience designer, was at the whiteboard sketching out an app for a smart refrigerator that would solve the universal problem of what to make for dinner.

Starting with a drawing of a husband trying to plan a surprise meal for his wife, Ms. Karyampudi depicted the internet-connected refrigerator looking at what food was inside, sending over relevant recipes, telling him what extra ingredients he needed to pick up, and playing a video showing him how to cook it all.

IBM’s outsize presence in India today is all the more striking given that it left the country entirely in 1978 after a dispute with the government about foreign ownership rules.

IBM re-entered the country through a joint venture with Tata in 1993, initially intending to assemble and sell personal computers. IBM’s leaders soon decided that India’s potential was far bigger — both as a market and as a base from which to serve customers around the world. The company took full control of the venture, established an Indian branch of its famed research labs, and in 2004, landed a landmark 10-year, $750 million contract from Bharti Airtel, one of India’s biggest phone companies, which remains a major customer.

IBM’s chief executive at the time, Samuel J. Palmisano, was so proud of his India initiative that he rented out the grounds of the Bangalore Palace in June 2006, flew out the board, and told a crowd of 10,000 that IBM would invest $6 billion in India over the next three years.

Today, India does not just deliver services to IBM’s global clients. It is also a crucial market and the center of IBM’s efforts to help businesses serve the next big slice of customers: the billions of poorer people who have been largely ignored by the tech revolution.

For example, teams here have been applying IBM technology to process very small loans so that banks can make a profit on them.

IBM has also been working with Manipal Hospitals, a chain based in Bangalore, to adapt Watson to help doctors treat certain cancers. Presented with a patient’s medical history, the system taps into a database that includes advice from doctors at Memorial Sloan Kettering Cancer Center in New York to recommend the best treatments — including the price, a big consideration since most Indians lack health insurance.

Dr. Ajay Bakshi, Manipal’s chief executive, said the biggest potential for the technology was in rural hospitals with few doctors. Manipal has just begun offering online “second opinions” from Watson for 2000 rupees, or about $31. “It never sleeps. It never forgets. It doesn’t get biased,” he said.

IBM executives say projects like these represent the company’s future. “I am looking for India to be my hub for affordable innovation,” Ms. Narayanan said.

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