Just a click away: The mathematics that revolutionized photography.

Crédito: Rodrigo Leão / R2 / ICM 2018

Taking a photo with your cell phone camera, sending it to friends online, and posting it on social media, all with impressive quality, are common and routine habits today. What you may not know is that this is possible thanks to the research of a mathematician, the Belgian Ingrid Daubechies.

The trajectory of the researcher, who revolutionized the world of algorithms four decades ago, was recounted in a report by the American newspaper The New York Times last week. Entitled " The Godmother of Digital Imaging ," the article tells how the researcher's work opened the doors to the technology we have today in the palm of our hand and to the entry of women into mathematics.

In the 1980s, Daubechies, a professor at Duke University in North Carolina, USA, discovered the "Daubechies wavelet," a mathematical concept used in applications such as high-definition transmissions that, along with other studies on so-called "wavelets," allowed the development of algorithms for image compression. Wavelet equations allow complex signals to be decomposed into their most basic and fundamental characteristics, leaving out irrelevant information.

One example is the JPG standard for digital images, whose evolution, named JPEG 2000, Ingrid herself helped to create. With it, it's possible to "compress" the pixels of a photo with minimal loss of resolution, reducing the original file size by up to 30 times. The mechanism allows images to be reproduced in the way the human eye naturally sees them, with more detail in the focal points and less sharpness in the rest, with minimal loss.

The algorithm revolutionized the way we use and share images in digital format. Photo compression not only saves storage space, but also reduces the amount of computing resources needed to display them and the bandwidth used for transmission.

Although known for her pioneering work in image compression, the scientist has conducted research in various fields that have enabled the digital transformation of society. Her work involves knowledge of mathematics, technology, and biology to, for example, extract information from bones or teeth, contributing to the field of evolutionary morphology. In another study, she developed a way to "X-ray" the Earth from seismic data, revealing previously unknown information.

ICM 2018

In 2013, Daubechies was at IMPA to give a plenary lecture at the 29th Brazilian Mathematics Colloquium. Five years later, she returned to Rio de Janeiro as one of the public speakers at ICM 2018 (International Congress of Mathematicians, held by the institute). On that occasion, the American spoke about another research project, carried out using more than one hundred high-resolution photographs of Van Gogh's works. The group, led by Ingrid Daubechies, revealed surprising information about the artworks, such as the discovery that the number of brushstrokes the artist used is greater during his time in Paris compared to Arles, both in France.

But Daubechies' pioneering spirit wasn't limited to her discoveries: she was the first woman to hold the position of president of the International Mathematical Union (IMU). Today, she is one of the directors of the Enhancing Diversity in Graduate Education (EDGE) Foundation, which encourages women to pursue careers in mathematical sciences.

Click here to read the full article from The New York Times .