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Carola Schönlieb

05/10/18

@ Y Combinator

During my research, I discovered that the Cahn-Hilliard equation was used for image restoration, which involves replacing damaged parts of a digital image with suggested content from surrounding areas.

Video

Mathematical Approaches to Image Processing with Carola Schönlieb

@ Y Combinator

Mathematical Approaches to Image Processing with Carola Schönlieb

05/10/18

Related Takeaways

Carola Schönlieb

05/10/18

@ Y Combinator

My PhD focused on image restoration, specifically using differential equations to solve problems similar to those addressed by Photoshop's content-aware fill.

Carola Schönlieb

05/10/18

@ Y Combinator

The technique used for image restoration is similar to the content-aware fill feature in Photoshop, but it predates Photoshop's development.

Carola Schönlieb

05/10/18

@ Y Combinator

The stability analysis of solutions to the Cahn-Hilliard equation helps understand how systems react to perturbations, particularly in the context of creating alloys.

Carola Schönlieb

05/10/18

@ Y Combinator

In my postdoc, I shifted towards inverse imaging problems, where the observed data is not a direct image but a transform, such as in CT scans.

Carola Schönlieb

05/10/18

@ Y Combinator

My first paper was on the Cahn-Hilliard equation, which describes phase separation in metallic alloys when cooled to a certain temperature.

Carola Schönlieb

05/10/18

@ Y Combinator

In collaborations with hospitals, we focus on developing algorithms that maximize the quality of high-resolution images from limited data, particularly in medical imaging.

Carola Schönlieb

05/10/18

@ Y Combinator

Successful image denoising methods focus on preserving edges, which are crucial for maintaining the integrity of the image's features.

Carola Schönlieb

05/10/18

@ Y Combinator

The idea of virtual restoration allows us to create digital copies of historical manuscripts without physically altering them, preserving their original state.

Carola Schönlieb

05/10/18

@ Y Combinator

Denoising is integrated into the image reconstruction process, addressing both the lack of data and the noise present in measurements.