Computer Vision News - September 2022

35 Weighted Metamorphosis for... method that was considered very hard and slow to implement a decade ago, ” he reveals. “ I implemented it in a modern fashion, with a GPU and everything, so it’s now competitive with deep learning methods, but it isn’t one. As mathematicians, we prefer to do things where we understand what’s happening! ” Could it be a new way to work in parallel to deep learning? “ Matthis Maillard , a PhD student working under Pietro Gori, is implementing the same kind of method as me, but from the deep learning point of view, ” he tells us. “ They’re very compatible. I’m developing the theory and the best algorithms we can apply to a low data population. If we want to process lots of data fast, deep learning is way faster than my methods at inference time. Matthis uses the same geodesics I am, but he’s running it, so it’s more dependent on the data. It’s an in- between method, but both our works are complementary . ” This WBIR paper is the first step in a more significant piece of work, which Anton will follow up with soon in his new journal paper, tentatively titled Constraint Metamorphosis . Could it be another winner? He laughs: “ If it’s a paper, it’s enough for me! ” registering two images without much data but perhaps some prior knowledge. LDDMM can also be used to build the shape space. “ We build the shape space by building the Karcher mean of all data and then connecting this data by the deformation from the mean, also called a template, ” Anton explains. “ When we have this shape space, we can do any statistics on it because it is a Hilbert space . For example, we can say we want to move from one point to another, and one point will be an image, and another point another image, which will have to be natural because of how we built the space. The path between the two spaces will be the registration. ” Anton is almost at the end of his thesis and hopes that afterward, someone, maybe Anton himself, will be able to make atlases with Metamorphosis . We cannot make atlases of glioblastoma or data with different topologies at the moment, but there may be a method to do so in the future. The use case for this work was images of the brain with glioblastoma, but the theory and the method are general. It doesn’t have to be applied to images; it could be points. What does Anton think the judges saw in the work that made it stand out from the competition? “ I have an old-school non-deep learning