  The magnitude of a finite metric space has recently emerged as a novel
invariant quantity, allowing to measure the effective size of a metric space.
Despite encouraging first results demonstrating the descriptive abilities of
the magnitude, such as being able to detect the boundary of a metric space, the
potential use cases of magnitude remain under-explored. In this work, we
investigate the properties of the magnitude on images, an important data
modality in many machine learning applications. By endowing each individual
images with its own metric space, we are able to define the concept of
magnitude on images and analyse the individual contribution of each pixel with
the magnitude vector. In particular, we theoretically show that the previously
known properties of boundary detection translate to edge detection abilities in
images. Furthermore, we demonstrate practical use cases of magnitude for
machine learning applications and propose a novel magnitude model that consists
of a computationally efficient magnitude computation and a learnable metric. By
doing so, we address the computational hurdle that used to make magnitude
impractical for many applications and open the way for the adoption of
magnitude in machine learning research.
