Deviation Magnification: Revealing Departures from Ideal Geometries by Neal Wadhwa, Tali Dekel, Donglai Wei, Frédo Durand, William T. Freeman.
Abstract:
Structures and objects are often supposed to have idealized geome- tries such as straight lines or circles. Although not always visible to the naked eye, in reality, these objects deviate from their idealized models. Our goal is to reveal and visualize such subtle geometric deviations, which can contain useful, surprising information about our world. Our framework, termed Deviation Magnification, takes a still image as input, fits parametric models to objects of interest, computes the geometric deviations, and renders an output image in which the departures from ideal geometries are exaggerated. We demonstrate the correctness and usefulness of our method through quantitative evaluation on a synthetic dataset and by application to challenging natural images.
The video for the paper is quite compelling:
Read the full paper here: http://people.csail.mit.edu/nwadhwa/deviation-magnification/DeviationMagnification.pdf
From the introduction to the paper:
Many phenomena are characterized by an idealized geometry. For example, in ideal conditions, a soap bubble will appear to be a perfect circle due to surface tension, buildings will be straight and planetary rings will form perfect elliptical orbits. In reality, however, such flawless behavior hardly exists, and even when invisible to the naked eye, objects depart from their idealized models. In the presence of gravity, the bubble may be slightly oval, the building may start to sag or tilt, and the rings may have slight perturbations due to interactions with nearby moons. We present Deviation Magnification, a tool to estimate and visualize such subtle geometric deviations, given only a single image as input. The output of our algorithm is a new image in which the deviations from ideal are magnified. Our algorithm can be used to reveal interesting and important information about the objects in the scene and their interaction with the environment. Figure 1 shows two independently processed images of the same house, in which our method automatically reveals the sagging of the house’s roof, by estimating its departure from a straight line.
Departures from “idealized geometry” make for captivating videos but there is a more subtle point that Deviation Magnification will help bring to the fore.
“Idealized geometry,” just like discrete metrics for attitude measurement or metrics of meaning, etc. are all myths. Useful myths as houses don’t (usually) fall down, marketing campaigns have a high degree of success, and engineering successfully relies on approximations that depart from the “real world.”
Science and computers have a degree of precision that has no counterpart in the “real world.”
Watch the video again if you doubt that last statement.
Whether you are using science and/or a computer, always remember that your results are approximations based upon approximations.
I first saw this in Four Short Links: 12 November 2015 by Nat Torkington.