Dense Scale Invariant Descriptors for Images and Surfaces

Local descriptors are ubiquitous in image and shape analysis, as they allow the compact and robust description of the local content of a signal (image or 3D shape). A common problem that emerges in the computation of local descriptors is the variability of the signal scale. The standard approach to cope with this is scale selection, which consists in estimating a characteristic scale around the few image or shape points where scale estimation can be performed reliably. However, it is often desired to have a scale-invariant descriptor that can be constructed densely, namely at every point of the image or 3D shape. In this work, we construct scale-invariant signal descriptors by introducing a method that does not rely on scale selection; this allows us to apply our method at any point. Our method relies on a combination of logarithmic sampling with multi-scale signal processing that turns scaling in the original signal domain into a translation in a new domain. Scale invariance can then be guaranteed by computing the Fourier transform magnitude (FTM), which is unaffected by signal translations. We use our technique to construct scale- and rotation- invariant descriptors for images and scale- and isometry-invariant descriptors for 3D surfaces, and demonstrate that our descriptors outperform state-of-the-art descriptors on standard benchmarks.