This paper presents a novel, highly distinctive and robust local surface feature descriptor. Our descriptor is predicated on a simple observation: instead of describing the points in the vicinity of a feature point relative to a reference frame at the feature point, all points in the region describe the feature point relative to their own frames. Isometry invariance is a byproduct of this construction. Our descriptor is derived relative to the extended convolution – a generalization of the standard convolution that allows the filter to adaptively transform as it passes over the domain. As such, we name our descriptor the Extended Convolution Histogram of Orientations (ECHO). It exhibits superior performance compared to popular surface descriptors in both feature matching and shape correspondence experiments. In particular, the ECHO descriptor is highly stable under near-isometric deformations and remains distinctive under significant levels of noise, tessellation, complex deformations and the kinds of interference commonly found in real data.

@article{Mitchel:2020:EEC,
   author = "Thomas W. Mitchel and Szymon Rusinkiewicz and Gregory S. Chirikjian and
      Michael Kazhdan",
   title = "{ECHO}: Extended Convolution Histogram of Orientations for Local
      Surface Description",
   journal = "Computer Graphics Forum",
   year = "2021",
   month = feb,
   volume = "40",
   number = "1",
   pages = "180--194"
}