A novel set of rotationally and translationally invariant features for images based on the non-commutative bispectrum

By Risi Kondor. 2007

43 citations recorded by the source corpus.

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the original image than most existing systems of invariants. Our construction is based on the generalization of the concept of bispectrum to the three-dimensional rotation group SO(3), and a projection of the image onto the sphere.

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Citations in the corpus

Group Equivariant Convolutional Networks (2016, methodology): “Invariance can be achieved by pose normalization using an equivariant detector (Lowe, 2004; Jaderberg et al., 2015) or by averaging a possibly nonlinear function over a group (Reisert, 2008; Skibbe, 2013; Manay et al., 2006; Kondor, 2007).”
On representing chemical environments (2012, methodology): “Using some basic concepts from representation theory, we now prove that the second-order bond-order parameters are indeed rotationally invariant, then we show a more general set of third order invariants, 35 of which the Q s and the W s are a subset.”
The skew spectrum of graphs (2008, background): “Copyright 2008 by the author(s)/owner(s).”
Group theoretical methods in machine learning (2008, methodology): “This work was published in preprint form in [Kondor, 2007a].”
Bispectrum Inversion with Application to Multireference Alignment (2017, background): “The more general setting of bispectrum over compact groups was considered in [57]–[60].”