3D rotation invariants by complex moments

Suk, Tomáš; Flusser, Jan; Boldyš, Jiří

doi:10.1016/j.patcog.2015.05.007

Cited by 25 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar approach was followed by Canterakis [31] and later Novotni and Klein [32] who both used Zernike polynomials [33] as radial basis functions to arrive at 3D rotation invariants. More recent work by Suk et al [34] has demonstrated a systematic way of arriving at independent invariants from complex moments which we detail below.…”

Section: B Spherical Harmonic Based Momentsmentioning

confidence: 99%

“…The flexibility to expand to arbitrary order is particularly appealing given the recent evidence that three-and four-body atomcentered features are insufficient to unambiguously describe all possible atomic environments [11]. We follow the procedure of Suk et al [34] who use ideas from Lo and Hon-Son [30] and encourage the reader to refer to these sources for a more complete description.…”

Section: Rotation Invariantsmentioning

confidence: 99%

See 1 more Smart Citation

Through the eyes of a descriptor: Constructing complete, invertible descriptions of atomic environments

Uhrin

2021

Phys. Rev. B

View full text Add to dashboard Cite

In this work we apply methods for describing three-dimensional images to the problem of encoding atomic environments in a way that is invariant to rotations, translations, and permutations of the atoms and, crucially, can be decoded back into the original environment modulo global orientation without the need for training a model. From the point of view of decoding, the descriptor is optimally complete and can be extended to arbitrary order, allowing for a systematic convergence of the fidelity of the description. In experiments on molecules ranging from 3 to 29 atoms in size, we demonstrate that positions can be decoded with a 97% success rate and positions plus species with a 70% rate of success, rising to 95% if a second fingerprint is used. In all cases, consistent recovery is observed for molecules with 17 or fewer atoms. Additionally, we evaluate the descriptor's performance in predicting the energies and forces of bulk Ni, Cu, Li, Mo, Si, and Ge by means of a neural network model trained on DFT data. When comparing to six machine learning interaction potential methods that use various descriptors and regression schemes, our descriptor is found to be competitive, in several cases outperforming well established methods. The combined ability to both decode and make property predictions from a representation that does not need to be learned lays the foundations for a novel way of building generative models that are tasked with solving the inverse problem of predicting atomic arrangements that are statistically likely to have certain desired properties.

show abstract

Section: B Spherical Harmonic Based Momentsmentioning

confidence: 99%

Section: Rotation Invariantsmentioning

confidence: 99%

Through the eyes of a descriptor: Constructing complete, invertible descriptions of atomic environments

Uhrin

2021

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Due to a recent development of 3D imaging devices and technologies, which have become widely accessible, 3D rotation moment invariants started to attract an increasing attention of the researchers [30,31,32,33,34,35,36]. The problem of numerical instability of non-orthogonal moments appears in 3D even more seriously because it influences lower moment orders than in 2D.…”

Section: Extension To 3dmentioning

confidence: 99%

Rotation of 2D orthogonal polynomials

Yang

Flusser

Kautský

2018

Pattern Recognition Letters

Self Cite

View full text Add to dashboard Cite

Orientation-independent object recognition mostly relies on rotation invariants. Invariants from moments orthogonal on a square have favorable numerical properties but they are difficult to construct. The paper presents sufficient and necessary conditions, that must be fulfilled by 2D separable orthogonal polynomials, for being transformed under rotation in the same way as are the monomials. If these conditions have been met, the rotation property propagates from polynomials to moments and allows a straightforward derivation of rotation invariants. We show that only orthogonal polynomials belonging to a specific class exhibit this property. We call them Hermite-like polynomials.

show abstract

“…For the first time, the 3D moment invariants of the second order were derived in the paper [5]. In [6], Lo and Don found twelve invariants of the third order, but as it was shown in [7] there are several interdepended among them. In the book [8], the author derived 13 invariants and stated that they generate all 3D geometric moments of the third order.…”

Section: Introductionmentioning

confidence: 98%

“…Today, there exists a huge massive of the literature on the 3D geometric moments invariants, but a big amount of it is devoted to the application of the invariants, along with the different ways of their constructions which sometimes are rather elegant and ingenious. For instance, the methods of the quantum mechanics used in [6], [7] and [10] are very impressive.…”

Section: Introductionmentioning

confidence: 99%

2D Geometric Moment Invariants from the Point of View of the Classical Invariant Theory

Bedratyuk

2020

J Math Imaging Vis

View full text Add to dashboard Cite

Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the algebras of joint polynomial and rational SO(2)-invariants of binary forms. Also, to simplify the calculating of invariants we pass from an action of Lie group SO(2) to an action of its Lie algebra so 2 . This allow us to reduce the problem to standard problems of the classical invariant theory.

show abstract

3D rotation invariants by complex moments

Cited by 25 publications

References 18 publications

Through the eyes of a descriptor: Constructing complete, invertible descriptions of atomic environments

Through the eyes of a descriptor: Constructing complete, invertible descriptions of atomic environments

Rotation of 2D orthogonal polynomials

2D Geometric Moment Invariants from the Point of View of the Classical Invariant Theory

Contact Info

Product

Resources

About