Fast and Efficient Calculations of Structural Invariants of Chirality

  title={Fast and Efficient Calculations of Structural Invariants of Chirality},
  author={He Zhang and Hanlin Mo and You-Zeng Hao and Shirui Li and Hua Li},
  journal={Pattern Recognit. Lett.},

Differential and integral invariants under Mobius transformation

This work focuses onMobius transformation and proposes two differential expressions that are invariable under 2-D and 3-D Mobius transformation respectively and a conjecture about the structure of differential invariant under conformal transformation according to the observation on the composition of the above two differential invariants.

Dual affine moment invariants

A general framework to derive moment invariants under DAT for objects in M-dimensional space with N channels is proposed, which can be called dual-affine moment invariant (DAMI), which proves that DAMI is robust for DAT.

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

A comprehensive survey of the orthogonal moments for image representation, covering recent advances in fast/accurate calculation, robustness/invariance optimization, definition extension, and application.



A moment invariant for evaluating the chirality of three-dimensional objects

It is shown that the occurrence of the conformations of the macromolecular polypeptide backbone is related to the value of the CI of the constituting peptide fragments, and how the CI can be used to assess the quality of a crystallographic electron density map.

On Quantifying Chirality

Since Pasteur's epochal discoveries a century and a half ago, the concept of chirality has continued to play a central role in chemistry and biochemistry. Can chirality be measured? It has long been

Shape DNA: Basic Generating Functions for Geometric Moment Invariants

This paper shows that Hu's seven well known GMIs in computer vision have a more deep structure, which can be further divided into combination of simpler PIs, which are simpler to use, and some of which are newly reported.

Chirality and Symmetry Measures: A Transdisciplinary Review

Relations between chirality, symmetry, and other concepts such as similarity, disorder and entropy, are discussed.

Chiral Derivatives of Achiral Molecules: Standard Classes and the Problem of a Right‐Left Classification

Chemistry judging by its applications, physics according to its methods, and heavily reliant upon the tools of mathematics—that is what makes theoretical chemistry. And yet that is where its strength

Partial and approximate symmetry detection for 3D geometry

A new algorithm is presented that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries, which captures important high-level information about the structure of a geometric model which enables a large set of further processing operations.

Reflection Invariant and Symmetry Detection

Reflection invariants are introduced and the directional moment to detect symmetry for shape analysis and object recognition is defined and it is demonstrated that all the reflection lines or planes can be deterministically found using directional moments up to order six.

Three-Dimensional Moment Invariants

  • F. SadjadiE. Hall
  • Mathematics
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 1980
A set of three-dimensional moment invariants which are invariant under size, orientation, and position change is proposed which is highly significant in compressing the data which are needed in three- dimensional object recognition.

Registration for 3D surfaces with large deformations using quasi-conformal curvature flow

A novel method for registering 3D surfaces with large deformations is presented, which is based on quasi-conformal geometry and uniquely determines the registration mapping by solving Beltrami equations using curvature flow.