Publication Date

1-1-2023

Journal

Journal of Structural Biology: X

DOI

10.1016/j.yjsbx.2023.100089

PMID

37398937

PMCID

PMC10314203

PubMedCentral® Posted Date

6-2-2023

PubMedCentral® Full Text Version

Post-print

Published Open-Access

no

Keywords

Bispectrum, Wilson statistics, Shape analysis

Abstract

Correlation functions play an important role in the theoretical underpinnings of many disparate areas of the physical sciences: in particular, scattering theory. More recently, they have become useful in the classification of objects in areas such as computer vision and our area of cryoEM. Our primary classification scheme in the cryoEM image processing system, EMAN2, is now based on third order invariants formulated in Fourier space. This allows a factor of 8 speed up in the two classification procedures inherent in our software pipeline, because it allows for classification without the need for computationally costly alignment procedures. In this work, we address several formal and practical aspects of such multispectral invariants. We show that we can formulate such invariants in the representation in which the original signal is most compact. We explicitly construct transformations between invariants in different orientations for arbitrary order of correlation functions and dimension. We demonstrate that third order invariants distinguish 2D mirrored patterns (unlike the radial power spectrum), which is a fundamental aspects of its classification efficacy. We show the limitations of 3rd order invariants also, by giving an example of a wide family of patterns with identical (vanishing) set of 3rd order invariants. For sufficiently rich patterns, the third order invariants should distinguish typical images, textures and patterns.

ga1 (1).jpg (37 kB)
Graphical Abstract

Comments

Associated Data

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.