Transformations between rotational and translational invariants formulated in reciprocal spaces

Area of Science:

• * Physics
• * Computer Vision
• * Structural Biology

Background:

• * Correlation functions are crucial in physical sciences, particularly scattering theory.
• * Their application has expanded to computer vision and cryo-electron microscopy (cryoEM) for object classification.
• * EMAN2 software utilizes third order invariants in Fourier space for its primary classification scheme.

Purpose of the Study:

• * To explore formal and practical aspects of multispectral invariants.
• * To develop efficient classification methods for cryoEM image processing.
• * To enhance the speed and accuracy of pattern recognition in complex datasets.

Main Methods:

• * Formulation of invariants in the most compact signal representation.
• * Explicit construction of transformations between invariants across different orientations, orders, and dimensions.
• * Application of third order invariants in Fourier space for classification.

Main Results:

• * A factor of 8 speed-up in classification procedures within the EMAN2 pipeline.
• * Demonstrated ability of third order invariants to distinguish 2D mirrored patterns, unlike the radial power spectrum.
• * Identification of limitations, including a family of patterns with vanishing third order invariants.

Conclusions:

• * Third order invariants provide a computationally efficient method for cryoEM image classification.
• * These invariants are effective in distinguishing certain types of patterns, crucial for classification efficacy.
• * While powerful, the limitations of third order invariants necessitate careful consideration for complex or specific pattern types.