Class of transforms invariant under shift, rotation, and scaling

Area of Science:

• Signal Processing
• Image Analysis
• Mathematical Transforms

Background:

• Traditional transforms often require extensive preprocessing for invariance.
• Achieving simultaneous shift, rotation, and scaling invariance is computationally challenging.
• Existing methods may not be suitable for direct application to multidimensional data.

Purpose of the Study:

• To introduce a new class of nonreversible transform.
• To achieve simultaneous invariance under shift, rotation, and scaling.
• To enable efficient processing of multidimensional data without preprocessing.

Main Methods:

• Developed a general transformation where the kernel incorporates the function to be transformed.
• Utilized a self-mapping approach to achieve inherent invariances.
• Designed the algorithm for direct application to multidimensional data.
• Explored fast implementation using look-up tables.

Main Results:

• The proposed transform demonstrates simultaneous invariance to shift, rotation, and scaling.
• The algorithm eliminates the need for preprocessing steps like centroid determination or coordinate transformation.
• The transform is applicable to multidimensional datasets.
• Fast implementation strategies using look-up tables are feasible.

Conclusions:

• The novel nonreversible transform offers a computationally efficient solution for invariant data analysis.
• This method simplifies signal and image processing pipelines by removing preprocessing requirements.
• The transform's applicability to multidimensional data and potential for fast implementation make it valuable for various scientific domains.