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This study introduces a polynomial expansion for optical invariant pattern recognition, enabling real-time implementation under various lighting conditions. The method achieves shift and scale invariance for robust pattern recognition applications.

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Area of Science:

Optics and Photonics
Image Processing
Computer Vision

Background:

Optical invariant pattern recognition is crucial for applications requiring consistent identification despite transformations.
Existing methods often face limitations in implementation flexibility or invariance capabilities.
The need for robust recognition techniques under diverse illumination conditions persists.

Purpose of the Study:

To propose a novel polynomial expansion for achieving optical invariant pattern recognition.
To develop a method theoretically implementable under both coherent and incoherent illumination.
To demonstrate the efficacy of the expansion for various invariance scenarios.

Main Methods:

A polynomial expansion is derived using the Gram-Schmidt algorithm applied to Laurent series.
Orthonormality is achieved through the Gram-Schmidt procedure.
The expansion order is determined by the selection of the initial Laurent term.

Main Results:

The proposed polynomial expansion results in a real function, suitable for diverse illumination.
The method is demonstrated to achieve shift-invariant and scale-invariant pattern recognition.
Effectiveness is shown for both one-dimensional and two-dimensional scale-invariant recognition tasks.

Conclusions:

The polynomial expansion offers a flexible and theoretically sound approach to optical invariant pattern recognition.
This method enhances the applicability of pattern recognition under varying illumination conditions.
The demonstrated invariance capabilities pave the way for advanced optical recognition systems.