Amplitude compensated matched filters using circular harmonic expansion and a Mellin transform

Area of Science:

• Optical signal processing
• Image recognition and analysis

Background:

• Classical matched spatial filtering (MSF) faces limitations in discrimination and autocorrelation peak sharpness.
• Existing techniques often lack invariance to rotation or scale changes, crucial for real-world applications.

Purpose of the Study:

• To introduce and evaluate novel amplitude compensated matched filtering techniques.
• To demonstrate enhanced discrimination and autocorrelation properties compared to classical MSF.
• To achieve rotation and scale invariance using specific advanced filtering methods.

Main Methods:

• Development and application of amplitude compensated circular harmonic expansion (AC-CHE) matched filtering.
• Development and application of amplitude compensated Mellin transform (AC-MT) matched filtering.
• Computer simulations to verify performance and compare with classical matched spatial filtering.

Main Results:

• AC-CHE and AC-MT filtering significantly improve discrimination capabilities.
• Sharper autocorrelation peaks are achieved, enhancing localization accuracy.
• AC-CHE filtering demonstrates rotation invariance.
• AC-MT filtering demonstrates scale invariance.

Conclusions:

• The presented AC-CHE and AC-MT techniques offer substantial improvements over classical matched spatial filtering.
• These novel methods provide valuable rotation and scale invariance, expanding applicability in pattern recognition.
• Computer simulations validate the unique advantages and effectiveness of the proposed amplitude compensated filtering approaches.