Research on the Robustness of Focus Measure Operators Based on RRMSE

Area of Science:

• Image processing
• Computer vision
• Signal processing

Background:

• Focus measure operators are crucial for image autofocusing.
• Their performance degrades under noisy conditions.
• Existing methods lack quantitative robustness analysis.

Purpose of the Study:

• To establish a quantitative model for the relationship between RRMSE and noise parameters.
• To introduce a novel metric, the noise response slope, for evaluating operator robustness.
• To analyze the robustness of squared-type and absolute-value type focus measure operators.

Main Methods:

• Theoretical derivation of RRMSE dependence on noise variance (σ²) and standard deviation (σ).
• Classification of operators into squared-type and absolute-value type based on operation structure.
• Experimental validation using linear regression fitting on selected operators.

Main Results:

• Squared-type operators' RRMSE is proportional to σ², while absolute-value type operators' RRMSE is proportional to σ at high noise levels.
• High coefficient of determination (>0.999 for squared-type, >0.98 for absolute-value type) validates the model.
• Experimental slopes closely match theoretical values, with minor discrepancies in specific image sequences.

Conclusions:

• The proposed noise response slope effectively characterizes operator robustness.
• The model allows for robustness estimation without adding noise, aiding operator design.
• This provides an analytical method for evaluating focus measure operator robustness.