Image modeling using inverse filtering criteria with application to textures.

Area of Science:

• Digital Image Processing
• Statistical Signal Processing
• Texture Analysis

Background:

• Traditional image modeling relies on first- and second-order statistics, limiting the capture of non-Gaussian random field phase properties.
• This often necessitates symmetric model parameters and spatial reversibility, assumptions not always valid for texture images.

Purpose of the Study:

• To develop and implement novel inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving-average (ARMA) image models.
• To utilize higher-than-second-order statistics for more comprehensive image modeling.

Main Methods:

• Derivation of two classes of inverse filtering criteria using higher-than-second-order statistics.
• Employment of Finite Impulse Response (FIR) inverse filters to handle models with zeros on the unit bicircle.
• Identification of the minimal set of cumulant lags for model identifiability.

Main Results:

• Successful parameter estimation for asymmetric noncausal ARMA image models.
• Demonstration that the proposed FIR inverse filters can handle models with zeros on the unit bicircle.
• Establishment of estimator consistency and evaluation of performance through simulations, texture classification, and synthesis.

Conclusions:

• The proposed methods effectively estimate parameters for asymmetric noncausal ARMA image models, overcoming limitations of traditional approaches.
• Higher-order statistics and FIR inverse filters provide a more robust framework for image modeling, especially for textures.
• The study advances texture analysis and synthesis capabilities through improved statistical modeling.