Image Equalization Using Weibull Space Segmentation

The patent segments the pixel intensity distribution into multiple amplitude regions (e.g., dark, mid-tone, bright regions) and applies separate best-fit line analysis to each region in Weibull space. This segmentation allows targeted adjustment of different intensity ranges, improving overall image quality by addressing specific distribution deficiencies in each region rather than applying a uniform transformation.

The patent transforms the pixel intensity analysis from linear space to Weibull space (a logarithmic transformation of the cumulative distribution function). This dimensional change enables better visualization and fitting of the amplitude regions, allowing more precise control over the equalization process and resulting in superior image quality that conventional linear methods cannot achieve.

The patent applies different equalization strategies to different amplitude regions based on their local characteristics. Each region's best-fit line in Weibull space is determined independently, allowing the transformation to preserve local features and characteristics while achieving global balance. This local quality approach ensures that dark regions, mid-tones, and bright areas each maintain their distinctive properties while contributing to an overall balanced image.

The patent changes the parameter space from linear intensity values to Weibull-transformed cumulative distribution values. By working in this transformed parameter space, the method can achieve better distribution control while maintaining the underlying structure and characteristics of different amplitude regions, thus avoiding information loss while achieving visual balance.

The patent performs preliminary analysis by fitting best lines to amplitude regions in Weibull space before applying the final equalization transformation. This preliminary action identifies the characteristic patterns of different regions, allowing the subsequent equalization step to be more efficient and effective. By preparing the data in this structured way beforehand, the method achieves superior image quality while managing computational resources through organized preprocessing.

The patent replaces conventional linear equalization mechanisms with a Weibull-space transformation approach. This substitution introduces a more sophisticated mathematical framework that better captures the non-linear relationships in pixel intensity distributions, resulting in enhanced image quality that justifies the additional computational resources required by this more advanced method.