Image Filtering Using Histograms for Large Pixel Value Ranges

The patent segments the continuous Gaussian spatial weighting function into discrete rectangular regions with constant weights. Instead of computing continuous Gaussian weights for each pixel pair, the image space is divided into rectangular zones where pixels within each zone share the same weight, reducing the computational burden while preserving the essential spatial decay behavior of the Gaussian function.

The patent changes the functional form of the spatial component from a continuous Gaussian function to a piecewise constant rectangular function. This parameter transformation allows the use of histogram-based techniques and reduces the computational complexity from O(n2) to O(n) operations per pixel, while maintaining the filtering effect through adjusted weight parameters.

The patent introduces a new dimension by combining spatial segmentation (rectangular regions in image space) with value-range segmentation (histograms). This two-dimensional approach allows the use of histograms not just for value distribution but also for spatial region characterization, enabling efficient filtering even when pixel values span large ranges by creating region-specific histograms that capture local statistics.

The patent performs preliminary computation by pre-calculating histograms for rectangular regions and storing them for reuse. These pre-computed histograms capture the distribution of pixel values within each spatial region, allowing subsequent filtering operations to quickly query and combine these pre-existing statistics rather than computing everything from scratch for each pixel.

The patent segments the large filter radius area into multiple rectangular regions, each with its own pre-computed histogram. Instead of processing all pixels within the large radius individually, the segmentation allows the algorithm to aggregate statistics from multiple regions efficiently, reducing the time complexity from quadratic to linear with respect to the filter radius while maintaining comprehensive coverage of the neighborhood.

The patent performs preliminary computation of histograms for all rectangular regions before the actual filtering pass. This pre-computation stores the essential statistical information needed for filtering, so that during the filtering phase, the algorithm only needs to query and combine these pre-existing histograms rather than re-processing the raw pixel data, significantly reducing processing time for large filter radii.