Recursive Filter for Space-Variant Images Using Pre-Computed Kernels

The patent segments the filtering process into multiple passes, where each pass applies a smaller kernel. Instead of using one large kernel that requires O(n²) computations, the method divides the filtering into sequential steps, each handling a portion of the variance reduction, thereby reducing the computational burden per pass while achieving the same overall filtering effect.

The patent pre-calculates and stores filter kernels in a database before processing the image. These kernels are computed offline based on desired variance reduction factors, so that during actual image filtering, only lookup and application of pre-computed kernels is needed, eliminating the need for real-time kernel calculation and reducing computational complexity during the filtering operation.

The patent pre-calculates filter kernels with specific variance reduction properties and stores them in a database. During image filtering, the system looks up the appropriate pre-computed kernel based on the desired variance reduction factor and applies it directly, eliminating the need for real-time kernel parameter calculation for each pixel while maintaining filtering accuracy.

The patent uses pre-computed kernel copies stored in a database rather than recalculating kernels for each pixel. The same kernel parameters are copied and reused across multiple pixels that require similar variance reduction, significantly reducing the computational overhead while maintaining consistent filtering accuracy across the image.

The patent segments the recursive filtering into separate forward and backward passes, where each pass handles one direction of recursion independently. The forward pass processes the image from top to bottom, and the backward pass processes from bottom to top, with each pass using minimal memory for its direction-specific calculations, thereby reducing the total memory footprint compared to storing all intermediate results simultaneously.

The patent extracts and processes the causal and anti-causal filtering components separately in distinct passes. By separating the forward recursion (causal) and backward recursion (anti-causal) into independent processing stages, the system only needs to store intermediate results for the current pass being executed, rather than storing all intermediate results from both directions simultaneously, thus reducing memory requirements.