Modified Closed-form Based Image Matting Algorithm

I have developed a modified version of the closed-form matting algorithm that achieves approximately twice the computational speed compared to the original foreign implementation. The enhanced algorithm maintains the core mathematical formulation while optimizing key computational steps, particularly in solving the large sparse linear systems using more efficient matrix operations. This implementation enables effective foreground extraction from images with complex backgrounds through minimal user interaction. Users simply need to draw a few foreground strokes (indicating definite foreground regions) and background strokes (marking definite background areas). The algorithm then employs the closed-form solution to compute alpha mattes by solving the sparse linear system derived from the color line model, where neighboring pixels with similar colors are constrained to have similar alpha values. Key optimizations include: - Improved handling of the Laplacian matrix construction - Optimized linear system solver selection based on matrix properties - Enhanced memory management for large image processing - Parallel processing implementation for matrix operations The resulting alpha matte accurately separates foreground objects from challenging backgrounds, making it particularly suitable for images with complex textures and color variations.