Binary Image Generation Using Ordered Dithering Algorithm

This documentation elaborates on the process of generating binary images using ordered dithering algorithms, including Bayer D4 and D8 matrices. Ordered dithering is a widely used image processing technique that converts continuous grayscale values into binary images by comparing pixel values with specific thresholds from dither matrices. For D4 and D8 matrices, different threshold comparisons yield varying dithering effects. In MATLAB implementation, this involves creating Bayer matrices of sizes 4×4 and 8×8 respectively, then performing element-wise comparison between the grayscale image and the tiled matrix pattern using threshold operations. The algorithm can be implemented using matrix replication and logical indexing for efficient pixel processing.

Additionally, we describe the error diffusion algorithm using Floyd-Steinberg filter for binary image generation. This error diffusion method maintains finer details and smoother transitions by redistributing quantization errors to neighboring pixels. The algorithm propagates the current pixel's quantization error to adjacent pixels according to specific weight distributions (typically 7/16 to right, 3/16 below-left, 5/16 below, 1/16 below-right). MATLAB implementation requires sequential pixel scanning with error accumulation, where each pixel's binarization error is distributed to its neighbors using predefined filter weights. This approach preserves image details through error propagation while achieving smooth tonal transitions.

In summary, both ordered dithering (Bayer D4/D8 matrices) and error diffusion (Floyd-Steinberg filter) methods produce binary images with distinct characteristics. These techniques allow adjustable dithering intensity and detail preservation levels, enabling optimized results for specific application requirements. The MATLAB code typically involves matrix operations for ordered dithering and iterative error propagation for diffusion algorithms, with both methods supporting grayscale-to-binary conversion through different quantization strategies.