Embedded Graphics Coding (EGC) is used to encode images with sparse histograms. In EGC, an image is divided into blocks of pixels. For each block, the pixels are converted into binary representations. For each block, the pixels are scanned and encoded bit-plane by bit-plane from the most significant bit-plane (MSB) to the least significant bit-plane (LSB). The pixels in the block are partitioned into groups. Each group contains pixels with the same value. From the MSB to the LSB, the groups in the current bit plane are processed. During the processing, a group is split into two, if pixels in the group have different bit values in the bit-plane being encoded. Then, the encoder sends the refinement bit for each pixel in the group and the encoder splits the original group into two. A method is described herein to compress the refinement bits which employs context-adaptive prediction and binary run-length coding.