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A new method for lossy compression of bilevel images based on Markov random fields (MRFs) is proposed. It preserves key structural information about the image, and then reconstructs the smoothest image that is consistent with this information. The smoother the original image, the lower the required bit rate, and conversely, the lower the bit rate, the smoother the approximation provided by the decoded image. The main idea is that as long as the key structural information is preserved, then any smooth contours consistent with this information will provide an acceptable reconstructed image. The use of MRFs in the decoding stage is the key to efficient compression. Experimental results demonstrate that the new technique outperforms existing lossy compression techniques, and provides substantially lower rates than lossless techniques (JBIG) with little loss in perceived image quality.

An effective, low complexity method for lossy compression of scenic bilevel images, called lossy cutset coding, is proposed based on a Markov random field model. It operates by losslessly encoding pixels in a square grid of lines, which is a cutset with respect to a Markov random field model, and preserves key structural information, such as borders between black and white regions. Relying on the Markov random field model, the decoder takes a MAP approach to reconstructing the interior of each grid block from the pixels on its boundary, thereby creating a piecewise smooth image that is consistent with the encoded grid pixels. The MAP rule, which reduces to finding the block interiors with fewest black-white transitions, is directly implementable for the most commonly occurring block boundaries, thereby avoiding the need for brute force or iterative solutions. Experimental results demonstrate that the new method is computationally simple, outperforms the current lossy compression technique most suited to scenic bilevel images, and provides substantially lower rates than lossless techniques, e.g., JBIG, with little loss in perceived image quality.

We discuss a new approach for lossy compression of bilevel images based on Markov random fields (MRFs). The goal is to preserve key structural information about the image, and then reconstruct the smoothest image that is consistent with this information. The image is compressed by losslessly coding the pixels in a square grid of lines and adding bits when needed to preserve structural information. The decoder uses the MRF model to reconstruct the interior of each block bounded by the grid, based on the pixels on its boundary, plus the extra bits provided for certain blocks. The idea is that, as long as the key structural information is preserved, then the smooth contours of the block having highest probability with respect to the MRF provides acceptable reconstructions. We propose and consider objective criteria for both encoding and evaluating the quality and structure preserving properties of the coded bilevel images. These include mean-squared error, MRF energy (smoothness), and connected components (topology). We show that overall, for comparable mean-squared error, the new approach provides perceptually superior reconstructions than existing lossy compression techniques at lower encoding rates.

In this paper we explore tradeoffs, regarding coding performance, between the thickness and spacing of the cutset used in Reduced Cutset Coding (RCC) of a Markov random field image model [10]. Considering MRF models on a square lattice of sites, we show that under a stationarity condition, increasing the thickness of the cutset reduces coding rate for the cutset, increasing the spacing between components of the cutset increases the coding rate of the non-cutset pixels, though the coding rate of the latter is always strictly less than that of the former. We show that the redundancy of RCC can be decomposed into two terms, a correlation redundancy due to coding the components of the cutset independently, and a distribution redundancy due to coding the cutset as a reduced MRF. We provide analysis of these two sources of redundancy. We present results from numerical simulations with a homogeneous Ising model that bear out the analytical results. We also present a consistent estimation algorithm for the moment-matching reduced MRF for the cutset U .