On the applications of Gibbs random field in image processing: from segmentation to enhancement

The Gibbs random field (GRF) has been proved to be a simple and practical way of parameterizing the Markov random field (MRF) which has been widely used to model an image or image related process in many image processing applications. In particular, Gibbs random field can be employed to construct an efficient Bayesian estimation that often yields optimal results. In this paper, we describe how the Gibbs random field can be efficiently incorporated into optimization processes in several representative applications, ranging from image segmentation to image enhancement. One example is the segmentation of CT volumetric image sequence in which the GRF has been incorporated into K-means clustering to enforce the neighborhood constraints. Another example is the artifact removal in DCT based low bit rate image compression in which GRF has been used to design an enhancement algorithm that smooths the artificial block boundary as well as ringing pattern while still preserve the image details. The third example is an elegant integration of GRF into a wavelet subband coding of video signals in which the high-frequency bands are segmented with spatial constraints specified by a GRF while the subsequent enhancement of the decompressed images is accomplished with the smoothing function specified by another corresponding GRF. With these diverse examples, we are able to demonstrate that various features of images can all be properly characterized by a Gibbs random field. The specific form of the Gibbs random field can be selected according to the characteristics of an individual application. We believe that Gibbs random field is a powerful tool to exploit the spatial dependency in various images, and is applicable to many other image processing tasks.