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

The Gibbs random field (GRF) has proved to be a simple and practical way of parameterizing the Markov random field, which has been widely used to model an image or image-related process in many image processing applications. In particular, the GRF can be employed to construct an efficient Bayesian estimation that often yields optimal results. We describe how the GRF 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 discrete-cosine-transform-based low-bit-rate image compression where GRF has been used to design an enhancement algorithm that reduces the blocking effect and ringing effect while still preserving the image details. The third example is the integration of GRF in a wavelet subband coding of video signals in which the high-frequency bands are segmented and quantized with spatial constraints specified by a GRF, and the subsequent enhancement of the decompressed images is accomplished by smoothing with another type of GRF. With these diverse examples, we are able to demonstrate that various features of images can all be properly characterized by a GRF. The specific form of the GRF can be selected according to the characteristics of an individual application. We believe that the GRF is a powerful tool to exploit the spatial dependency in various images, and is applicable to many image processing tasks.