Image coding using Markov models with hidden states

Abstract

Summary form only given. Lossless image coding may be performed by applying arithmetic coding sequentially to probabilities conditioned on the past data. Therefore the model is very important. A new image model is applied to image coding. The model is based on a Markov process involving hidden states. An underlying Markov process called the slice process specifies D rows with the width of the image. Each new row of the image coincides with row N of an instance of the slice process. The N-1 previous rows are read from the causal part of the image and the last D-N rows are hidden. This gives a description of the current row conditioned on the N-1 previous rows. From the slice process we may decompose the description into a sequence of conditional probabilities, involving a combination of a forward and a backward pass. In effect the causal part of the last N rows of the image becomes the context. The forward pass obtained directly from the slice process starts from the left for each row with D-N hidden rows. The backward pass starting from the right additionally has the current row as hidden. The backward pass may be described as a completion of the forward pass. It plays the role of normalizing the possible completions of the forward pass for each pixel. The hidden states may effectively be represented in a trellis structure as in an HMM. For the slice process we use a state of D rows and V-1 columns, thus involving V columns in each transition. The new model was applied to a bi-level image (SO9 of the JBIG test set) in a two-part coding scheme.