Lossless predictive coding for images with Bayesian treatment

A Stochastic Model for Block Segmentation of Images Based on the Quadtree and the Bayes Code for It

In information theory, lossless compression of general data is based on an explicit assumption of a stochastic generative model on target data. However, in lossless image compression, researchers have mainly focused on the coding procedure that outputs the coded sequence from the input image, and the assumption of the stochastic generative model is implicit. In these studies, there is a difficulty in discussing the difference between the expected code length and the entropy of the stochastic generative model. We solve this difficulty for a class of images, in which they have non-stationarity among segments. In this paper, we propose a novel stochastic generative model of images by redefining the implicit stochastic generative model in a previous coding procedure. Our model is based on the quadtree so that it effectively represents the variable block size segmentation of images. Then, we construct the Bayes code optimal for the proposed stochastic generative model. It requires the summation of all possible quadtrees weighted by their posterior. In general, its computational cost increases exponentially for the image size. However, we introduce an efficient algorithm to calculate it in the polynomial order of the image size without loss of optimality. As a result, the derived algorithm has a better average coding rate than that of JBIG.

IPAD: Intensity Potential for Adaptive De-Quantization

Display devices at bit depth of 10 or higher have been mature but the mainstream media source is still at bit depth of eight. To accommodate the gap, the most economic solution is to render source at low bit depth for high bit-depth display, which is essentially the procedure of de-quantization. Traditional methods, such as zero-padding or bit replication, introduce annoying false contour artifacts. To better estimate the least-significant bits, later works use filtering or interpolation approaches, which exploit only limited neighbor information, cannot thoroughly remove the false contours. In this paper, we propose a novel intensity potential (IP) field to model the complicated relationships among pixels. The potential value decreases as the spatial distance to the field source increases and the potentials from different field sources are additive. Based on the proposed IP field, an adaptive de-quantization procedure is then proposed to convert low-bit-depth images to high-bit-depth ones. To the best of our knowledge, this is the first attempt to apply potential field for natural images. The proposed potential field preserves local consistency and models the complicated contexts well. Extensive experiments on natural, synthetic, and high-dynamic range image data sets validate the efficiency of the proposed IP field. Significant improvements have been achieved over the state-of-the-art methods on both the peak signal-to-noise ratio and the structural similarity.