Stereo image compression using wavelet coefficients morphology

Abstract

In this paper, we propose a new stereo image compression scheme that is based on the wavelet transform of both images and the disparity estimation between the stereo pair subbands. The two images are decomposed by using a Discrete Wavelet Transform (DWT) and coded by employing the morphological representation of the wavelet coefficients, which is a technique that exploits the intraband–interband statistical properties of them. The progressive pixel-to-pixel evaluation of the disparity has been incorporated to the morphological coder so that a dense disparity field to be formed for every subband. The proposed method demonstrates very good performance as far as PSNR measures and visual quality are concerned and low complexity.

Introduction

A stereo pair consists of two images of the same scene recorded from two slightly different perspectives. The two images are distinguished as the Left and the Right image and from the data of this pair the information in the depth-dimension of the shot scene can be evaluated. Moreover, one can perceive a 3D image of the scene, when at the same time his left eye sees the Left image and his Right eye sees the right image. Therefore, stereo image pairs provide a two-dimensional means to represent 3D scenes.

The stereoscopic vision has a very wide field of applications in robot vision, virtual machines, medical surgery etc. These stereo imaging applications require efficient compression techniques for fast transmission rates and small storage capacities. The way the stereo pair is constructed implies inherent redundant information in the two images. Consequently, a stereo pair is compressed more efficiently than the two images can independently be compressed, if this redundancy is exploited. A commonly used coding strategy in stereo pair compression is firstly to encode the Left image, which is called reference image, independently by taking into account its intra-spatial redundancy. Then the Right image, which is called target image, is encoded by taking into account both, its intra-spatial and the cross-image redundancy of the pair. Transform coding is a method used to remove intra-spatial redundancy both from the reference and the target images. The cross-image redundant information is evaluated by considering the disparity between the two images. The disparity estimation involves the disparity compensated prediction of the target image and produces the disparity compensated difference (DCD) or residual target image together with the disparity vectors (DVs) [1]. As, usually, the Left and Right images are taken by two cameras with parallel optical axes and coplanar image planes, DVs can be represented by scalars. The disparity compensated prediction applies either on the spatial or transform domain of the images. If the transform domain consists of the multiresolution subbands of a wavelet transform, then this approach is referred as wavelet-based disparity analysis.

Several methods have been developed for disparity estimation. The area-based methods, including either pixel or line or area matching, are simple approaches of the disparity estimation [2], [3]. The pixel-based disparity estimation method finds the distance between the pixels of the two images that have similar intensity. The advantages of this method are the small disparity distances in homogeneous areas and its simple form. The block-based matching method, either fixed or variable size (FSBM or VSBM), finds the distance between two blocks that have similar intensities. A simple method is by comparing and shifting horizontally a predefined block of one image with the corresponding equal sized block of the other image. This is repeated within a predefined window length and the DV is estimated for the best match [4]. The block-matching algorithm may also be applied on the objects that appear after the object contour extraction in the two images [5] or on the subbands of a wavelet decomposed stereo image pair, in a hierarchical way [6]. The most commonly used similarity measures are the mean-square error (MSE) and the mean absolute error (MAE), which is generally preferred due to its simplicity.

Some methods code the residual part of the predicted target image by using efficient coders for ‘still’ images, as zero tree wavelet coder (EZW), or mixed coding [7], [8], [9], [10], [11]. Another method predicts the blocks transform of one image from the matching blocks transform of the other [12]. Another method is the subspace projection technique that combines disparity compensation and residual coding by applying a transform to each block of the target image [13].

The aim of the present study is to employ a robust ‘still’ image encoder and to embed the disparity estimation process into it. The proposed coder decomposes both images of the stereo pair by a Discrete Wavelet Transform (DWT) and then employs the Morphological Representation of Wavelet Data (MRWD) encoder. Firstly, the morphological coder encodes the reference image. Then, the morphological coder starts encoding the target image and during this process it produces the residual target image, which is the difference of the subband coefficients of the original target image with the predicted ones after a pixel-to-pixel matching with the reference image. The term pixel-to-pixel matching, which is used throughout this work, refers to the subband coefficients of the wavelet transformed image. Alternatively, the coder completes the formation of the clusters in the subbands, which are groups of significant coefficients, and then produces the residual target image after a cluster-to-cluster matching. Finally, the reference image, the residual target image and the DVs are entropy coded and transmitted.

The encoding algorithm exploits the statistical properties of the wavelet coefficients to form clusters and uses a morphological operator to efficiently encode the significant ones together with their positions [14]. The coarsest detail subbands are partitioned into significant and insignificant coefficients and the corresponding coefficients of the finer subbands are predicted by morphology causing the entropy of the resulting partitions to be lower than if the subbands were encoded as a whole. This algorithm provides a simple and efficient way of coding a ‘still’ image and is applied to the constituent images of a stereo pair, as that of Fig. 1.

The disparity field in this paper, which consists of the DV and the DCD, is estimated simultaneously with the morphological operations on the subbands in order to form a single framework. This is very important since the disparity compensated subband coefficients and the DVs of the residual target image form partitions, which lower their entropy. The disparity estimation has been implemented with pixel-to-pixel and cluster-to-cluster matching. The pixel-to-pixel matching allows the estimation of a dense disparity field when a better quality image is required, whereas the cluster-to-cluster matching allows the estimation of a sparse disparity field when low complexity is required.

The outstanding features of this proposed novel method are the inherent advantages of the wavelet transform, the morphological compression algorithm and the incorporation of the disparity estimation process into it. The main assets of the wavelet transform are the creation of almost uncorrelated coefficients, energy compaction and variable resolution. The morphological coder creates partitions between significant and insignificant coefficients that reduce the entropy. The proposed disparity estimation method builds dense disparity fields, avoids the blocking artifacts of the block matching methods and is of low complexity.

This paper is organized as follows: Section 2 provides an overview of the proposed coding algorithm and the disparity estimation. In Section 3 the proposed algorithm is explained and experimental results are presented in Section 4. Finally, conclusions are summarized in Section 5.