Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 613714, 12 pages

http://dx.doi.org/10.1155/2015/613714

## A Novel High Efficiency Fractal Multiview Video Codec

Department of Measurement Control and Information Technology, School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China

Received 17 July 2014; Accepted 15 September 2014

Academic Editor: Guido Maione

Copyright © 2015 Shiping Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Multiview video which is one of the main types of three-dimensional (3D) video signals, captured by a set of video cameras from various viewpoints, has attracted much interest recently. Data compression for multiview video has become a major issue. In this paper, a novel high efficiency fractal multiview video codec is proposed. Firstly, intraframe algorithm based on the H.264/AVC intraprediction modes and combining fractal and motion compensation (CFMC) algorithm in which range blocks are predicted by domain blocks in the previously decoded frame using translational motion with gray value transformation is proposed for compressing the anchor viewpoint video. Then temporal-spatial prediction structure and fast disparity estimation algorithm exploiting parallax distribution constraints are designed to compress the multiview video data. The proposed fractal multiview video codec can exploit temporal and spatial correlations adequately. Experimental results show that it can obtain about 0.36 dB increase in the decoding quality and 36.21% decrease in encoding bitrate compared with JMVC8.5, and the encoding time is saved by 95.71%. The rate-distortion comparisons with other multiview video coding methods also demonstrate the superiority of the proposed scheme.

#### 1. Introduction

In recent years, multiview video (MVV) is attracting considerable attention. This is because MVV can provide consumers with depth sense to the observed scene as if it really exists in front of consumers, allow consumers to freely change views, and interactively modify the properties of a scene. This type of video may be offered in the future home electronics devices, such as immersive teleconference, 3DTV [1], 3 D mobile phone, and home video camcorder. For example, in immersive teleconference, there is an interaction between consumers. Participants at different geographical sites meet virtually and see each other in either free viewpoint or 3DTV style. The immersiveness provides a more natural way of communications. However, in such a low bit rate communication channel such as the wireless mobile network, owing to the insufficient bit budget, MVV compression will cause the heavy loss of visual detail information.

MVV contains a large amount of statistical dependencies since it is a collection of multiple videos simultaneously captured in a scene at different camera locations. Therefore, efficient compression techniques are required for the above consumer electronic applications [2].

Fractal compression, which has the advantages of high compression ratio, resolution independence, and fast decoding speed, is considered as one of the most promising compression methods. The basic idea of fractal image coding is to find a contractive mapping whose unique attractor approximates the original image. For the decoding, an arbitrary image with the same size of the original image is input into the decoder, and, after several times of iteratively applying the recorded contractive mappings to the input image, the reconstructed image will be obtained. Much effort [3–5] has been made to the fractal still image compression after Jacquin’s fractal block coding algorithm [6]. However, a little work has been reported on the fractal video compression, let alone the fractal multiview video compression [7]. For fractal video compression, there are two extensions of still image compression, which are cube-based compression [8] and frame-based compression [9]. In the former method, video sequences are partitioned into nonoverlapping 3D range blocks and overlapping 3D domain blocks with larger size than range blocks. Then the key issue turns to find the best matching domain cuboid and the corresponding contractive mapping for every range cuboid, which is very complicated. In the latter method, each frame is encoded using the previous frame as a domain pool except the first frame which is encoded using a still image fractal scheme or some other methods. The main advantage of the frame-based algorithm is that decoding a frame consists of just one application of mapping so that iteration is not required at the decoder. However, the temporal correlation between the frames may not be effectively exploited, since the size of the domain block is larger than that of the range block [10].

In this paper, a novel highly efficient fractal multiview video codec by combined temporal/interview prediction is proposed. The anchor viewpoint video is encoded by improved frame-based fractal video compression approach, which combines the fractal coder with the well-known motion compensation (MC) technique. The other viewpoint videos are not only predicted from temporally neighboring images but also from the corresponding images in adjacent views.

This paper is organized as follows. The fractal compression theory and mathematical background is summarized in Section 2. The anchor viewpoint video compression algorithm is presented in Section 3 and then the proposed high efficiency fractal multiview video codec is presented in Section 4. The experimental results are shown in Section 5. Finally the conclusions are outlined in Section 6.

#### 2. The Fractal Compression Theory and Mathematical Background

##### 2.1. Mathematical Background

The mathematical background of fractal coding technique is the contraction mapping theorem and the collage theorem [11].

For the complete metric space , where is a set and is a metric on , the mapping, is said to be contractive if and only ifwhere is called the contractivity factor of the contractive mapping.

For a contractive mapping on ; then there exists a unique point, , such that, for any point ,Such a point is called a fixed point or the attractor of the mapping , where represents the th iteration application of to . This is the famous Banach’s fixed point theorem or contractive mapping theorem [11].

For the fractal image coding, if the encoder can find a contractive mapping whose attractor is the original image, then we only need to store the mapping with less bits instead of the original pixel values. But in the practical implementation, it is impossible to find a contractive mapping whose attractor is exactly the original image. Instead, the fractal encoder attempts to find the contractive mapping whose collage is close to the original image.

The collage theorem is as follows.

For the complete metric space , is the contractivity factor of contractive mapping ; then the fixed point of the contractive mapping satisfies

This means that the decoded attractor is close to the original image , if the collage is close to the original image . Therefore it converts to the minimization problem of the collage error.

##### 2.2. Fractal Image Coding

In the practical implementation of the fractal image encoding process, the original image is firstly partitioned into nonoverlapping range blocks, covering the whole image, and overlapping domain blocks, usually twice the size of the range blocks in both width and height. For each range block the goal is to find a domain block and a contractive mapping that jointly minimize a dissimilarity (distortion) criterion. Usually the RMS (root mean square) metric is used. The contractive mapping applied to the domain block classically consists of the following parts [12]:(i)geometrical contraction (usually by downsampling the domain block to the same size of the range block),(ii)affine transformation (modeled by the 8 isometric transformations which contain the identity, rotation by 90°, 180°, and 270° and reflection about the midhorizontal axis, the midvertical axis, the first diagonal, and the second diagonal),(iii)gray value transformation (a least square optimization is performed in order to compute the best values for the parameters and which are scaling factor and offset factor, resp.).

Here, and can be computed by minimizing the following equation:where is the pixel value of the domain block after geometrical contraction and affine transformation and is the pixel value of the range block.

Then and can be obtained by making and equal to zero. So that

The fractal encoding process can be finished by storing all the data necessary for each range block including the location of the corresponding domain block, the index of the applied isometric transformation, and the values and . The decoding process is to iteratively apply the stored transformations to an arbitrary initial image.

#### 3. The Anchor Viewpoint Video Compression

The most well-known fractal video codec is a hybrid fractal coder of circular prediction mapping (CPM) and noncontractive interframe mapping (NCIM) [13], in which the first four frames are encoded by CPM and the remaining frames are encoded by NCIM. In both the CPM and the NCIM, each range block is motion compensated by a domain block in the adjacent frame, which is of the same size as the range block. The main difference between the CPM and the NCIM is that the CPM should be contractive and the decoding process needs iteration, while the NCIM need not be contractive. The simulation results show better performance for the NCIM-coded frames than that for the CPM-coded frames.

Different from the abovementioned approach, in our proposed scheme, we first partition the video sequences into groups of frames (GOFs) to avoid error propagation. Every first frame in each GOF is encoded by intraframe prediction without depending on the previous frames, and the remaining frames in each GOF are encoded by combining fractal with the motion compensation (CFMC) as shown in Figure 1. In CFMC, each range block is motion compensated by a domain block in the adjacent previously predicted frame rather than the previous source frame, which is of the same size as the range block.