Multimedia requirements demand efficient compression techniques for large data files such as image, video, and 3D data. While the relative price of storage has steadily decreased in the past decades, the amount of generated image and video data has increased exponentially. This is more evident on large data repositories such as YouTube and cloud storage. The increased growth in network traffic and storage requirements means that data compression algorithms can have a large impact on data centres concerning bandwidth, physical storage space, and energy usage. This paper proposes an efficient data compression algorithm based on the discrete cosine transform (DCT) together with several novel steps including the minimization of high-frequency components, a differential process, and a lookup table based search by concurrent binary algorithms at decompression stage.
High pass tends to transmit more of the high frequency parts and low pass tends to pass more of the low frequency parts. They can be simulated in software. A walking average can act as a low pass filter for instance and the difference between a walking average and it's input can work as a high pass filter. If the control input switches faster than the input signal then the output will reflect the control input short term (high frequency component) but the signal input long term (low frequency component).
The DCT has been extensively used [1, 2] in image compression. The image is divided into segments and each segment is then subjected to the transform, creating a series of frequency components that correspond with detail levels of the image. Several forms of encoding are applied to store only the relevant coefficients. The DCT is the basis of the popular JPEG file format, and most video compression methods and multi-media applications [3, 4].
JPEG2000 is based on the discrete wavelet transform (DWT) which is one of the mathematical tools for hierarchically decomposing functions. The wavelet transform is the preferred technique for compressing images at higher compression ratios with higher PSNR values [5, 6]. Its superiority in achieving high compression ratios, error resilience and wide adoption has led to the JPEG2000 ISO standard. The JPEG2000 codec is more efficient than its predecessor JPEG and overcomes many of its drawbacks [7]. It also offers higher flexibility compared to other codes such as region of interest, high dynamic range of intensity values, multi component, lossy and lossless compression, efficient computation, and compression rate control. The robustness of JPEG2000 stems from the DWT which supports multi-resolution representations in both spatial and frequency domains. In addition, the DWT supports progressive image transmission and region of interest coding [8, 9].
To demonstrate the effectiveness of the proposed approach, we focus on compressing 2D image data appropriate for 3D reconstruction. This includes 3D reconstruction from structured light images, and 3D reconstruction from multiple viewpoint images. Previously, we have demonstrated that while geometry and connectivity of a 3D mesh can be tackled by several techniques such as high degree polynomial interpolation [10] or partial differential equations [11, 12], the issue of efficient compression of 2D images both for 3D reconstruction and texture mapping has not yet been addressed in a satisfactory manner. Moreover, in most applications that share common data, it is necessary to transmit 3D models over the Internet. For example, to share CAD/CAM assets, e-commerce applications, update content for entertainment applications, or to support collaborative design, analysis, and display of engineering, medical, and scientific datasets. Bandwidth imposes hard limits on the amount of data transmission and, together with storage costs, calls for more efficient 3D data compression for exchange over the Internet and other networked environments. Using structured light techniques for 3D reconstruction, surface patches can be compressed as a 2D image together with 3D calibration parameters, transmitted over a network and remotely reconstructed (geometry, connectivity and texture map) at the receiving end with the same resolution as the original data [13, 14].
Related to the techniques proposed in this paper, our previous work on data compression is summarised as follows. Focused on compressing structured light images for 3D reconstruction, Siddeq and Rodrigues [13] proposed a method where a single level DWT is followed by a DCT on the LL sub-band yielding the DC components and the AC-matrix. A second DWT is applied to the DC components whose second level LL2 sub-band is transformed again by DCT. A matrix minimization algorithm is applied to the AC-matrix and other sub-bands. Compression ratios of up to 98.8% were achieved. In Siddeq and Rodrigues [13], similar transformations are applied to variant arrangements of data blocks followed by arithmetic coding. The novel aspect of that paper is at decompression stage, where a parallel sequential search algorithm is proposed and demonstrated. Compression ratios of up to 98.5% were achieved. In Siddeq and Rodrigues [15], a two-level DWT was applied followed by a DCT to generate a DC-component array and an MA-Matrix (Multi-Array Matrix). The MA-matrix is then partitioned into blocks and a minimization algorithm codes each block followed by arithmetic coding. At decompression stage a new proposed algorithm, Sequential-search algorithm is used to estimate the MA-matrix. Compression ratios up to 98.1% were achieved. In Siddeq and Rodrigues [16], compression consists of two level DWT followed by two level DCT. A minimize-matrix-size (MMS) algorithm is applied to the AC-matrix and to the other high frequencies followed by arithmetic coding to the output of previous steps. A novel fast-match-search decompression algorithm is used to reconstruct all high-frequency matrices by computing all compressed data probabilities through a binary search algorithm to estimate the data from a look up table. A comparative analysis of various combinations of DWT and DCT block sizes is performed, with compression ratios up to 98%.
In Siddeq and Rodrigues [17], the issue of compressing 3D data geometry, connectivity and texture is addressed through a novel geometry minimization algorithm (GM-algorithm) applied to mesh vertices and triangulated faces with arithmetic coding. First, each vertex (x, y, z) coordinates are encoded to a single value by the GM-algorithm. Second, triangle faces are encoded by computing the differences between two adjacent vertex locations, which are compressed by arithmetic coding together with texture coordinates. The method was demonstrated on large data sets achieving compression ratios between 87—99% without reduction neither in the number of reconstructed vertices nor triangulated faces. Finally, in Siddeq and Rodrigues [18], work is focused on 3D data only under various formats. The GM-algorithm is used to compress vertices and triangulated faces, where faces are encoded by computing the differences between two adjacent vertex locations, and then again coded by the GM-Algorithm and arithmetic coding. High compression ratios over 90% were achieved. A comparative analysis of compression ratios is provided with several commonly used 3D file formats showing the advantages and effectiveness of the approach.
![Frequency Frequency](/uploads/1/2/5/5/125562719/554999203.png)
In the research above we focused on a combination of DWT, DCT, matrix minimization, geometric minimization and arithmetic coding. In this paper, we describe a new method for lossy image compression based on DCT alone with quantisation process leading to the creation of two matrices of low and high frequencies (DC-components and AC-coefficients). A high-level view of the proposed method is depicted in Fig. 1. The new aspects of this research are related to the compression of the matrix of AC-coefficients which involves eliminating zeros, followed by a minimization of high-frequency data resulting in a minimized-array. At decompression stage, the recovery of the data from the minimized-array requires a new binary search algorithm which is implemented in a concurrent fashion. These are described in the following sections.
This paper is organized as follows. Section 2 introduces the DCT and how it is applied over an image by the proposed method. Section 3 describes the high-frequency minimization algorithm and Section 4 describes how such compressed data are recovered through a concurrent binary search algorithm. Section 5 describes experimental results for both 2D image compression followed by 3D reconstruction from 2D structured light images and 3D reconstruction from multiple viewpoint images. Finally, Section 6 summarizes and concludes the paper.