Investigating Polynomial Fitting Schemes for Image Compression

Image compression is a means to perform transmission or storage of visual data in the most economical way. Though many algorithms have been reported, research is still needed to cope with the continuous demand for more efficient transmission or storage. This research work explores and implements polynomial fitting techniques as means to perform block-based lossy image compression. In an attempt to investigate nonpolynomial models, a region-based scheme is implemented to fit the whole image using bell-shaped functions. The idea is simply to view an image as a 3D geographical map consisting of hills and valleys. However, the scheme suffers from high computational demands and inferiority to many available image compression schemes. Hence, only polynomial models get further considerations. A first order polynomial (plane) model is designed to work in a multiplication- and division-free (MDF) environment. The intensity values of each image block are fitted to a plane and the parameters are then quantized and coded. Blocking artefacts, a common drawback of block-based image compression techniques, are reduced using an MDF line-fitting scheme at blocks’ boundaries. It is shown that a compression ratio of 62:1 at 28.8dB is attainable for the standard image PEPPER, outperforming JPEG, both objectively and subjectively for this part of the rate-distortion characteristics. Inter-block prediction can substantially improve the compression performance of the plane model to reach a compression ratio of 112:1 at 27.9dB. This improvement, however, slightly increases computational complexity and reduces pipelining capability. Although JPEG2000 is not a block-based scheme, it is encouraging that the proposed prediction scheme performs better in comparison to JPEG 2000, computationally and qualitatively. However, more experiments are needed to have a more concrete comparison. To reduce blocking artefacts, a new postprocessing scheme, based on Weber’s law, is employed. It is reported that images postprocessed using this scheme are subjectively more pleasing with a marginal increase in PSNR (<0.3 dB). The Weber’s law is modified to perform edge detection and quality assessment tasks. These results motivate the exploration of higher order polynomials, using three parameters to maintain comparable compression performance. To investigate the impact of higher order polynomials, through an approximate asymptotic behaviour, a novel linear mapping scheme is designed. Though computationally demanding, the performances of higher order polynomial approximation schemes are comparable to that of the plane model. This clearly demonstrates the powerful approximation capability of the plane model. As such, the proposed linear mapping scheme constitutes a new approach in image modeling, and hence worth future consideration

INFORMATION THEORETIC CRITERIA FOR IMAGE QUALITY ASSESSMENT BASED ON NATURAL SCENE STATISTICS

Measurement of visual quality is crucial for various image and video processing applications. It is widely applied in image acquisition, media transmission, video compression, image/video restoration, etc. The goal of image quality assessment (QA) is to develop a computable quality metric which is able to properly evaluate image quality. The primary criterion is better QA consistency with human judgment. Computational complexity and resource limitations are also concerns in a successful QA design. Many methods have been proposed up to now. At the beginning, quality measurements were directly taken from simple distance measurements, which refer to mathematically signal fidelity, such as mean squared error or Minkowsky distance. Lately, QA was extended to color space and the Fourier domain in which images are better represented. Some existing methods also consider the adaptive ability of human vision. Unfortunately, the Video Quality Experts Group indicated that none of the more sophisticated metrics showed any great advantage over other existing metrics. This thesis proposes a general approach to the QA problem by evaluating image information entropy. An information theoretic model for the human visual system is proposed and an information theoretic solution is presented to derive the proper settings. The quality metric is validated by five subjective databases from different research labs. The key points for a successful quality metric are investigated. During the testing, our quality metric exhibits excellent consistency with the human judgments and compatibility with different databases. Other than full reference quality assessment metric, blind quality assessment metrics are also proposed. In order to predict quality without a reference image, two concepts are introduced which quantitatively describe the inter-scale dependency under a multi-resolution framework. Based on the success of the full reference quality metric, several blind quality metrics are proposed for five different types of distortions in the subjective databases. Our blind metrics outperform all existing blind metrics and also are able to deal with some distortions which have not been investigated