Automatic production of quantisation matrices based on perceptual modelling of wavelet coefficients for grey scale images
Introduction
Wavelet algorithms have been widely studied for certain image processing applications. Image compression and watermarking are the most common among these applications [33], [14]. Hence, wavelets are considered a powerful tool due to their characteristics of performing multiresolution decomposition [19] which allows for identifying and separating the more significant and the less significant coefficients. Wavelets can also decorrelate the coherent portions of the image for the purpose of reducing the number of significant coefficients required to represent this portion locally [3].
Wavelet coefficients should exhibit a certain structure or behaviour that can be well modelled to extract the relevant information. The feature extraction depends on the requirements of that certain application. However, modelling wavelet coefficients is a complex task because it must involve different factors, e.g. the nature of the image, the human visual perception and a response of the visualisation device.
Feature extraction that satisfy the human perception and display factors requires choosing an appropriate domain to process the image information. A non-linear representation of images is required to bring the human visual perception and/or the characteristics of the display device into consideration. In addition, when a non-linear domain is chosen, choosing the type of transform function is essential. The γ-correction function and the logarithmic scaling function are the most popular transform functions in the image processing field. Non-linear representation of the images is also widely used within the computer graphics community to code the brightness and colour [26]. The model presented in this paper is motivated by Weber–Fechner’s Law. Weber–Fechner’s Law describes the differential sensitivity of the human perception using a logarithmic transfer function to represent the perceived intensity of a certain source.
The work presented in this paper describes a wavelet-based statistical mode. The proposed model provides an automatic production of a quantisation matrix that serves image compression application. The model exploits the differential sensitivity of the human visual system to 8-bits grey scale images to produce quantisation matrix. The derived quantisation matrix produces errors below the visibility threshold of the human eye.
The image compression mechanism that is proposed by the Joint Photographic Expert Group (JPEG) [2] is todays still image lossy compression standard and it is used for natural images. It combines block implementation of the Discrete Cosine Transform (DCT) quantisation technique and then Huffman coding. Although these methods are efficient even if lower average bit-rate is employed, the block noise (artifact) appears in the resulting image [9], [13]. Nevertheless, none of the existing proposed techniques provide an automatic way to calculate a wavelet-dependent and image-content adapting quantisation matrix as we are proposing.
The organization of the paper is as it follows: In Section 2, an overview on modelling wavelet coefficients as well as the theoretical justifications of processing the wavelet coefficients in the non-linear domain are given. The proposed model and feature extraction on subband basis, is detailed in Section 3. Results on tests of the effectiveness of the subband-based features are reported in Section 4. Conclusions and future research directions can be found in Section 6.
Section snippets
Theoretical background
Due to the multi-channel nature of the human visual system (HVS), researchers in the field have paid attention to the wavelet multi-channel features. This is because it supports representing the image into spatial-frequency and orientation components. Hence, this representation facilitates integration of HVS properties into the quantisation stage. The invisibility of quantisation errors in the reconstructed image necessitates a good representation of the image contents and appropriately chosen
Logarithmic modelling of wavelet coefficients
Motivated by the non-linearity of the human visual perception, non-linearity of display devices γ, and non-Laplacian behaviour of the wavelet coefficients, the transform function derived in the previous section (Eq. (7)) is proposed in order to transform the image coefficients in the wavelet domain. This function is proposed because it: (a) approximates the human visual perception, and (b) takes the display’s γ into consideration, and (c) provides a uniform distribution of the wavelet
Producing image content dependent quantisation matrices
From this model, a quantisation matrix can be automatically computed based on defining a visibility threshold which produces quantisation errors just below the visibility threshold of the human eye. The procedure to compute this matrix is independent of the wavelet basis functions but it produces image-dependent quantisation matrices (Qlog) for a specific wavelet. In one sense, one can also say that this leads to a basis-dependent quantisation matrices. The idea is to achieve better perceptual
Experimentation results
Objective methods for assessing perceptual image quality attempted to quantify the visibility of differences between a distorted image and a reference. The most widely used full-reference quality metric are the mean squared error (MSE) computed by averaging the squared intensity differences of distorted and reference image pixels, along with the related quantity of peak signal-to-noise ratio (PSNR). Due to the simplicity and the clear interpretation, these objective quality metrics are
Conclusions
In this paper we presented a statistical model of the wavelet coefficients that provides an automatic way to generate a scalable and image-dependent quantisation matrices for wavelet-based compression. A proposed log-based model that generates quantisation matrices for grey scaled-images and produces quantisation errors below the visibility threshold.
The proposed logarithmic transform function of the wavelet coefficients is based on Werber–Fechner’s Law on human perception. The proposed
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