A multi-resolution image compression method based on human visual quality

Abstract

The present application belongs to the field of image compression processing. Image compression coding technology is an important part of modern multimedia and information technology. With the continuous maturity of today's storage technology and network transmission technology, the demand for image information of various users is increasing day by day, and the consumption of image data on storage and network transmission resources is also gradually increasing. The traditional image compression coding technology still needs to be improved in meeting the requirements of human visual quality and multi-resolution processing of images. In order to improve the efficiency of image storage and transmission, so that users can more quickly obtain image information, the present application proposes an image compression coding method with human visual quality and display resolution as parameters. On the one hand, two-dimensional discrete wavelet transform conforms to the characteristics of human visual system perception and supports multi-resolution image processing. On the other hand, using the visual threshold model based on the principle of human visual quality in the present application, the image code stream can be effectively optimized, the visual redundancy of the image can be eliminated, and the compression performance can be improved. Based on the above two points, the present application can compress and encode images to different degrees according to the requirements of different resolutions and human visual quality. Compared with the traditional image compression method, the present application can reduce the image compression coding rate, improve the image coding efficiency, and effectively reduce the resource consumption of image data storage and network transmission under the premise of a certain visual quality and image resolution.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of compressed image coding, and particularly relates to a multi-resolution image compression method based on human visual quality. The present application relates to image compression coding, human visual quality, discrete wavelet transform technology, multi-resolution image display, and visual masking effect. BACKGROUND

[0002] With the continuous development of image processing technology and multimedia technology, users' demand for high-quality image storage and code stream transmission is increasing. In the 20th century, discrete wavelet transform (DWT) was gradually adopted in image processing technology. Compared with the early image decorrelation transform, two-dimensional discrete wavelet transform is closer to the characteristics of human visual system perception. And the unique scale function and wavelet function of discrete wavelet transform make multi-resolution image processing possible. Therefore, discrete wavelet transform is widely used in various occasions, such as image denoising, image compression coding, etc.

[0003] An image can be compressed because there is redundancy in image data. Image compression coding technology is to remove the correlation between image data, and to retain image information with a smaller amount of data. The redundancy of an image includes spatial redundancy, structural redundancy, visual redundancy, etc. Based on wavelet transform, the data of an image is compressed usually in the following two ways:

[0004] (1) Image compression coding technology based on minimizing arithmetic error

[0005] In traditional image compression coding technology, the coding result is often optimized by minimizing the arithmetic error (e.g. Mean Square Error (MSE)) during coding. In 1993, Shapiro proposed the Embedded Zero-Tree Wavelet Algorithm (EZW) based on the tree data structure of wavelet coding. The EZW algorithm finds the correlation between the wavelet coefficients of different levels in the same direction and the same spatial position through the zero-tree structure, and uses this correlation to reduce the coding of high-frequency wavelet coefficients, greatly improving the coding efficiency. In 1996, A. Said and W. A. Pearlman proposed the Set Partitioning in Hierarchical Trees (SPIHT) algorithm. This data structure retains the effective organization of wavelet coefficients with correlation between different scales by the zero-tree structure, and increases the organization of wavelet coefficients with correlation in the same scale, thereby more effectively organizing the wavelet coefficients. However, the three coefficient lists generated by the SPIHT algorithm during coding require a large amount of memory, and the energy concentration characteristics of wavelet transform are not fully utilized, so A. Islam and W. A. Pearlman proposed the set partitioned embedded block algorithm (SPECK) in 1999. The complexity of the SPECK algorithm is lower than that of SPIHT, and the dynamic memory occupied when scanning the list of coefficients is smaller, so it has an advantage in coding rate. In order to solve the problem of large memory occupation during coding, Lin and Burgress proposed the LZC (listless zero codes) algorithm, which is a new algorithm more suitable for hardware implementation. By reducing the encoder performance of the algorithm to some extent, the memory demand is improved. Xiong and Ramchandran proposed the SFQ algorithm (Space-Frequency Quantization). It uses a joint optimal method to constantly search for the best zero-tree structure and scalar quantization step, at the cost of a significant increase in coding complexity, to minimize the distortion of the reconstructed image. In 2000, the JPEG2000 image coding standard was proposed. JPEG2000 can freely combine code streams according to different orders of spatial position, image component, image quality based on MSE, image resolution, etc., and supports progressive coding of images. As part of the JPEG image compression standard system, JPEG2000 has become one of the mainstream standards for image compression coding today.

[0006] (2) Image compression coding technology based on human visual quality

[0007] In recent years, the perception of the human visual system (HVS) has become increasingly important in the field of image coding, and image compression based on human visual quality has become the focus of research. In the 1990s, Chou and Li proposed a wavelet band image coding scheme that uses a suitable difference model to simulate the HVS perception and achieves nearly transparent coding. Watson et al. introduced a model for evaluating the visibility of quantization distortion in discrete wavelet transform. This model was later incorporated into JPEG2000 by Liu et al. for grayscale image coding. Han et al. introduced a DWT coefficient model and a quantization distortion model for the Deadzone quantization in JPEG2000, and developed a visual lossless image coding method using visual threshold (VT) for image coding. After that, the model and the visual lossless image coding method were further developed for multi-resolution and remote browsing mechanisms. Unlike earlier literature, Oh et al.'s work achieved HVS perception-based image code stream optimization for grayscale and color images, and adopted a subjective and objective evaluation method in their methodology.

[0008] Due to the consideration of human visual characteristics, the existing image compression method based on human visual quality has certain improvement in performance compared with the traditional image compression method based on minimizing arithmetic error. However, in these works, image coding based on HVS perception quality above the threshold is not studied, and it is not possible to provide images with corresponding resolution and visual quality according to the user's requirements for different resolutions and visual quality, which to some extent causes waste of network transmission resources.

[0009] Based on the principle of human visual quality and image wavelet transform, the present application proposes a visible threshold image compression coding method that takes into account the browsing of multi-resolution images and human visual quality, and achieves code stream optimization for grayscale and color images with different visual quality and different resolution. The algorithm has low complexity, meets the user's demand for image quality, and enhances the performance of image compression. The method can also be used for remote transmission of image big data code stream, thereby occupying less network resources and improving transmission efficiency under the premise of ensuring certain decoded image resolution and human visual quality. This has good application in remote medical treatment and other occasions that require remote browsing of super large images. SUMMARY

[0010] The present application aims to solve the problems that the traditional image compression technology cannot completely eliminate the image coding redundancy according to human vision, and the existing technology is inefficient in multi-resolution image coding based on human visual sensitivity. The present application focuses on the measurement of human visual sensitivity and the processing of wavelet transform coefficients based on human visual quality. Based on the data obtained by processing, entropy coding and other methods can be used to finally form the image compression coding stream, and then provide users with flexible image visual quality and resolution coding selection.

[0011] The specific technical solution of the present application to solve the above problems is: a multi-resolution image compression method based on human visual quality, comprising the following steps:

[0012] (1) decompose the image into components to obtain image data under each component (for color images, the decomposed components can be RGB components or YCbCr components, etc., and for grayscale images, this step can be omitted);

[0013] (2) select a wavelet transform for image compression coding, which can sparsify the image component data and divide the wavelet coefficients of each frequency band into a series of coding units;

[0014] (3) in the context of grayscale images, measure the just noticeable amplitude of each wavelet coefficient of each component and each wavelet frequency band under full resolution for a specific display device and observation distance, to represent the sensitivity of the human eye to detect wavelet coefficients under different wavelet frequency bands;

[0015] (4) using the just noticeable amplitude of the wavelet coefficients obtained at full resolution, calculate the just noticeable amplitude of the wavelet coefficients at other resolutions (different display devices or observation distances can be converted to the corresponding image resolution by the pixel pitch of the display device and the observation distance);

[0016] (5) according to the human visual quality required for image compression coding and combining the visual masking effect, calculate the visual threshold of each coding unit using the calculated just noticeable amplitude of the wavelet coefficients at the given relative resolution;

[0017] (6) quantize the wavelet transform data of each coding unit using the Deadzone quantization method, and process the precision of the image wavelet transform coefficients according to the calculated visual threshold and wavelet quantization step, and then optimize the binary data length of the wavelet transform result;

[0018] (7) using entropy coding and other methods, compress and encode the data obtained in step 6 to finally obtain the compression coding result of the image.

[0019] The present application realizes multi-resolution of image compression coding based on the resolution-selectable characteristics of wavelet transform results. Meanwhile, the visual quality control of decoded images is realized through the control of Deadzone quantization and visual threshold on the quantization precision of image wavelet transform. In the visual threshold system of the present application, the minimum visual threshold of each wavelet band is used to generate the encoding data corresponding to the full-resolution human visual lossless image. The above seven steps are performed reversely to generate the decoded image corresponding to the encoding data. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is the system framework structure of the present application;

[0021] Figure 2 is the multi-resolution processing mode of wavelet transform;

[0022] Figure 3 is the schematic diagram of Deadzone quantizer;

[0023] Figure 4 is the flow chart of the method for calculating visual threshold by using bisection method;

[0024] Figure 5 is the flow chart of quantization coding controlled by visual threshold;

[0025] Figure 6 is the schematic diagram of 3AFC visual psychology experiment in verification experiment; DETAILED DESCRIPTION

[0026] The core content of the present application is the wavelet band visual threshold calculation method based on human visual quality and the multi-resolution image compression coding method. The system framework structure is shown in Figure 1 , which can be characterized by the following two parts:

[0027] (1) Measurement and calculation scheme of human visual detection sensitivity of wavelet coefficients

[0028] It has been shown that the human visual system is sensitive to different spatial modulation frequencies of the light source contrast, and the human visual perception mechanism can be simulated by two-dimensional wavelet transform. In the two-dimensional wavelet transform, the transform is developed through levels. In each level, the wavelet frequency band after the transform can be divided into four wavelet frequency bands of HH, HL, LH and LL. The HH represents that the result of the wavelet frequency band is obtained by performing high-pass filtering and 2 times down-sampling on the horizontal and vertical directions of the image; the HL represents that the result of the wavelet frequency band is obtained by performing high-pass and low-pass filtering and 2 times down-sampling on the horizontal and vertical directions of the image respectively; the LH represents that the result of the wavelet frequency band is obtained by performing low-pass and high-pass filtering and 2 times down-sampling on the horizontal and vertical directions of the image respectively; and the LL represents that the result of the wavelet frequency band is obtained by performing low-pass filtering and 2 times down-sampling on the horizontal and vertical directions of the image. The wavelet frequency band of the next level is obtained by further decomposing the LL wavelet frequency band of the current level.

[0029] According to the characteristics of the wavelet decomposition, the present application measures the just noticeable amplitude of each wavelet coefficient of each wavelet frequency band of a specific display device and observation distance under different image component channels (such as RGB, YCbCr and the like), and then measures the sensitivity of the human visual system to the spatial contrast modulation frequency (the greater the just noticeable amplitude, the smaller the sensitivity).

[0030] In theory, in the gray image background (that is, in the YCbCr space, if each pixel has 8 bits for each component, Y=128, and the Cb and Cr components are 0), the probability that a single coefficient in the wavelet frequency band can be detected by the human visual system is subject to:

[0031]

[0032] where y is the value of the wavelet coefficient. β is a constant, which is 2 in the present application. γ depends on the design of the visual psychological test. For example, if the human experimenters are asked in the psychological visual test whether there is a single non-zero wavelet coefficient in an image (i.e. "yes / no" test), then γ=0. If the human experimenters are required to select one of the two images containing a single non-zero wavelet coefficient (i.e. 2-alternative-forced-choice test, 2AFC test), then γ=1 / 2; if the human subjects are required to select one of the three images containing a single non-zero wavelet coefficient (i.e. 3-alternative-forced-choice test, 3AFC test), then γ=2 / 3.

[0033] In formula (1), T c,(b，l),rThis is the detectability value of wavelet coefficients for a specific display device and viewing distance. In T c,(b，l)，r In this diagram, 'c' represents the image component, corresponding to the component decomposition of the image. (b, l) represents the wavelet frequency band, where 'b' represents the decomposition direction, selected from LL, HL, LH, HH, and 'l' represents the wavelet decomposition level. 'r' represents the relative resolution of the image, which is the ratio between the current resolution and the full resolution of the image; that is, the ratio of the number of pixels occupied by the current image in one dimension to the full resolution image. Therefore, the value of 'r' is between 0 and 1, and when the image is at full resolution, the value of 'r' is 1.

[0034] It is worth noting that T c，(b,l)，r This is equivalent to making the formula satisfy e in visual testing. -1 The values ​​of the wavelet coefficients. In different visual tests, the amplitude equals T. c,(b，l),r Non-zero wavelet amplitudes will have different detection probabilities. For example, the detection probability is approximately 63% in the "yes / no" test, approximately 82% in the 2AFC test, and approximately 75% in the 3AFC test. Therefore, T c,(b,l),r It can be used to describe the sensitivity of HVS to individual components and wavelet bands, where higher T values ​​are used to describe the sensitivity of HVS to individual components and wavelet bands. c,(b，l),r The value corresponds to a lower HVS sensitivity.

[0035] T c,(b，l)，r The value was obtained through actual testing by human experimenters. During the testing process in each wavelet band, the candidate T was continuously adjusted. c,(b,l)，r The value of T is obtained, ultimately yielding the required T. c,(b，l)，r The measurement results. This invention suggests using a 3AFC experiment to measure T. c,(b,l),r At this point, it is necessary to adjust the alternative T. c,(b，l)，r The value of ...

[0036] For a given component and decomposition level, because the sensitivity of HVS to the HL and LH wavelet bands is very close, T c,(HL，l)，1 and T c,(LH，l)，1 Merging. This invention is in T c，(b，l)，r During the testing process, depending on the specific situation (based on the parameter requirements in the formula in Part II later), it is necessary to test T within a certain wavelet decomposition depth. c,(b，l)，r Take measurements.

[0037] like Figure 2 As shown, wavelet transform can perform multi-resolution processing on images. If the relative resolution of the image is reduced by 2... -utimes the original image, the spatial frequency covered by the wavelet band (b, l) in the original image will shift into the wavelet band (b, l-u). Thus, for a given component and relative resolution r, the sensitivity of human vision to the wavelet band (b, l) is the same as the sensitivity of human vision to the wavelet band (b, l-u) at relative resolution r-2 -u In the form of T c，(b，l),r , we have:

[0038]

[0039] From equation (2), for any positive integer u, the value of T c,(b，l-u)，1 can be chosen. In the case where r is not an integer power of 2, and there is always a positive integer m such that T c,(b,l)，r equals and

[0040] For T c,(b，l)，r can be derived by the following method: first, generate a full resolution gray scale image that contains only one unit value wavelet coefficient in the wavelet band (b, 2) and is located at the center. Then, scale the image according to the relative resolution r and pad it with zeros at the periphery to reach the size of the original image. After that, process the image using a two-level two-dimensional wavelet transform. Collect the resulting wavelet coefficients. Assuming that the HVS sensitivity to each non-zero wavelet coefficient is independent in this case, then according to equation (1), T c,(b，l)，r is modeled as follows:

[0041]

[0042] where β = 2, the coefficient represents the sum of the βth power of the wavelet coefficients in the wavelet band (b0, k).

[0043] (2) Calculation of visual threshold and encoding scheme

[0044] The present application defines a human visual perception quality metric Q (Q > 0) that is related to the theoretical detection probability of quantization error in the field of view (FOV), and is defined as follows:

[0045]

[0046] where γ has the same meaning as in equation (1).

[0047] From equation (4), the higher Q is, the lower the probability that the image is resolved is. This means that the image has a higher visual quality.

[0048] The image encoding of this invention uses a deadzone quantizer to quantize the wavelet transform result. The deadzone quantizer and its reconstruction method are as follows: Figure 3 As shown. To control the quality of the decoded image, a visual threshold (VT) is introduced for each wavelet band coding unit. For a certain image coding unit (such as a wavelet coefficient code block) after component decomposition and wavelet coefficient transformation, this invention uses VT to control the actual quantization error, thereby controlling the visual quality of image compression. VT is defined as the deadzone quantization step size for image quality Q at a given relative resolution r. From equation (4), we can obtain:

[0049]

[0050] In the specific encoding process, the visual threshold VT c,(b，l),r Obtained through numerical calculation. f(x) is the quantization error probability density function, which can be modeled as follows in the LL wavelet band:

[0051]

[0052] Where σ is the standard deviation of the wavelet transform coefficients of a certain coding unit's wavelet band, and Δ represents the Deadzone quantization step size.

[0053] The quantization error probability density distribution in the LH, HL, and HH wavelet bands can be modeled as follows:

[0054]

[0055] in

[0056] The field of view is the range within which the human eye focuses when observing an object, N (b,l)，r The number of wavelet coefficients in the wavelet frequency band (b, l) included in the field of view at a relative resolution r can be calculated using the following formula:

[0057]

[0058] Where d0 is the distance from the human eye to the screen, in mm; θ is the human viewing angle, which is 2° here; and p is the pixel pitch of the display, in mm.

[0059] m c，(b，l)，r This is a visual masking factor used to eliminate the visual masking effect. The specific formula is as follows:

[0060]

[0061] Where e = 2.718281828459, which is the natural constant, and α is a constant with a value range of 0 ≤ α ≤ 1.

[0062] There are many ways to calculate VT for a specific coding unit within a specific wavelet band of a given image component. For example, the binary search method can be used to calculate the value of VT in each coding unit. The specific algorithm flow is as follows:

[0063] like Figure 4 As shown, when calculating VT, a very small threshold VT1 and a very large threshold VT2 are first set. Then, using the monotonicity of the function, the threshold is determined according to equation (5). Is the corresponding Q value greater than the set image quality value? If so, then let... Otherwise Repeat the above steps several times in sequence until the threshold interval width approaches 0, thereby calculating the VT value required for the corresponding coding unit.

[0064] Due to the use of the Deadzone quantizer, if a wavelet transform coefficient is Deadzone quantized based on a certain quantization step size, then in the resulting binary quantization result, each reduction of the least significant bit is equivalent to doubling the quantization step size. The binary bitstream truncation and encoding strategy of this invention can be as follows: Figure 5 As shown. This strategy can be summarized as follows:

[0065] For a specific coding unit within a wavelet frequency band, the quantized wavelet coefficient binary code stream can be encoded progressively from the most significant bit to the least significant bit. When the quantization error of each wavelet coefficient within the coding unit first becomes lower than the quantization error caused by a quantization step size of VT, all subsequent coding channels can be discarded, thus completing the truncation of the binary code stream. The truncated code stream can then be encoded using any entropy coding method to achieve image data compression.

[0066] After encoding is completed, the above steps are repeated in reverse: entropy decoding, deadzone quantization reconstruction, rearranging the order of encoding units according to the original positions of the wavelet transform results, inverse wavelet transform, and component synthesis (for color images), thus completing the image decoding.

[0067] This invention can be verified based on the JPEG2000 lossy coding framework. Standard JPEG2000 lossy coding uses YCbCr color transformation and performs image sparsification and quantization processing based on 9 / 7 wavelet transform and Deadzone quantizer. Traditional JPEG2000 lossy image compression coding optimizes the encoded bitstream by minimizing the mean square error (MSE) of the decoded image.

[0068] Using the human visual sensitivity measurement method in the present application, the present application carries out visual sensitivity measurement verification experiment on ASUS PA328Q display. The pixel pitch of the display is 0.1845mm, and the display brightness is 350cd / m 2 . The visual psychology experiment adopts 3AFC experiment, and the experimental setting is as shown in Figure 6 , wherein the distance between the human experimenters and the display is 60cm, and the human experimenters need to point out which one of the three images contains non-zero wavelet coefficients within 10 seconds in each test.

[0069] Using 3AFC visual psychology experiment and QUEST toolbox, the measured T c,(b,l)，1 data is as shown in Table 1:

[0070] Table 1 Measured T c，(b，l)，1

[0071]

[0072] In order to evaluate the effectiveness of the "human visual-based multi-resolution image compression encoding method" of the present application, 29 images from the original color landscape image database of Granada University are subjected to image encoding experiment. The quality index Q takes 1, 0.7, 0.3 and 0.1, and the relative resolution takes 1, 0.75 and 0.5. The specific encoding code rate results are as shown in Table 2:

[0073] Table 2 Image compression experiment results

[0074]

[0075] In Table 2, the greater the code rate of the image, the greater the volume of the file generated after image compression. As can be seen from Table 2, the code rate of the image decreases with the decrease of the visual quality Q and the relative resolution r. This shows that in the case of a certain resolution, to improve the visual quality of the image and reduce the probability of the image being resolved, a higher code rate is required for encoding the image. On the other hand, when the visual quality of the image is certain, the image displayed at a lower resolution will generate a lower code rate code stream.

[0076] In addition, different images under the same visual quality and the same resolution have different code rates. This means that the encoding method in this paper can take different degrees of compression for different images. For images with rich details, the compression degree of the encoder will be lower to retain more image details. In combination with the above two points, it can be seen that the present application can take different degrees of compression according to the actual needs of the user, provide images that meet the needs of the user, and reduce unnecessary storage or transmission resource consumption.

[0077] In order to verify the effectiveness of the model and the encoder, visual experiments are also conducted on the decoded images. The images with quality indicators Q of 1 and 0.1 and relative resolutions of 1, 0.75 and 0.5 are tested, and a visual experiment of images generated by a conventional MSE encoder under the same average code rate is set as a control. The specific experimental results are shown in the following tables:

[0078] Table 3 Correct recognition rate of compressed images of the encoder based on visual quality

[0079]

[0080] Table 4 Correct recognition rate of compressed images of the MSE encoder under the same code rate

[0081]

[0082] By observing Tables 3 and 4, comparing the experimental results under different visual qualities at the same resolution, it can be concluded that for a higher Q value, the correct recognition rate of the image is often lower, which means a higher visual quality. If the experimental results of the improved encoder and the conventional MSE encoder are compared, it can be found that in most cases, the improved encoder has a lower correct recognition rate. This shows that the algorithm adopted in the present application has a certain performance improvement compared with the conventional MSE encoding algorithm.

Claims

1. A method for calculating wavelet band visual threshold based on human visual quality and a method for multi-resolution image compression coding, comprising the following steps: S1. For different color components c of an image, using visual psychology experiments, a display device and an observation distance are self-determined by a subject, and using the distance, the just noticeable magnitude of a single wavelet coefficient in each wavelet band at full resolution is measured; S2 defines the relative resolution as the ratio of the number of display pixels occupied by the current image in one dimension to the number of display pixels occupied by the full resolution image in the same dimension, and using the just visible amplitude of the individual wavelet coefficients at full resolution obtained in S1, the just visible amplitude T of the individual coefficients of the b-th wavelet band of the l-th level for the color component c is calculated in the case of a relative resolution of r c，(b，l)，r There are: wherein is a u positive integer, and where β = 2, represents the sum of the βth power of the wavelet coefficients in the kth b0 wavelet band after the full-resolution wavelet transform of the single coefficient of the (u+1)th b wavelet band at the relative resolution r. S3 uses the T obtained in S2 c，(b，l)，r , to calculate the visual masking factor m c，(b，l)，r , which is: where 0≤α≤1, and σ is the standard deviation of the wavelet band coefficients of the corresponding coding unit; S4 uses T obtained in S2 c，(b，l)，r and m obtained in S3 c，(b，l)，r Calculate the visual threshold VT for each wavelet frequency band. c，(b，l)，r The calculation follows the formula: wherein Q is a pre-set image quality parameter of human visual perception, N (b，l)，r is the number of wavelet coefficients of color component c, wavelet band (b, l) within the observation view angle under the image display relative resolution r, and f(x) is the probability density function of wavelet quantization error in the Deadzone quantization. S5. The wavelet band coefficients of each component of the image are quantized using a dead zone quantizer, and the wavelet coefficient bitstream is optimally coded: when the maximum quantization error in the coding unit first appears to be lower than the quantization error caused by the quantization step obtained in S4, all subsequent coding channels are discarded, and finally the processed bitstream is entropy coded.

2. The psychovisual experiment method of claim 1, wherein The step S1 comprises: by a subject, a display device and an observation distance are self-determined, and using the display device and the observation distance, the magnitude of a single wavelet coefficient in a wavelet band that can be correctly detected at a probability of 63% in a "yes / no" visual psychology test, or at a probability of 82% in a two-alternative forced-choice (2AFC) visual psychology test, or at a probability of 75% in a three-alternative forced-choice (3AFC) visual psychology test is measured, and the magnitude is defined as the just noticeable magnitude of a single wavelet coefficient in the wavelet band at full resolution.

3. The method of claim 1, wherein the number of wavelet coefficients within a viewing angle is determined by human visual perception of image quality parameters. In the step S4: let Q be the image quality parameter of human visual perception, P d is the probability of distinguishing a quantization error image from a lossless image of the observed visual field size in a visual psychology test, then For the "yes / no" visual psychophysics test, γ = 0, for the 2AFC visual psychophysics test, γ = 1 / 2, for the 3AFC visual psychophysics test, γ = 2 / 3, let N (b，l),r be the number of wavelet coefficients of color component c, wavelet band (b, 1) within the viewing angle of the image presentation at relative resolution r, then d0 is the distance of the human eye to the screen in mm, θ = 2 o p is the pixel pitch of the display in mm, and f(x) is the probability density function of the wavelet quantization error in the Deadzone quantization. The probability density function of the quantization error in the LL wavelet band is where σ is the standard deviation of the wavelet transform coefficients of a certain coding unit, and Δ denotes the deadzone quantization step size, The probability density functions of the quantization errors in the LH, HL and HH wavelet bands are wherein

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