ES2310157A1 - Compression of colour images, based on non-linear perceptual representations and machine learning - Google Patents

Abstract

The invention relates to the compression of colour images, based on non-linear perceptual representations and machine learning. More specifically, the invention relates to a method for the compression of colour images, comprising the following steps: (1) expressing the coefficients of a local space/frequency representation of the opposing chromatic and achromatic channels in units of perceptual contrast (2) applying a non-linear transform with divisive normalisation to each channel, such that they include relationships between the coefficients of the achromatic and chromatic contrast channels and (3) using statistical learning algorithms to select the relevant data from the non-linearly normalised channels. Psychophysical and numerical experiments have been conducted in order to estimate and validate the parameters of the divisive normalisation and contrast transforms. In addition, the above method has been compared experimentally with a JPEG implementation. In both cases, 16x16 DCT blocks were used and, in each case, comparable values were used for the frequency-dependent and chromatic transform parameters. Under these conditions, the experimental results provide an average compression gain of 50% in relation to JPEG for different distortion measurements (RMSE, SSIM and S-CIELab) in the realistic commercial range of [1, 2.2] bits/pix. The invention also relates to the apparatus and code used to implement said method.

Description

Compression of color images based on nonlinear perceptual and learning representations of machine.

Field of the Invention

The present invention comprises the methods, apparatus and program for compressing color images, in particular to images and sequences of color images.

Context of the invention

Currently the volume of image data is increases exponentially in a wide range of applications such as remote sensing, digital photography and video cameras, medical image, digital libraries and documents, movies and video conference This raises different problems and needs to transmit, store and retrieve images. In consecuense, Digital image compression is a crucial technology. Is important to highlight that compressing an image is significantly different from compressing other types of data, due to their particular statistical properties, and therefore the application direct from other compression methods is far from producing optimal results Therefore, statistical knowledge of problem is of extreme importance to develop schemes Efficient coding.

The ISO / IEC 10918-1 standard, known as JPEG [1], it has become the compression method more popular. Different methods have been proposed to increase compression while maintaining the same level of quality, well based in machine learning techniques such as neural networks or well by including perceptual knowledge in the process of coding.

US Patent No. 5,005,206 [2] describes the use of neural networks for image coding. At proposed scheme, the image is defined by the weights associated to a neural network trained in a linear domain particular.

US Patent No. 6,798,914 [3] also describes the use of neural networks for image compression. The method combines artificial intelligence and neural networks to convert digital data into symbolic data that is compressed using a run-length encoding . In all these schemes, the problems of using neural networks are present, namely: instability in training, selection of the appropriate algorithm for training, network structure, and the choice of free parameters.

WO 03/050959 [4] describes the use of another machine learning algorithm, the support vector machine (or SVM), working on a linear transformation - the Discrete Cosine Transform (DCT) - for lossy data compression. The method is used in particular to compress images in gray levels. The introduction of SVM offers several advantages and control over the learning process: interpretation of the free parameters, weediness in the application space, and no need for training heuristics since the resulting optimization problem is convex and the only solution. However, the application of the method to color images or how the scheme could treat them is unknown. In addition, the direct application of the standard SVM in the specified work domain (the DCT linear domain) is not a good choice. In [5] this last problem is solved by introducing an adaptive SVM that takes into account the different perceptual relevance of the coefficients in the linear domain. Certainly the inclusion of perceptual (or statistical) a priori knowledge is of paramount importance for image coding. In this regard, US Patent No. 5,426,512 [6] describes DCTune technology to optimize static image compression. DCTune calculates the best JPEG quantization matrices to achieve maximum compression possible for an established perceptual error, given a particular image and a set of display conditions. This method is based on a pointless non-linear masking model (self-masking), but does not consider relationships between coefficients (cross-masking) nor does it propose the use of any machine learning method.

These methods produce good results and competitive compared to standard JPEG methods. But nevertheless, They have at least the following limitations: (i) to date none of the methods integrates perceptual knowledge and methods of machine learning for color image compression; (ii) the Existing methods do not propose transformation schemes for work with contrast in color images, or how they can be calculated and introduced in the already known schemes; (iii) the existing methods do not introduce transformations non-linear perceptual with interactions between coefficients before eventually applying a method of machine learning; and (iv) machine learning is not formulated to be independent of the application domain.

The present invention aims to solve these inconvenience

The method and apparatus of this invention extends the proposals made in [6, 7, 8] applying a transformed non-linear perceptual that includes interaction between coefficients after a transform space-frequency Also, regarding JPEG2000 [9], allows a matrix of interaction between general coefficients (not causal) including relationships between chromatic channels. Further, The proposed method solves the problems found in [8, 10] since in these a stage of obtaining the contrast is not applied chromatic with the consequent error in the nonlinear transform (already  be punctual or based on divisive normalization). The method it also differs from neural network based algorithms proposed so far in US Patent No. 5005206 [2], and No. 6798914 [3], since an algorithm of general purpose learning, which must necessarily be adapted to the statistical or perceptual relevance of the coefficients in the work domain where the coding. In [5] the regression method with support vectors (SVR) was applied in the DCT domain, as in [4, 12]. But nevertheless, given the characteristics of the domain, the algorithm was adapted to incorporate the perceptual relevance of the coefficients in this domain, which had not been considered in [4, 12]. SVR has also been applied in a nonlinear perceptual domain to coding of achromatic images in [13], and due to the characteristics of the domain used (perceptually Euclidean as and as discussed in [14]) an SVR can be applied correctly static However, when working in other domains it is it is necessary to use an adaptive SVR as illustrated in [5] and it analyze in more detail in [14].

Summary of the Invention

It is an object of the present invention provide methods, apparatus and programs that define a new general purpose framework for image coding in color.

Another object of the present invention is provide, methods, apparatus and programs to improve the compression performance of color images for an effort Computing comparable with existing methods.

In a first aspect, these and other objects are they get with a color image compression method that It comprises the following steps:

- Receive color image data expressed in RGB channels.

- Transform from RGB channels to a space of opponent color obtaining an A channel, an RG channel and a channel YB

- Transform channels A, RG and YB to a domain space frequency as a sum of base functions multiplied by the corresponding set of coefficients and encode low frequency waste.

- Express the coefficients of the aforementioned local space-frequency representation of achromatic channels and chromatic opponents in contrast units with perceptual meaning.

- Apply a transform non-linear parametric to achromatic channels and Chromatics expressed in contrast.

- Estimate the coefficients of the aforementioned nonlinear perceptual transform using a learning procedure

- Perform the quantification of the description obtained and codify the results.

Preferably the method uses one of the following space-frequency transforms Local: DCT or any form of discrete transform based in Gabor functions or in wavelets.

Preferably the method calculates the contrast of the achromatic channel as a function of the number of parameters relevant and the contrast of the chromatic channels as a function of the number of relevant parameters including parameters obtained through psychophysical and numerical experiments.

Preferably the method includes obtaining of parameters with respect to the proportions of average luminance of the chromatic functions through psychophysical experiments and the obtaining parameters regarding maximum color modulation through the use of numerical experiments.

Preferably the non-linear transform applied to chromatic channels is divisive normalization general, and perceptual nonlinear transforms applied to the color channels are transformed from divisive normalization with frequency sensitivities adapted to these channels.

Preferably the method uses a procedure of learning to identify the sequence of base functions and their corresponding weights, with an appropriate criterion for optimize the compactness of the encoded data stream and / or the encoded image quality

Preferably the method uses as a procedure of learning the SVR or a procedure implemented with any of The following machine learning procedures: networks neural, spline based techniques, kernel based methods, Bayesian networks, Gaussian processes or fuzzy logic.

Preferably the method encodes the flow of data using entropic coding.

Optionally the method includes steps additional to process phase information separately of the amplitude coefficient information.

In a second aspect, the objects of this invention are achieved by a program stored in a means that when it is executed on a device (computer, PDA, mobile phone, ...) performs the described method previously.

In a third aspect, the objects of this invention are achieved by an apparatus that produces data color image tablets comprising the mechanism for reception of color image data and the mechanism for perform the processing to perform the following steps:

- Transform from RGB channels to a space of opponent color obtaining an A channel, an RG channel and a channel YB

- Transform channels A, RG and YB to a domain space frequency as a sum of base functions multiplied by the corresponding set of coefficients and encode low frequency waste.

- Express the coefficients of the aforementioned local space-frequency representation of achromatic channels and chromatic opponents in contrast units with perceptual meaning.

- Apply a transform non-linear parametric to achromatic channels and Chromatics expressed in contrast.

- Estimate the coefficients of the aforementioned nonlinear perceptual transform using a learning procedure

- Perform the quantification of the description obtained and codify the results.

Other features and advantages of the invention present will be clear from the following description detailed of the illustrative concretions of its objects in relationship with the figures provided.

Description of the figures

Figure 1 shows a block diagram of a method according to the present invention. See page 10 and following where each block is described.

Figure 2 shows an example of a network purely chromatic sinusoidal in the chromatic direction yellow-blue (YB). In this case, a base function DCT size 16x16 with frequency fx = 8 and fy = 0 cycles per grade The average color is T_ {0} = [80 80 80] T in RGB NTSC or T 0 = [80 0 0] T in YUV linear, the color contrast is C (2) chrom = 0.85 assuming a maximum modulation \ DeltaT_ {2max} = 45 in the channel U. The top row shows the two networks against phase of extreme chromaticity e_ {1} (2)} (yellow on the left), and e_ {2} ^ {(2)} (blue in the center), used to generate the network pure color (on the right). The average luminance values (ordered) of the yellow and blue networks have been chosen to obtain constant brightness in the final network (\ eta_ {Y \ B} B = 0.14, see section 2.2), which isolates the response in the channel Yellow-Blue (\ DeltaT_ {2} \ neq 0 and ΔT 3 = 0). The center row shows the luminance of the networks shown in the first row. The graph below shows the CIE xy color coordinates of extreme colors (luminance unit) e_ {j} ^ {(2)} with j = 1, 2 (stars) and colors current on the network (circles). Increase the color contrast means to simultaneously increase the amplitudes of the luminances \ DeltaY_ {j} ^ {(2)}, therefore increasing the chromaticity range covered by the circles in the graph plus lower. In the extreme case (unit contrast), the color range could be determined exactly by extreme colors e_ {j} ^ (2)}. Reducing color contrast means reducing the amplitudes of the luminance ΔY_ {j} {2}}, and by both the color range is reduced. In the zero contrast limit, the only color of the mesh would be the average color T_ {0} (the circle central in the lower diagram).

Figure 3 shows sample images that limit maximum modulation in directions U and V (above) and the corresponding colors (below).

Figure 4 shows the parameters if (f) for each channel in equation 35.

Figure 5 shows parameter 0 (f) of equation 35.

Figure 6 shows three neighborhood examples of interaction between coefficients (rows of the matrix h (f, f ') reordered in 2-D) in equation 35. Each surface corresponds to the neighborhoods associated with different frequencies

Figure 7 shows the responses and thresholds of visibility associated with two sensors adjusted to frequencies 4 and 10 cycles per degree under conditions of self-masking (the background is the base function for which the sensor is set). It also shows the amount of distortion \ Deltac that must be applied to obtain an increase in response? for different contrasts (abscissa) of the input pattern.

Figure 8 shows the answers and associated visibility thresholds for two sensors set to frequencies 4 and 10 cycles per degree when there is a pattern of masking (ordered) of different frequency (6 cycles per grade) to different contrasts (abscissa): 0 (self-masking, solid line) and 0.5 (line dotted). In this case the amount of distortion required Δc to obtain a response increase τ to a stimulus contrast is increased when the contrast of the Masker is increased. A: Stimulus; B: Mask

Figure 9 shows a set of images considered to evaluate the compression capabilities of the method proposed.

Figures 10a, 10b and 10c show the curves compression ratio to distortion averages (abscissa: measure as entropy in bpp) on 25 images using different measures Distortion (ordered): (a) RMSE, (b) S-CIELab [28], and (c) Structural SIMilarity index (SSIM) [27], for Methods considered: 16x16 JPEG (dotted) and the proposed method C-NL-SVR (solid line).

Figure 11a shows the distortion curves (abscissa: measured as entropy in bpp) for two example images (top and bottom) using RMSE for 16 x 16 JPEG methods (dotted) and the C-NL-SVR (solid). Figure 11b illustrates a scheme to measure the gain of the method C-NL-SVR (solid line) versus 16x16 JPEG (dotted line). For a distortion level, the difference in ratio between the two methods is measured and compared.

Figure 12 shows the average gain (with standard deviation bars) of the method C-NL-SVR vs. 16x16 JPEG in terms of different distortion measures (abscissa): (a) RMSE, (b) SSIM [27] and (c) S-CIELab [28]; ordered: entropy (bpp).

Figure 13 shows examples of images "Parrot" (eye area) decoded with 16x16 JPEG (row top) and C-NL-SVR (bottom row) at different compression ratios (from left to right: {1.0,1.4,1.8,2.2} bits per pixel, bpp).

Figure 14 shows examples of images "Lena" decoded with 16x16 JPEG (top row) and C-NL-SVR (bottom row) a different compression ratios (from left to right: {1.0,1.4,1.8,2.2} bits per pixel, bpp).

Figure 15 shows examples of images "Roof" decoded with 16x16 JPEG (top row) and C-NL-SVR (bottom row) a different compression ratios (from left to right: {1.0,1.4,1.8,2.2} bits per pixel, bpp).

Figure 16 shows examples of images "Flower 3" decoded with 16x16 JPEG (top row) and C-NL-SVR (bottom row) a different compression ratios (from left to right: {1.0,1.4,1.8,2.2} bits per pixel, bpp).

Figure 17 shows examples of images "Face 1" decoded with 16x16 JPEG (top row) and C-NL-SVR (bottom row) a different compression ratios (from left to right: {1.0,1.4,1.8,2.2} bits per pixel, bpp).

Detailed description of the invention

In order to better understand this invention, and considering that it provides a general purpose framework novel to encode color images that combines techniques known and new, let's first describe a scheme full of the invention, secondly we will describe in details the key blocks focusing on the novel aspects and inventive of this invention, and thirdly we will describe the experimental results. Finally we will refer to the Method implementation

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1. Scheme of the invention

Figure 1 shows a general scheme of the invention that includes the following blocks:

Block 1.- Start the values of the parameters

Block 1.A.- User selection of the compression ratio (size of the encoded image) or of the distortion (encoded image quality level).

Block 1.B.- Selection of own parameters of the learning procedure and the resolution of the quantification applicable to the description obtained by the process Learning. To do this, the elections are taken into account considered in Block 1.A, for example through a look-up table (LUT) that relates the parameters Free and distortion / ratio over a set of images appropriate. In subsequent steps, Block 1.B allows the adaptation of the preset parameters taking into account the deviation from the desired ratio / distortion and values actuals obtained in Blocks 16 and 17. For example, if the learning is done through an SVR, must be established or modify the following parameters: the values of \ varepsilon_ {f}, the penalty factor \ lambda and the parameters associated with kernel K (see Block 9 and section 4.2) and the number of bits used in quantifying weights associated to the selected support vectors (see Block 10).

Block 2.- Receiving the image data in color expressed in RGB digital channels (denoted as RGB)

Block 3.- Transformation of the RGB signal to a Opponent color space, beginning with the characterization of the color dependent on the digital device, getting first place a description of the color in a tristimulus space device independent (such as CIE XYZ). This requires the the calibration parameters of the acquisition device. Yes such parameters are not available, curves can be used Gamma and generic primaries. Second, the images X, Y, Z They are combined in the following three channels: Achromatic (A), Red-Green (RG), Yellow-Blue (YB) according to a linear or non-linear opponent transformation.

Blocks 4.A, 4.B, 4.C.- Transformation of each opponent color channel, A, RG, YB to a domain local space-frequency, using for example, the discrete cosine transform (DCT), wavelet transform or any other appropriate linear or nonlinear transform.

Blocks 5.A, 5.B, 5.C.- Obtain contrast of each channel with appropriate transforms (based on perception), that is, express the amplitudes of the local frequency signals in the appropriate contrast units to use models of perception in blocks 7.A, 7.B and 7.C. For channel A you can use Michelson's contrast, but for each of the RG and YB channels it is necessary to perform both psychophysical experiments  with the chromatic base functions of the transformed as numerical experiments on a database of color images (see section 2).

Block 6.- Waste disposal coding frequency of channels A, RG and YB. This coding can consist of the application of a DPCM followed by an encoder entropic

Blocks 7.A, 7.B, 7.C.- Application of a Perceptual nonlinear transform to each channel. In the case of achromatic channel and assuming that DCT has been used in the block 4.A, non-linear transformation can be applied introduced in [11, 14]. In the case of chromatic channels the transformation to be applied must be different (see section 3 for You work explicitly).

Block 8.- (Optional) Storage of the original phase information of the transformed channels no linearly This block is necessary only if the information of the phase is encoded independently of the information over amplitude (related to Blocks 11 and 12).

Block 9.- Application and training of a machine learning procedure with parameters established in Block 1.B. This procedure selects the most representative and informative coefficients that best approximate to the signal on each channel. In case the path is followed optional towards Block 8, the learning process is applied about the absolute values of the signals. If not, put that the phase signal is not processed separately from the signal, the learning process is applied directly to the signals that they come from Blocks 7.A, 7.B and 7.C. See section 4 for a training example using SVR and saving weights and associated support vectors.

Block 10.- Perform a quantization of the description obtained in block 9 using the parameters of quantization obtained / adjusted in block 1.B. In the case of using an SVR, a uniform quantization of the weights associated with the selected support vectors.

Block 11 (Optional) - Making a channel-to-channel reconstruction from the quantized weights of the Block 10. This Block is needed only if it is coded phase information independently of the information over amplitude (Block 8). The result of this reconstruction is used to discard unnecessary phase information that comes from Block 8 in Block 12. To reverse the non-linear transformations of Blocks 7.A, 7.B and 7.0 ago A proper procedure is missing. In case you have done a transform with divisive normalization [15], can be used a recursive procedure [11]. It must be ensured that no linearities in 7.A, 7.B and 7.0 are invertible. In [11] it was tested that the transform of 7.A was. The study of the conditions necessary to reverse the proposed transforms in the Blocks 7.B and 7.0 can be seen in section 3.

Block 12 (Optional) - Elimination process of the phase information from Block 8 (optional), based in the discarded coefficients in the reconstruction process (Block 11, optional), after the quantization performed in the Block 10.

Block 13.- Whenever they are processed separately phase and amplitude information, Block 13 takes the selected amplitude information (from Block 10) and the phase one (from Block 12) and combines them for use later in Block 14. Otherwise, Block 13 is limits to transmit to Block 14 the quantized weights with their corresponding phase information.

Block 14.- Entropy coding of the signs. There are a variety of coding mechanisms of the entropy that could be used for this purpose.

Block 15.- Generation of a data flow to from the encoded entropy signals of Blocks 6 and 14. The decoder, which is not shown here, should reverse everything the process until reconstructing the image. As noted in the Block 11, the only investment process that is not trivial is the associated with the nonlinear transforms of blocks 7.A, 7.B and 7.C. In section 3 the invertibility of the transformed proposals.

Block 16.- Calculation of the entropy or of the distortion.

Block 17.- Return to Block 1.B, unless already quality (distortion) or size parameters have been reached (entropy) specified previously.

Block 18.- Storage or transmission of the color coded image.

2. Change the contrast metric (Blocks 5.A, 5.B, 5C)

The first key element is the use of a suitable contrast metric in the local representation in frequencies of the A, RG, and YB channels. This initial processing is a necessary preliminary step before applying the perceptual transforms: so that it is possible to apply parameters obtained from psychophysical experiments to the non-linear transforms of Blocks 7.A, 7.B and 7.C, the input signal must Express in the appropriate contrast units.

The literature on psychophysical experiments [15, 16] describes the non-linear response of the sensors of the human visual system against periodic signals expressed in contrast units. In addition, it has been shown that the shape of the non-linear response curve of chromatic sensors, tuned to different positions and frequencies, is similar to that found for achromatic sensors [16], provided that the stimulus is described in the units of adequate color contrast. However, there is no general procedure for defining such units for a particular set of base functions in the spatial domain (such as block DCT or a particular wavelet transformation) when the stimulation modulation is purely chromatic. Therefore, the transformation of the amplitude coefficients to contrast units is the key factor that will allow: (1) to perform the relative scaling of the parameters of the achromatic and chromatic channels (for example, the relative sensitivity as a function of frequency [ 17]), and (2) design the parameters that will control the shape of the chromatic nonlinearities, taking as the starting point those of the achromatic case. The contrast transforms of Blocks 5.A, 5.B and 5.0 are key to simplify the formulation of Blocks 7.A, 7.B and 7.C.

The definition of contrast in the literature psychophysics is closely linked to the procedure that has been followed to build the stimuli used in the experiment. By For example, the color contrast can be defined from the luminance modulation of two base functions of two colors, which we will call "extremes", e_ {1} ^ {(i)} and e_ {2} ^ {(i)}, added together to generate networks of perceived luminosity constant [17]. The maximum variations of luminance and color (the maximum amplitude of the stimuli, which would define the unit of contrast) is limited by the range of colors that can be generated by the particular color generation device used in the experiment.

To apply a contrast definition comparable we must: (1) obtain the equations that relate the amplitudes of the local frequency coefficients and the maximum modulation of color space with luminance and extreme colors of equivalent equiluminous nets, and (2) ensure the calculated extreme colors, with the equations described above, from an image database wide enough, they are within the color gamut playable by the usual playback devices. The underlying idea is to define the unit of contrast from the maximum variations of luminance and color found in the natural images and at the same time be consistent with the definition of color contrast of psychophysical literature.

According to the above, the definition of contrast Chromatic and achromatic of Blocks 5.A, 5.B and 5.C, are based on Two steps:

First, obtaining the equations that relate chromatic and achromatic contrast to the amplitudes of the local frequency transform of the achromatic and chromatic channels (see subsection 2.1). These equations, for a chromatic channel @ i @ depend on the pair of extreme colors e_ {1} {(i)} and e_ {2} {(i)}, obtained at from the maximum variation, ΔT_ {max} ^ (i)} in the address that isolates that channel. Also, if a model is used linear color vision, to generate an equiluminous network, the average luminance of the colors that is mixed cannot be the same, since colors of different chromaticity have different luminosities at equal luminance. Therefore, a psychophysical experiment to determine the appropriate proportion of luminance in the mixture. In Sub-section 2.2, describe this procedure as well as the particular results of an experiment designed for the base functions of the DCT, used in a possible implementation of the invention.

Second, range study of values of the maximum variation ΔT_ {max} ^ {(i)}, in a Representative image database. From the study empirical shown in sub-section 2.3, we estimate the maximum variation that allows a unit contrast definition consistent with psychophysical literature. These results are a example for the particular DCT transform chosen and for the YUV linear model.

Finally, in the sub-section 2.4 the resulting transform is summarized with the definition of adequate contrast used in Blocks 5.A, 5.B and 5.C, when takes the DCT as an image and color representation system and linear YUV space.

2.1. Formulation: Contrast of achromatic networks and chromatic, obtained from the coefficients of the Transformed images described in color spaces opponents

Networks (particular base functions in the spatial domain) of frequency f used in experiments psychophysicists, have a different color, described by a three-dimensional vector T, in each spatial position, x:

one

where T_ {0} is the average color, ΔT (f) represents the maximum color variation (peak) for that frequency with respect to the average color, and B (f, x) is the selected base function of f, e.g. one of those of the DCT. He index f, which identifies the base function, can symbolize something more general than frequency: in the case of a transform wavelet, f would have both spatial and frequency significance. In the ec. 1, we have added the index f also to the variation color ΔT (f), because in images that contain more of a base function the amplitude of the chromatic modulation can be different for each base function, B (f, x).

In an opposing and linear color space, such as, for example, the linear YUV space, the three components of the vectors T = [T1, T2, T3] T, are the luminance, T1 = Y, the Yellow-Blue (YB) component, T2 = U, and the Red-Green component (RG), T3 = V. Networks described above are used in psychophysical experiments to stimulate specific achromatic or chromatic sensors, selected by modifying the modulation components ΔT (f). The modulations ΔT_ {i} (f), are can easily relate to the coefficients of the discrete spatial transform of the corresponding image with the ec. 1 (see ecs. 20 below). The problem is that chromatic contrasts in the directions Yellow-Blue and Red-Green, as and as they are defined in the psychophysical literature, [17], no are trivially related to ΔT2 (f) and ΔT 3 (f). For clarity, in what follows, we will omit temporarily index f in color modulations \ DeltaT_ {i} (f).

Let's start with the simplest case, the achromatic. In this case, there is no modulation in the channels chromatics (ΔT 2 = ΔT 3 = 0), so the network that would isolate the achromatic channel is:

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2

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and achromatic contrast is defined simply as Michelson's contrast of the achromatic network (only of luminance):

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3

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where T_ {01} is the luminance average (or the luminance of the average color), and the amplitude ΔT1 can be obtained from the coefficients of the local frequency luminance channel transform corresponding using Ecs. 20 20. This definition is extendable to more complex wavelet bases, without more than dividing each coefficient of each sub-band per residue low pass corresponding to that resolution. How result, achromatic contrast is in the range C_ {achrom} \ in [0, 1] since \ DeltaT_ {1} \ in [0, T_ {01}].

However, in [17], the definition of color contrast takes into account the way they are designed Experimentally the chromatic networks. To generate a modulation purely chromatic around a certain average color, T_ {0}, at along a given address T_ {i}, with i = 2, 3, are added in contraphase (see upper line of fig. 3) two luminance networks with the chromaticity of the extreme colors e_ {1} ^ {(i)} and e_ {2} ^ {(i)} (the luminance of which is considered unity):

4

where the modulations of luminance \ DeltaY_ {j} ^ {(i)} are in the ranges:

100 , with the following restrictions:

- The average color is obtained by adding the extreme colors e_ {j} ^ {(i)} with their luminance scaled in a particular proportion (given by the factor \ eta_ {i}):

5

- Luminance modulations ΔY_ {j} {(i)}, are linked together:

6

- Total variation in the chromatic direction i, ΔT (i)} does not induce any modulation in the channel orthogonal chromatic This is:

7

8

Note that, given the difference between luminosity and luminance , in order to obtain an equiluminous network with two networks of different color, these must have different average luminances (which induces a residual modulation of luminance η_ {i} T_ {01}). The variation with respect to the average luminance (the factor η) must be determined experimentally for each chromatic channel.

Section 2.2 is dedicated to obtaining this factor for DCT base functions with frequency and color Average dice.

In psychophysical literature, the contrast chromatic in channel i is defined as Michelson's contrast of either of the two luminance networks added in contracted that generate the purely chromatic network:

9

From Ecs. (1), (4) and (9), can deduce the relationship between chromatic modulation in the direction chromatic i, \ Deltat ^ (i)}, and the corresponding contrast chromatic:

10

If we consider the case of chromatic contrast unit (making C (i)} chrom = 1) we get the relationship between what is considered maximum modulation on that channel, ΔT (1) max, and the extreme colors, e_ {j} ^ {(i}):

eleven

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12

In psychophysical experiments, modulation maximum is chosen so that the extreme colors are within the range of colors that can be generated by the playback device used. Following this criterion, in section 2.3 we explore a representative image database to obtain a estimation of the maximum possible modulation around the color average of each image, so that the extreme colors are always within the range of generable colors on monitors standard (for example, within the triangle that appears represented in dotted lines within the color diagram of the fig. 3).

Using ec. 10, you can derive the contrast chromatic C (i) chrom from modulation \ DeltaT_ {i}:

13

Known achromatic and chromatic contrasts depending on the modulation in each opposing channel (ecs. 3 and 13), the last data required to be able to express the amplitudes of the local frequency transforms depending on the contrasts, is the relationship between the coefficients of the discrete transform and the corresponding modulations.

In the case of DCT, this relationship may found in the literature [18]. Here, the indexes x, f previously used are explicitly declared as x = (m, n) and f = (p, q). With this notation, the coefficients a (p, q) of the two-dimensional DCT, corresponding to the representation of a block of MxN image in the spatial domain, A (m, n), are [18]:

14

The inverse of the DCT is written as:

fifteen

If the acquired image is a simple function base (in the chromatic channel i) defined as follows:

16

It is then possible to write the appropriate relationship between the image coefficients in channel i, a_ {i} (p, q) and the actual chromatic modulation for that frequency ΔT_ {i} (p, q):

17

18

19

twenty

2.2. Experiment 1: Proportions Blue-Yellow and Red-Green in nets of constant brightness

In this section, we describe the experiments psychophysicists performed to assess what relationship they should be in the average luminance of the achromatic networks used to generate purely chromatic networks - with uniform luminosity - in the U and V addresses, that is, the factors \ eta_ {i} of the previous equations.

Stimuli The stimuli were generated in computer-controlled CRTs, with an 8-bit resolution graphics card. The systems were colorimetrically calibrated and controlled using Matlab®, with the COLORLAB function library (available at http://www.uv.es/vista/vistavalencia).

The colors e_ {j} ^ {(i)} were chosen in the directions of the color space that nullified one of the YUV space color channels, verifying that:

- The modulations that occur throughout the direction i, from an average color T_ {0}, only differ in sign. The average color selected was the average of one Public image database [19]. In the NTSC color space RGB we have that T_ {0} = [132 116 90] T, with a luminance of 117.8 cd / m2.

- Induced modulation was the maximum allowed By the range of ~ monitor colors. Two pure DCT networks of luminance, both of 8 cpd, and. each with the chromaticity of a extreme color, were generated in counter phase. initially with the same average luminance, and they joined. The resulting image, which subtended 0.25 degrees, was presented on a gray background of 50 cd / m2 in a dark room.

Before starting the measurement batches, proper, it was modified by successive adjustment, the luminance of the achromatic point, T_ {0}, so that:

- Luminance stayed within range of possible monitor values, in all pixels of the image resulting.

- The range of luminance variation of the networks, set by the average value, were sufficient for the observers could modify the luminance of one of them until Reach the condition of constant brightness.

With these restrictions, the chosen luminance for the average color it was 80 cd / m2.

Measure. The networks described above were shown to the observer, who fixed them briefly, after a period of adaptation of one minute to the gray background. The observer's task was to adjust the variable η_ {i}, so that the two half-periods of the resulting network seemed of equal luminosity. For this, the adjustment method (MOA) [20] was used. For each observer, the result of the experiment was obtained as the average of five measurement batches. The result
Final tado is the average of a set of 4 untrained observers, in the age range between 20 and 40 years.

Results The factors found for the Blue-Yellow and Red-Green networks of the described experiment are:

twenty-one

22

Since the values of \ eta_ {i} depend on (1) the chromaticity of the extreme colors e_ {j} ^ (i)}, (2) the network frequency, and (3) the nature of the base function, the Values shown are strictly valid only for experimental conditions described. The change of base functions (e.g. if wavelets are used instead of block DCT) or opponent color space, would require experiments specific following the procedure described. As is currently implemented the invention, we assume that the proportions that we have encountered with the conditions described above are approximately valid for different average colors and functions  base.

It should be noted that the use of models does not linear color vision, in which the achromatic channel corresponding better describe the perception of brightness, could alleviate the need for this experimental step to generate networks purely chromatic

2.3. Experiment 2: Maximum modulation in images natural represented in opposing spaces

In this section, we describe the numerical experiment by which reasonable values of the maximum modulation in natural images were estimated, along the directions of the linear YUV space. These values (ΔT (i) max) i
they are necessary in the definition of color contrast given in ec. 13. To be consistent with the experimental restrictions that apply in the psychophysical literature, any particular choice of maximum modulation values must meet the following condition: for a typical natural image, with average color T_ {0}, the extreme colors of the ecs. 12 must be within the range of colors that can be generated by a typical display.

Experiment. To find these values, we start from an arbitrary initial estimate, eg (ΔT {(i)} _ {max}) {i} = 256, and check if the previous condition was met for e_ {j} ^ {( YB)} and e_ {j} ^ {(RG)} (calculated with ec. 12 and experimental proportions 22) in a representative set of natural color images (see the following section for a detailed description of the database) . If, for a given image, any of the extreme colors were outside the color range of a typical CRT monitor, the corresponding maximum modulation, ΔU_ {max} or ΔV_ {max}, was reduced by 5%. The search process stopped when all the images in the database verified the condition.

Due to database limitations (e.g. a limited range of average luminance), of the procedure described only results in a set of recommended values. These Recommended values do not guarantee an upper limit in the color contrast: images with contrast may exist chromatic superior to the unit, particularly in conditions of low luminance and / or high saturation. For such images, the use of higher maximum modulation values could lead to contrast values more convenient.

Database. We performed the previous numerical experiment on a database consisting of 100 images of the McGill University color image database [19] (mainly images of flora and fauna) and 25 raw images taken in our laboratory (mainly human faces). In the latter case, a Canon EOS 20 D camera was used to capture the images calibrated with the COLORLAB library and a PhotoResearch SpectraScan PR650 spectroradiometer.

Results Figure 3 shows two images that limit maximum modulation in directions V and U respectively. The CIE xy color diagrams at the bottom of the figure show the colors of the corresponding image (in gray), the average color (in black), and the extreme colors (red and blue). The dotted triangle in the chromatic diagrams represents the range of colors available on a typical CRT monitor (similar to primary NTSC or PAL RGB). As can be seen in the chromatic diagrams, the image on the left limits the modulation in the V (red-green) direction, while the image on the right limits the modulation in the U (yellow-blue) direction.

The maximum modulations compatible with the Psychophysical assumptions in the analyzed database were:

2. 3

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24

The associated error, ± 2, corresponds to the step 5% in the search procedure. In addition, due to previous considerations on the limitations of the base of data, these values are simply a recommendation that could be improved by introducing some kind of dependency with the medium luminance through a more refined implementation.

2.4. Summary: definition of color contrast and achromatic

According to the general scheme of the invention (see Figure 1), the set of transformations of the signal is carried out in blocks 3, 4.X and 5.X, and it can be summarize like this:

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25

where the components of the vectors, A '(x), are the triestimulo values of the color in the pixel x in the initial color space (not opponent) such as NTSC RGB; the vectors, A (x), obtained from the chromatic transformed in block 3, are the corresponding colors in an opposing representation (such as linear space YUV); the elements of the vectors, a (f), are the local transform coefficients space-frequencies applied to images A_ {i} (x), i.e., a_ {1} (f) represents the coefficients of the achromatic image transform, a_ {2} (f) are the coefficients of the transform of the Blue-Yellow image, and a_ {3} (f) are the image transform coefficients red-green (obtained using blocks 4.A, 4.B and 4.C, respectively). Finally, the contrast transform express each amplitude, a_ {(}), in units of contrast chromatic and achromatic, giving the vectors c (f). The components of the contrast vector are: c_ {1} (f) = C_ {achrom} (f), c_ {2} (f) = C (YB) chrom (f), and c 3 (f) = C (RG) chrom (f).

According to the formulation and results experimental presented in this section, if the representation color is linear YUV, and the spatial representation selected is DCT to blocks with a block size M x N, the Recommended contrast transformations are those listed down:

For the luminance channel (Y) (block 5.A):

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26

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27

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28

For the channel blue-yellow (U) (block 5.C):

29

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30

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31

For the channel red-green (V) (block 5.B):

32

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33

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3. 4

3. Nonlinear perceptual transformations

This section focuses on the description of the nonlinear perceptual transformations applied to local frequency transforms expressed in units of achromatic and chromatic contrast.

3.1. Transformations of divisive normalization (achromatic, blue-yellow and Red Green)

The second key point of the present innovation it focuses on the application of a nonlinear transformation perceptual to the chromatic and achromatic channels. The basics of this transformation are motivated by facts and findings fundamentals both perceptual (control of perceptual gain and masking experiments) as statistics (theory of efficient coding).

Perceptual transformation is modeled in three steps: the first consists of a set of linear filters applied to each channel (this step corresponds to blocks 4A, 4B and 4C in Figure 1); then the contrast of each coefficient is obtained using the procedure described in the previous section (Blocks 5A, 5B and 5C in Figure 2); Y, finally, a non-linear transformation is applied to the output of the second stage (blocks 7A, 7B and 7C in Figure 2). This last transformation can be a nonlinear transformation point-to-point or a transformation nonlinear preferably [15]. In the latter case, the energy of each coefficient is normalized by a combination of energies of its neighbors in frequency, and therefore for each channel the response to a particular frequency is obtained as follows:

35

where the subscript i = 1, 2, 3 denotes the channel; c_ {i} (f) are the outputs of local frequency analyzers in contrast units; s_ {i} (f) are the CSF type functions; γ is an exponent; the (f) is a regularization function; u h (f, f ') determines the neighborhood of interaction between the coefficients in the non-linear normalization of energy.

36

where 360 , | f | It is given in cycles per degree ( cycles per degree , cpd), and the Gaussian is normalized to have unit volume.

The previous interaction kernel is just an example that includes frequency relationships within the same block but could be generalized to include spatial and chromatic interactions.

This general model of divisive normalization is well established for the achromatic case based on thresholds increments of achromatic contrasts from sinusoids or Gabor blocks [15] and from psychophysical experiments equivalent. This achromatic model has been used successfully in various image processing applications, including achromatic image compression [11, 14] and restoration of achromatic images [13].

In the chromatic case, a similar nonlinear behavior in both the sinusoidal and Gabor [16, 21]. This is the reason why in the present invention, the parameters that control the non-linearity in the chromatic case (γ, the, h) have the same values as in the case achromatic. However, total frequency sensitivities adapt by color channel, based on previous work with linear models [17].

Since all psychophysical results and psychological are based on measures using sinusoidal networks or Gabor functions, experimental parameters must be adapted to the particular domain of image representation (e.g. DCT, Wavelets, ICA, etc.). If the image representation is in shape from block-DCT, we recommend using the values particulars illustrated in figures 4, 5 and 6 thus following the recommendations of Dr. Uriegas [21], Dr. Watson [22] and Dr. Heeger [2. 3].

The response in the achromatic channel has been calculated under two input conditions to illustrate how the model in eq. 35 takes into account different perceptual facts. First, the response, r_ {1} (f), of a sensor tuned to a frequency f , is calculated when the input is c1 = [0, c_ {1} (f), 0] (Figure 7 shows the results of two specific sensors: r_ {1} (f = 4) and r_ {1} (f = 10)). Second, the response of a sensor, r_ {1} (f), has been obtained in the presence of an additional pattern with a different spatial frequency, that is, when the input is c_ {1} = [0, c_ {1} (f), 0, c_ {1} (f '), 0] (Figure 9 shows the results obtained by the sensors r_ {1} (f = 4) and r_ {1} (f = 10) when the inputs are c_ {1} = [0, c_ {1} (4), 0, c_ {1} (6), 0] and c_ {1} = [0, c_ {1} (6), 0, c_ { 1} (10), 0] respectively). The perceptual facts introduced are:

Frequency selectivity: the visibility of the distortions depends on the spatial frequency. Note that in Figure 7, the slope of the response curve is greater than 4 cpd than 10 cpd, and therefore, greater distortion at 10 cpd is needed to obtain the same perceived distortion. In other words, a noise of 4 cpd is more visible than a noise of the same energy at 10 cpd. This general behavior is given by the pass-band function s_ {1} (f) (see Figure 5).

Auto masking: the amount of distortion needed to obtain a constant perceptual distortion increases with the contrast of the input. See in Figure 7 how Δc increases with stimulus contrast This is due to the fact that the response is attenuated when the contrast given by the normalization term in the denominator of Eq increases. (35).

Cross-masking: Attenuation (and the corresponding saturation of the response and decrease in sensitivity) also occurs when other patterns c_ {1} (f ') with f' \ neq f are present. Note in Figure 8 that the amount of distortion required increases with the contrast of the mask at different frequencies increases. Moreover, given the Gaussian form of the interaction neighborhood, nearby frequency patterns mask the distortion more effectively than those of very different frequency. Thus, the mask at 6 cpd induces a greater variation of acceptable noise at 4 cpd than at 10 cpd.

A similar behavior occurs in the color channels

3.2 Experiment 3: inversion of transform no linear perceptual Invertibility condition

Nonlinear transforms must be invertible to be able to reconstruct the image in the decoder to from the transmitted or stored data. In [11] it was proposed an investment procedure based on an explicit form, and studied the invertibility for the achromatic case. This procedure requires matrix inversion (I - D_ {ri} \ h), where I is the identity matrix, D_ {ri} is the matrix diagonal containing the absolute values of the elements of r_ {i} (f), and h is the matrix that models the relationship between coefficients The investment condition ensures that all Dri \ cdot h eigenvalues must be less than one. Does not exist a theoretical guarantee that this condition is met for all images, both in the proposed achromatic case and in the Chromatic presented here. Therefore, the invertibility of non-linear chromatic transformed (Blocks 7.B and 7.C) only They can check empirically.

Checking the invertibility condition in chromatic cases. The invertibility condition was empirically verified by calculating the highest self-value of the Dr2 \ cdot and Dr3 \ hd matrices for 25600 16x16 blocks of a set of color images [19]. The invertibility condition was also checked for the reconstructed signal \ hat {r} i from the weights quantized by SVM at different compression rates in the range [0.2, 2.2] bits / pix. In these experiments, the highest self-value for each block was, in all cases, less than 1.

4. Support Vector Regression (SVR) with profile adaptive

The third block of the coding scheme presented is the inclusion of a machine learning method ("machine learning") so that it is responsible for the selection of the most relevant coefficients in the domain concrete representation. The method should consider the particular characteristics of the domain, and therefore the different perceptual importance of each coefficient in the domain. In this section we illustrate the block of machine learning through a specific method, the vector machine support for regression ('support vector regression, SVR), which has shown good results in a great number of regression problems and approximation of functions, using few parameters (samples or support vectors) [24]. In the next section we review the standard SVR. Given the this approach defines a constant insensitivity parameter and independent of the perceptual relevance of each sample, to Below we present a new formulation of the SVR for work in non-Euclidean domains of representation. Finally, we summarize some points to This important feature to consider.

4.1. Standard SVR

In the proposed compression scheme, three SVR models must be applied independently on the coefficients of each nonlinear representation r (f) = [r_ {1} (f), r_ {2} (f), r_ {3} (f )] T. Next, and for clarity, we present the SVR notation only for the generic case of a non-linear representation of a particular channel, r. In essence, for the development of the model, we have a set of pairs of positions and coefficients (f, r), where
f = 1, ..., N represents the spacio-frequency index of the coefficients r \ in R in the corresponding nonlinear perceptual transformed channel (r_ {1} (f), r_ {2} (f) or r_ {3 }(F)).

The standard SVR formulation maps the input data f to a larger dimensional space where applies a linear regression, which is not linearly related with the input representation space. Therefore, you can define the regression model as:

37

where \ hat {r} f are the estimates of the coefficients r, (.,.) represents the scalar product operation, \ phi is a nonlinear mapping to a larger Hilbert space \ phi: 370 ; w is a vector of weights in the space of larger features; and b is a model bias term.

The SVR consists in solving the following regularization problem with linear restrictions:

38

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subject to:

39

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40

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41

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The free parameter \ lambda must be set and controls the importance of data adjustment (minimization of data errors \ varepsilon_ {f} and \ varepsilon * _ f) versus keep a model with small weights || w || (force softness on the features space). The method uses the so-called cost function \ varepsilon-insensitive [24], which penalizes errors greater than \ varepsilon linearly. Notice that the \ varepsilon parameter represents the error or distortion allowed

The usual procedure to solve this optimization problem is to introduce the restrictions linear (39) - (41) in Eq. (38) by multipliers of Lagrange associates \ alpha_ {f} ^ {(\ text {*})}, then calculate the conditions of Karush-Kuhn-Tucker, with whom Solves Wolfe's dual problem [25]. This leads to having to solve a quadratic programming (QP) problem in a space of parameters or dual weights \ alpha_ {f} ^ {(\ text {*})} instead of having to do it in the space of the parameters of the model w, of which the dimension is unknown. A very important result This optimization results in that, by nullifying the derivative of the functional dual, we obtain a relation of the vector of weights in the feature space expressed as a linear combination of mapped samples, this is:

42

Now, by entering (42) in (37), the solution for a particular entry f 'can be obtained in this way:

43

which explicitly depends on the scalar product of the mapped samples and on the dual weights obtained α_ {f} and \ alpha_ {f} ^ {(\ text {*})}. This result allows us to work in a space of higher dimension without having to know the coordinates of the samples in this space, only the scalar products between them. These products are called kernel functions, K (f, f '), and define the regression function:

44

where the inner (scalar) \ langle \ phi (f), \ phi (f ') \ rangle products are represented by a kernel matrix K (f, f'). Note that only samples with non-zero Lagrange \ alpha_ {f} ^ {(\ text {*})} multipliers intervene in the solution and are called support vectors ( "support vectors", SVs ). The immediate advantage of the method is that functions can be approached very flexibly with relatively few parameters, bringing this concept of sparsity to the inherent idea of compression.

The matrix of Gram (or kernel) K (f, f ') = \ langle \ phi (f), \ phi (f ') \ rangle can be seen as a matrix of similarity between samples, and a definition appropriate is the key to the proper functioning of a method SVR In all our experiments employed a basic function radial (RBF):

Four. Five

This method introduces a third free parameter. to be optimized, the kernel width or scale length \sigma.

4.2. SVR with adaptive insensitivity

The main problem when considering the previous solution is that it assumes equal relevance for each sample, which is not true in general. This can be solved using a different penalty factor for each of the samples f according to a certain confidence function k_ {f} . This idea can also be extended to the design of one sensitivity per sample. The SVR with adaptive insensitivity [26] increases or decreases the insensitivity region? Depending on the training sample. Thus, the function to minimize is:

46

and restrictions on auxiliary variables now depend on the sample in particular:

47

Therefore, now each sample has a sensitivity to error \ varepsilon_ {f} = \ varepsilon / k_ {f}, which intuitively means that an error is allowed different to each of them depending on their relevance (in our case, perceptual). Including restrictions (47) - (49) in the corresponding functional (46), the solution in the same way as in the standard case, since Again you get an analogous QP problem.

4.3 Punctuations: adaptive insensitivity and work domain

In SVM based coding schemes as presented in [5, 12, 14], the signal is described by Lagrange multipliers associated with support vectors necessary to keep the regression error below thresholds \ varepsilon_ {f}. Increasing these thresholds reduces the number of support vectors, thus reducing the entropy of the encoded image but increasing distortion. The key point is therefore the choice of suitable values for \ varepsilon_ {f} according to some criteria appropriate to the work domain. For example, in a Euclidean domain, you can work with constant values of \ varepsilon_ {f} for all f. This condition is met in the nonlinear perceptual transform included in the scheme of the present invention, but not in DCT or wavelet linear domains as the employees in [12], where each coefficient has relevance different in the representation of the signal. See [5, 13, 14] for A more detailed discussion.

5. Experimental results to evaluate the method behavior

This section illustrates the behavior of a implementation of the method for compressing a set of color images compared to an implementation of JPEG standard.

5.1. Algorithms, comparison set and experiments

The implementation of the proposed method, identified by the acronym C-NL-SVR (Color-Non-Linear-SVR), includes the representation of color in the linear space YUV, the representation of special information in the domain DCT-local with 16X16 blocks, transformations of contrast as those referred to in section 2, transformed non-linear perceptuals of each chromatic channel with the parameters given in section 3, and a process of learning of this last non-linear representation using SVR as described in section 4. Finally, the description selected by the regression algorithm (weights) are uniformly quantized and coded according to the scheme described in section 1.

The JPEG implementation used here uses the same color representation and the same local DCT with blocks 16X16. In the case of JPEG, quantization matrices based on in the achromatic and chromatic CSFs of Mullen [17].

The experiments were performed on a set of color images consisting of 25 natural images representative (see figure 9). All images of this set were compressed at different rates in the range [0.1, 2.2] bits / pix It should be noted that the usual electronic volume of consumption (mobile phones, low-end digital cameras, cameras semi-professional and professional digital cameras high-end) ranges in the range between 1 bit / pix for JPEG files Low quality and 2.2 bits / pix for high JPEG files quality.

In all experiments, three were trained SVR models (one for each chromatic channel and transformed block), and we model the (signed) value of the coefficients of the answer, r_ {i} (f), i = 1, 2, 3. In our domain of non-linear representation, r, we use SVRs with RBF kernel, constant insensitivity \ varepsilon parameter, and we set an arbitrarily high value of λ. In all the cases, ε and the size of the quantization steps were jointly modified to meet the specifications of desired distortion and / or entropy (see Figure 1).

After training, the signal is described by Lagrange multipliers of support vectors necessary to keep the error below thresholds ?, these multipliers being quantized evenly. The last step is the entropic coding of the quantized weights The compression rate (or distortion introduced) is essentially controlled by a factor applied to the thresholds.

5.2. Numerical comparison between C-NL-SVR and JPEG: curves distortion rate and compression gain

In order to evaluate the quality of the images encoded at the same compression rate, three were used distortion measures: the standard mean square error (RMSE), and two significantly significant measures; the Structural SIMilarity (SSIM) index [27] and the S-CIELab metric [28].

The average curves of distortion rate for all images in the training set of figure 9 are shown in figure 10. In the rate-distortion graphs the bars indicate the standard error deviation for each rate of compression. These graphs show that the Proposed C-NL-SVR is greater than JPEG (the continuous line is below the dashed line for distortions and outperforms the other in the case of the similarity in the range of entropies of commercial interest). Without However, a naïf interpretation of the overlay of the bars of standard deviation can lead to questioning the significance of this eventual gain.

Note however, that in the graphs of distortion rate, the overlap between these bars does not necessarily mean that the behavior is the same or that the gain is statistically negligible: in this case, the overlap comes from the fact that different images in the database have intrinsically different complexity leading to very different distortions when they are encoded to A certain rate. Figure 11 (a) shows an example of what Previous: In this case, the behavior is shown distortion rate of the two methods (continuous lines and discontinuous) for two different images of the database (black and blue lines). Naturally, if averaged over such a class of images the standard deviation is going to be very large, but the relevant fact is that the gain of the proposed method is consistent in each image: notice for example that, taking some particular entropy value for the JPEG result, in both images (for example red or purple dots in Figure 11 (a)), the entropy of the result C-NL-SVR with the same distortion is consistently much smaller.

Therefore, it makes more sense to define some type of compression gain measurement for each image and rate, and average these gains for the set of images in the base of data.

Here, we define the compression gain (compression gain) of one method over another reference for a given entropy, G (H), in terms of the ratio of the rates for the same level of distortion:

48

Fig. 11 (b) shows an illustrative scheme to determine the compression gain for a distortion measurement on a particular image (zoom of the RMSE rate-distortion curve for the black lines of the graphic on the left). In the example illustrated in Figure 12 (b) we consider the two possible cases (gain less than 1 at low entropy, and gain greater than 1 at high entropy). Note that gains greater than 1 imply that the proposed method uses fewer bits than the reference method to represent the image at the same distortion. This compression gain can also be expressed in percentage terms by:

49

In a practical way, for a given entropy, G = 2 or PG = 100% means that 20 images C-NL-SVR occupy the same volume (in bits) than 10 JPEG images (for the same quality of reproduction).

Of course, the particular values of compression gain will depend on the measure of distortion used and of the set of calibration images.

Figure 12 shows compression gains obtained by the C-NL-SVR method over JPEG for the three distortion measures considered (RMSE, SSIM and S-CIELab) for each entropy considered in The rate range analyzed. In these graphs we have included the standard deviation of earnings to assess the reliability of the approach.

Note that in the range commercially significant [1, 2.2] bits / pix, the proposed method exceeds widely to JPEG and allows improvements in the compression of the order of [60, 180]% for RMSE, [25, 60]% for SSIM, and [80, 275]% for S-CIELAB. As standard deviation bars do not cross below the line G = 1, the effective gain (higher a 1) is consistent over a wide range of images, therefore, The proposed method clearly exceeds JPEG.

5.3. Visual comparison

Figures 13-17 show representative results of the methods considered on 5 images ("Parrot", "Lena", "Roof", "Flower3", "Face1") at different rates in the range [1.0, 2.2] bits / pix . The visual results confirm that the numerical gains shown in Figure 13 also result in a perceptual gain. In general, JPEG results in worse results (with more block effect). In addition, it is worth noting that high frequency details are softened more in JPEG than the proposed method. These negative effects are reduced by the introduction of machine learning techniques such as SVRs in the non-linear perceptual domain. See for example Lena's eyes and cheeks (Fig. 14), the feathers of the hat (Fig. 14), the best reproduction of the high frequency pattern in the eye of the parrot (Fig. 13), the vertical slat under the roof the house (Fig. 15), or the patent effect of blocks on the flower (Fig. 16) and on the face of figure 17.

6. Method implementation

A possible device to implement the method previously described is a computer system that understands:

- An input and output interface to receive color image data that can be a simple channel of communication or multiple communication channels.

- A processor communicated with the interface of input / output to perform the steps of the method according to code stored in storage systems properly connected to the processor.

- Display systems (monitors) and graphics cards for the realization (off-line) of the psychophysical experiments described above.

- Memory systems to host the base of data used (off-line) in the experiments previously described.

Modifications can be made to the device just described, which would be in any case included in the scope included by the following claims.

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Bibliography

[1] GK Wallace . The JPEG still picture compression standard. Communications of the ACM , 34 (4): 31-43, 1991 .

[2] M. Naillon and JB. Theeten Method of and arrangement for image data compression by means of a neural network. US Patent No. 5,005,206, 1991 .

[3] RA Nanni and G. Abraham . Neural-network-based method of image compression. US Patent No. 6798914, 2004 .

[4] V. Kecman and J. Robinson . Method, apparatus and software for lossy data compression and function approximation. Patent Appl. No. WO 03/050959, 2003 .

[5] G. Gómez , G. Camps-Valls , J. Gutiérrez , and J. Malo . Perceptual adaptive insensitivity for support vector machine image coding. IEEE Transactions on Neural Networks , 16 (6): 1574-1581, Jun 2005 .

[6] AB Watson . Image data compression having minimum perceptual error. US Patent No. 5,426,512, 1995 .

[7] J. Malo , J. Gutiérrez , I. Epifanio , F. Ferri , and JM Artigas . Perceptual feed-back in multigrid motion estimation using an improved DCT quantization. IEEE Transactions on Image Processing, 10 (10): 1411-1427, October 2001 .

[8] J. Malo . Color technology, chapter Storing and transmitting color images, pages 117-164. Col. selected Materials. Servei de Publicacions of the University of Valencia , Valencia, 2002 .

[9] W. Zeng , S. Daly , and S. Lei . An overview of the visual optimization tools in JPEG2000. Signal Processing: Image Communication, 17 (1): 85-104, 2002 .

[10] Y. Navarro , J. Rovira , J. Gutiérrez , and J. Malo . Gain control for the chromatic channels in JPEG2000. Proc. of the 10th Intl. Conf. AIC., 1: 539-542, 2005 .

[11] J. Malo , I. Epifanio , R. Navarro , and R. Simoncelli . Non-linear image representation for efficient perceptual coding. IEEE Transactions on Image Processing , 15 (1): 68-80, 2006 .

[12] J. Robinson and V. Kecman . Combining Support Vector Machine learning with the discrete cosine transform in image compression. IEEE Transactions on Neural Networks , 14 (4): 950-958, July 2003 .

[13] J. Gutiérrez , G. Gómez-Pérez , J. Malo , and G. Camps-Valls . Perceptual image representations for support vector machine image coding. In G. Camps-Valls, JL Rojo-Alvarez, and M. Martínez-Ramón, editors, Kernel Methods in Bioengineering, Signal and Image Processing. Idea Group Publishing, Hershey, PA (USA), Jan 2007 .

[14] G. Camps-Valls , J. Gutiérrez , G. Gómez , and J. Malo . On the suitable domain for SVM training in image coding. Journal of Machine Learning Research, 9 (1): 49-66, 2008 .

[15] AB Watson and JA Solomon . A model of visual contrast gain control and pattern masking. Journal of the Optical Society of America A, 14 (9): 2379-2391, September 1997.

[16] E. Martinez-Uriegas . Color detection and color contrast discrimination thresholds. In Proceedings of the OSA Annual Meeting ILS-XIII , page 81, Los Angeles, 1997 .

[17] KT Mullen . The contrast sensitivity of human color vision to red- green and yellow-blue chromatic gratings. Journal of Physiology , 359: 381-400, 1985 .

[18] JS Lim . Two-dimensional signal and image processing. Prentice-Hall, Inc., Upper Saddle River, NJ, USA , 1990.

[19] A. Parraga . McGill Calibrated Color Image Database. Dept. of Vision Science, McGill University, 2003 . Available at http://tabby.vision.mcgill.ca.

[20] TT Norton , DA Corliss , and JE Bailey . The Psychophysical Measurement of Visual Function. Butterworth Heinemann, 2002 .

[21] EM Uriegas . Personal communication on contrast incremental thresholds for chromatic gratings measured at Stanford research international. Unpublished results , May 1998 .

[22] AB Watson . Personal communication on plausible parameters for divisive normalization in DCT basis. Unpublished results , March 2001 .

[23] D. Heeger . Personal communication on plausible parameters for divisive normalization in DCT basis. Unpublished results , March 2001 .

[24] AJ Smola and B. Schólkopf . A tutorial on support vector regression. Statistics and Computing, 14: 199-222, 2004 .

[25] B. Schálkopf and A. Smola . Learning with Kernels - Support Vector Machines, Regularization, Optimization and Beyond. MIT Press Series , 2002 .

[26] G. Camps-Valls , E. Soria-Olivas , J. Pérez-Ruixo , A. Artés-Rodríguez , F. Pérez-Cruz , and A. Figueiras-Vidal . A profile-dependent kernel-based regression for cyclosporine concentration prediction. In Neural Information Processing Systems (NIPS) - Workshop on New Directions in Kernel-Based Learning Methods, Vancouver, Canada, December 2001 . No published proceedings. Available at http://www.uv.es/\simgcamps.

[27] Z. Wang , AC Bovik , HR Sheikh , and EP Simoncelli . Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13 (4): 600-612, 2004 .

[28] X. Zhang and B. Wandell . Color image fidelity metrics evaluated using image distortion maps. Signal Processing , 70 (3): 201-214, 1998 .

Claims (14)

1. A method of compressing color images which includes the following steps: a) reception of the input color image expressed in RGB channels; b) transformation of RGB channels to a opposing color rendering space to get a channel achromatic (A), a red-green channel (RG), and a channel blue-yellow (YB); c) transformation of said channels A, RG and YB to a local space-frequency domain, as a sum of a set of base functions multiplied by the set corresponding coefficients and waste coding low frequency; d) expression of the coefficients of said local spatio-frequency representations of the channels achromatic and chromatic opponents in contrast units perceptually significant; e) application of transformations non-linear divisive standardization type with parameters adjusted to the use of contrasts in the expression of starting representations, to each of the channels A, RG, YB; f) estimation of the coefficients of said perceptual nonlinear representations using a machine learning procedure; g) quantification of the description obtained, followed by the entropic coding of the results after quantization. 2. A color image compression method according to claim 1, characterized in that the local frequency space transform in step c) is selected from: the DCT or any type of transform based on Gabor or wavelet functions . 3. A color image compression method according to any of claims 1-2, characterized in that in step d) the achromatic channel contrast is calculated as a function of a number of relevant parameters obtained by experiments. Psychophysical and numerical and chromatic channel contrasts are calculated from a number of relevant parameters obtained from psychophysical and numerical experiments. 4. A color image compression method according to any of claims 1-3, characterized in that the parameters of the contrast transformation obtained by psychophysical means include the proportions of the average luminance of the components of the components. Chromatic base functions and the parameters obtained through numerical experiments include reasonable values of the maximum color modulation in a representative database of color images. 5. A color image compression method according to any of claims 1-4, characterized in that in step e) the non-linear perceptual transformation applied to the achromatic channel is a divisive normalization with a kernel of Totally general interaction, and the non-linear perceptual transformations applied to the chromatic channels are divisive normalizations with the frequency sensitivity parameters specifically adapted and scaled with respect to the achromatic channel. 6. A color image compression method according to any of claims 1-5, characterized in that in step f) the machine learning process is trained to identify a sequence of base functions and their weights corresponding, guided with appropriate criteria to optimize the compactness of the resulting encoded data stream and / or the quality of the encoded image. 7. A color image compression method according to any of claims 1-6, characterized in that in step f) the machine learning procedure is an SVR procedure. 8. A color image compression method according to any of claims 1-7, characterized in that in step f) the machine learning procedure is a procedure implemented by one of the following methods: networks Neural, spline-based techniques, kernel methods, Bayesian networks, Gaussian processes or fuzzy logic. 9. A color image compression method according to any of claims 1-8, characterized in that in step g) the sub-step of coding the results is performed by the entropic coding of the data stream . 10. A method of compressing color images according to any of claims 1-9, characterized in that in steps e) and g) additional sub steps are included for processing the phase information separately of the amplitude information. 11. Data storage system that Contains a program such that, when running on a processor, Have it perform the method described in any of the claims 1-10. 12. Apparatus for producing compressed data from color images comprising methods of receiving the Input color images and processing methods for: a) transform said input data to a Opponent color space consisting of an achromatic channel, A, and two color channels, red-green, RG, and blue-yellow YB; b) transform said channels A, RG and YB to local space-frequency domains as a sum of base functions multiplied by the corresponding set of coefficients and waste coding goes low; c) express the coefficients of said local space-frequency representations of A, RG e YB, in significantly significant contrast units; d) apply a transformation non-linear type divisive normalization to contrast channels A, RG and YB; e) estimate the coefficients of said nonlinear perceptual representation of the image using a machine learning procedure; f) quantify the description obtained and the coding of the results. 13. Apparatus for producing compressed data of color images according to claim 12 characterized in that it also comprises visualization systems and graphics cards for performing (off-line) psychophysical experiments for obtaining luminance ratios average of the components of the chromatic base functions. 14. Apparatus for producing compressed color image data according to any of claims 12-13 characterized in that it also comprises a color image database for performing numerical experiments to estimate the maximum modulation values of the color in each cardinal chromatic direction.