Foveated Model based on the Action Potential of Ganglion Cells to

Improve Objective Image Quality Metrics

Sergio A. C. Bezerra

1,2

and Alexandre de A. P. Pohl

Department of Higher Education (DES),

Federal Institute of Education, Science and Technology of the Amazonas (IFAM), 69020-120, Manaus, AM, Brazil

Graduate School of Electrical Engineering and Computer Science,

Federal University of Technology - Paran´a (UTFPR), 80230-901, Curitiba, PR, Brazil

Keywords:

Human Visual System, Objective Image Quality Metrics, Foveated Image, Ganglion Cells.

Abstract:

In this work, a foveated model (FM) based on the action potential of ganglion cells in the human retina is

employed to improve the results obtained by traditional and perceptual image quality metrics. LIVE and

VAIQ image databases are used in the experiments to test and validate this model. Statistical techniques,

such as the Pearson Linear Correlation Coefﬁcient (PLCC), the Spearman Rank-Order Correlation Coefﬁcient

(SROCC) and the Root Mean Square Error (RMSE), are used to evaluate the performance of Peak Signal-to-

Noise Ratio (PSNR) and Structural SIMilarity (SSIM) metrics, as well as their versions improved by the FM.

The results are encouraging because the model proposed improve the performance of the metrics investigated.

1 INTRODUCTION

Processing techniques, storage and transmission of

images and videos have been receiving plenty of at-

tention on the part of researchers in academia and

industry. In this context, processing algorithms are

widely used in multimedia applications, such as tele-

conferencing, video distribution on the Internet, CD,

DVD and digital TV (Sun et al., 2005), (Yu and

Wu, 2000). These algorithms allow great perfor-

mance beneﬁts concerning encoding and decoding of

videos and images, particularly because they provide

a convenient size reduction for storage and transmis-

sion purposes. However, the adoption of compression

techniques with losses causes several types of visual

distortions in the content. For this reason, the devel-

opment of methods to assess the quality of images and

videos has become indispensable. In general, quality

assessment is classiﬁed into subjective and objective

methods (Engelke and Zepernick, 2007).

The subjective method uses a minimum num-

ber of subjects in its procedure to assess the im-

age and video quality (Corriveau, 2006). The eval-

uation groups the opinions of subjects into a Mean

Opinion Score (MOS) or a Difference Mean Opinion

Score (DMOS), which provides a statistic based-score

for assessment of the subjective quality (Engelke and

Zepernick, 2007). In (ITU-R BT.500-11, 2002) and

(ITU-T P.910, 2008), recommendations on the appli-

cation of subjective tests are detailed. It is important

to note that results obtained with the subjective eval-

uation are used to validate objective quality methods

(VQEG, 2003), (VQEG, 2008). Although valuable,

its use in real-time applications is not practical due

to the high cost associated with maintaining an ac-

tive group of human observers to perform the tests

(Wang and Bovik, 2006), (Sheikh and Bovik, 2006).

Instead, objective methods were created with the pur-

pose of automatically evaluating the perceived visual

quality (Wang et al., 2004a). In the context of images,

such methods are referenced as objective image qual-

ity metrics (IQM), which can be further divided into

two classes: traditional and perceptual metrics (Wang

and Bovik, 2002), (Pappas et al., 2005).

Traditional IQMs are interesting because they are

mathematically easy to deal with for evaluation and

optimization purposes (Wang et al., 2004b). The sim-

plest and most widely used traditional IQMs are the

Mean Squared Error (MSE), Peak Signal-to-Noise

Ratio (PSNR), Root Mean Squared Error (RMSE),

Mean Absolute Error (MAE) and Signal-to-Noise Ra-

tio (SNR) (Pappas et al., 2005). Nevertheless, they

also have been widely criticized for not correlat-

ing well with perceived quality measurements (Wang

et al., 2004b).

On the other hand, perceptual IQMs consider

Bezerra S. and Pohl A..

Foveated Model based on the Action Potential of Ganglion Cells to Improve Objective Image Quality Metrics.

DOI: 10.5220/0005547200840091

In Proceedings of the 12th International Conference on Signal Processing and Multimedia Applications (SIGMAP-2015), pages 84-91

ISBN: 978-989-758-118-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

characteristics of the Human Visual System (HVS) in

an attempt to incorporate perceptual aspects into the

quality measures. For instance, the Structural SIMi-

larity (SSIM) metric proposed by (Wang and Bovik,

2002) is, perhaps, the most widely used perceptual

IQM. The SSIM assumes that the HVS is highly

adapted for extracting structural information (such as

contrast, luminance, chrominance and borders) from

a scene and has been proved to outperform traditional

IQMs. Extensions of the SSIM metric have also been

proposed for image (Wang et al., 2003),(Wang et al.,

2004a) and (Zhang et al., 2011) and video (Wang

et al., 2004b), (Seshadrinathan and Bovik, 2007), (Ye

et al., 2008), (Yang et al., 2008) quality metrics.

Given the above, this work raises the hypothesis

that the metrics will be most effective if they consider

the action potential of ganglion cells for a given point

of the image over the regions of interest (ROI), as well

as the viewing distance between the image and the ob-

server.

Thus, a foveated model, denominated FM, based

on the Action Potential of Ganglion Cells is pro-

posed to improve the results obtained by PSNR and

SSIM objective image quality metrics. The LIVE

(Sheikh et al., 2005) and VAIQ (Engelke et al.,

2009) image databases are used in the experiments

to test and validate the FM. Statistical techniques,

such as the Pearson Linear Correlation Coefﬁcient

(PLCC), the Spearman Rank-Order Correlation Co-

efﬁcient (SROCC) and the Root Mean Square Er-

ror (RMSE), recently suggested by VQEG (VQEG,

2008), are used to evaluate the PSNR and SSIM per-

formance, as well as their versions improved by the

FM, denominated FM

PSNR

and FM

SSIM

, respectively.

The results are encouraging because the FM could im-

prove the performance of the investigated metrics.

The remainder of this paper is organized as fol-

lows. Section 2 describes the proposed foveated

model and how it is implemented. Section 3 describes

details of the experiments. Statistical results on the

metric performance are discussed in Section 4, fol-

lowed by the conclusions in Section 5.

2 PROPOSED MODEL

The foveated model (FM) proposed consists of three

steps as speciﬁed in Figure 1. Each of the steps is

detailed in the following subsections. The overall

objective of the model is to provide a foveated image

related to an input image. For this, the ﬁrst model

also needs to know the visual attention point (vap)

of the ROI. Automatic discovery of the vap was

not included in this study because of its complexity.

Thus, in this work the vap corresponds to the ROI

center point of the visual attention map in (Engelke

et al., 2009).

Given an image formed by NxM pixels, the ﬁrst

step consists of calculating the eccentricity of a pixel

away from the vap, which has as input the viewing

distance and the height of the image in pixels. The

second step estimates the visual acuity of the HVS

to a certain point of the image. Based on the visual

acuity information available in (Engelke et al., 2009),

a closed expression is employed to obtain the eccen-

tricity values. The third step calculates the action

potential provided by the ganglion cells, which then

results in the effective perception of the image by the

primary visual cortex. Finally, the model generates

a new image, called the foveated image (I

). This

foveated image is represented mathematically by:

= FM(I,vap). (1)

Use and Importance of the Foveated Model

In the process, the metric reads the reference and test

images and provides an image quality index (iQI),

described as:

iQI = IQM(I

), (2)

where I

and I

represent the reference and the test

image, respectively. It is important to note that the

traditional PSNR and SSIM metrics ignore the visual

attention modeling and action potential, assuming

that the distribution of the ganglion cells is uniform

in the different areas of the retina. To correct this,

it is assumed that the metric must read and compute

foveated images, as follows:

iQI

= IQM(I

), (3)

where iQI

is the image perceptual quality index,

where I

and I

represent the reference and test

foveated images. This way, the metric corrects the

values initially given by (2). In the following subsec-

tions, the procedure is described in details.

2.1 Eccentricity Measure

Figure 2 illustrates the eye of a human observer

positioned away from the screen where an image is

projected. d

is the viewing distance and d

cmROI

is the

distance between a certain pixel of the image and the

vap, both given in cm. The eccentricity, denoted as e,

is calculated according to the visual angle θ formed

between the lines, one representing the imaginary

axis between the fovea and the vap and the other

FoveatedModelbasedontheActionPotentialofGanglionCellstoImproveObjectiveImageQualityMetrics

Figure 1: Steps for implementing the proposed Foveated Model (FM). I is the input image exempliﬁed by rapids, vap is the

visual attention point and I

is the foveated image produced by the model. x and y are the coordinates of the vap selected for

rapids.

representing the axis formed by the pixel of the image

away from the vap and its projection in the retina.

The vap is represented by the point in the center

of the hexagon that limits the ROI. Eccentricity is

calculated in degrees by the following equation:

e = f

(arctn(

cmROI

)), (4)

where f

is the function that converts a value in

radians to degrees. Equation (4) is applied to any

spatial dimension of the image.

Figure 2: Diagram representing the human eye and the

screen, where the image is projected.

The relationship between the length in cm and the

pixels can be obtained by:

cmROI

pROI

· h

, (5)

where h

is the height of the spatial sampling of

the image, in cm, h

is the image height in pixels,

and d

pROI

is the Euclidean distance in pixels, be-

tween the vap and the pixel under attention, where

pROI

= [(x

vap

− x

pixel

)

− (y

vap

− y

pixel

)

]

1/2

. The

parameter d

corresponds to the result of the mul-

tiplication of the perceptual weight, denoted as ω

by h

. Perceptual weight is a constant that serves to

adjust the value of d

. Viewing distance in general

depends on the applications (ITU-T P.910, 2008).

The parameter d

is then obtained, in cm, by:

= ω

· h

. (6)

Substituting (5) and (6) in (4) gives:

e = f

(arctn(

pROI

· h

)), (7)

where (7) is used to calculate the eccentricity in this

work.

2.2 Visual Acuity Estimate

The expression derived to estimate the density

distribution of ganglion cells in the retina is based

on experimental data published in (Curcio and Allen,

1990). Curcio and Allen made anatomical measure-

ments of the density distribution of ganglion cells

in human eyes in different areas of the retina (nasal,

temporal, superior and inferior). The average density

distribution can be described by an equation given by:

= f

· (

0.85

1+ (e/0.45)

0.15

1+ (e/e

)

), (8)

where f

is the ganglion cell density and represents

the HVS perception response for a pixel projected in

the retina. The f

is the ganglion cell density in the

center of the retina (fovea), e is the eccentricity in de-

grees and e

is a constant that differs from subject to

subject. In this work, a value of 36,000 cells/deg is

used for f

and 3.3

◦

is used for e

(Barten, 1999).

SIGMAP2015-InternationalConferenceonSignalProcessingandMultimediaApplications

For further calculations, Equation (8) is normalized in

the interval [0, 1].

2.3 Action Potential Estimation

The action potential provided by the ganglion cells in

the observation of each pixel is then used to correct

the viewed image as follows:

(x,y) = I(x,y) · f

, (9)

where I(x,y) is the pixel of an image without correc-

tion, f

is the visual acuity of this pixel and I

(x,y)

is the foveated pixel at the same coordinate. The FM

gives the foveated result when (9) is applied to all pix-

els of the image.

3 MATERIAL AND METHOD

3.1 Image Databases

In order to apply the proposed metric, two image

databases (IQAD) are used in the experiments, LIVE

(Sheikh et al., 2005) and VAIQ (Engelke et al., 2009).

LIVE contains reference and degraded images. The

Visual Attention for Image Quality (VAIQ) contains

visual attention maps of LIVE reference images. The

following subsections and Table I provide more infor-

mation on these IQADs.

3.1.1 LIVE Database

LIVE is provided by the Laboratory for Image and

Video Engineering in collaboration with the Center

for Perceptual Systems at the University of Texas at

Austin. The database include pictures of faces, peo-

ple, animals, close-up shots, wide-angle shots, nature

scenes, man-made objects, images with distinct fore-

ground and background conﬁgurations, and images

without any speciﬁc object of interest. Some images

have high activity, while some are mostly smooth.

Most important, all images are 768 x 512 pixels in

size.

LIVE contains 29 reference images and 779 test

ones, the latter being the results of distortions ap-

plied to the 29 reference images. Types of existing

distortions are White Noise, Gaussian Blur and Sim-

ulated Fast Rayleigh (wireless) Channel, JPEG and

JPEG2000 compression. However, test images with

White Noise are not included in the experiments of

the current work, because such distortion is not gen-

erated in true digital applications. To assess the qual-

ity of the images available in LIVE, 20 to 29 subjects

were employed to subjectivelyevaluatethe images us-

ing the single-stimulus method. Subjects viewed the

monitors from an approximate viewing distance of 2

to 2.5 screen heights, i.e., from 106.68 to 133.35 cm.

Table 1: Overview of parameters for the LIVE and VAIQ

Databases.

Database LIVE VAIQ

Reference images 29 42

Test images 779 -

Image width 480 - 768 512

480 - 768,

480 - 768

Image height 438 - 720 512,

438 - 720,

488 - 720

Viewing distance 106.68 - 133.35 60

Subjects 20 - 29 15

3.1.2 VAIQ Database

The VAIQ database is the result of an eye tracking

experiment at the University of Western Sydney, Aus-

tralia. A total of 15 subjects participated in the exper-

iment. Their ages ranged from 20 to 60 years with an

average age of 42. The experiment was conducted in

a laboratory with low light conditions. A 19” Sam-

sung SyncMaster monitor was used for image presen-

tation. The screen resolution was 1280 x 1024 pixel.

The eye tracker (EyeTech TM3) was used to record

the gaze of the human observers. It was installed un-

der the screen and the participants were seated at a

distance of approximately 60 cm from the screen.

3.2 Experiments using LIVE and VAIQ

Experiments performed in this work using LIVE and

VAIQ databases were accomplished according to the

steps illustrated in Figure 1. The model initially has

, I

and vap as its input. I

and I

are the refer-

ence and test images originating from LIVE. The vap

is selected manually for each reference image.This

choice is made according to the most intense region

of the map of visual attention obtained from the VAIQ

database for each LIVE corresponding image used in

the test. Experiments were performed for the ω

cho-

sen as 2.25. This value is obtained by the arithmetic

average of the viewing distances (2 to 2.5) available

in (H. R. Sheikh, 2006). The code available in (Wang,

2014) is used to measure the SSIM index. FM pro-

grams were developed in MATLAB, the same can be

obtained directly from the authors, as well as other

ﬁles used in the experiments.

Figure 3 presents an illustration of the process.

FoveatedModelbasedontheActionPotentialofGanglionCellstoImproveObjectiveImageQualityMetrics

In the ﬁrst column, Figure 3(a, d, g) are retrieved

from LIVE, respectively, studentculpture, building2

and caps. For each one of these images, there is a

corresponding ROI in the VAIQ database as shown in

column 2, Figure 3(b, e, h). In the third column, Fig-

ure 3(c, f, i) are foveated image to images (a), (d) and

(g), respectively, generated from a Visual Attention

Point (VAP) that was selected manually according the

ROI image (b), (e) and (h). Using (8) and (9) for one

chosen reference and test images, the corresponding

values of iQI in (2) and of iQI

in (3) can be calcu-

lated.

4 STATISTICAL ANALYSIS

The procedure recommended by VQEG in (VQEG,

2003) and (VQEG, 2008) was used to evaluate

the performance of the PSNR, SSIM, FM

SSIM

and

PSNR

metrics. The last two metrics deliver the

iQI

SSIM

and iQI

PSNR

, respectively. The procedure

adopted to check the performance assessments takes

three steps. The ﬁrst is the data mapping of the IQM

predictions for the subjective scale. The second step

uses statistical analysis to evaluate the performance of

each IQM. Finally, the statistical signiﬁcance of the

results is analyzed.

In order for results not to be masked, the sub-

jective evaluations of the reference images are dis-

carded. According to (VQEG, 2008), the discard

should be made when assessing the performance of

full-reference (FR) and reduced-reference (RR) met-

rics, as is the case in this work.

4.1 DMOS Values and Mapping to the

Subjective Scale

The data mapping requires the use of a nonlinear

mapping step. Therefore, to remove any nonlinearity

due to the subjective rating process and to facilitate

the comparison of IQMs in a common domain, the

relationship between each IQM predictions and the

corresponding subjective ratings is estimated using a

nonlinear regression between the IQM set of image

quality ratings (IQRs) and the corresponding DMOS

(VQEG, 2003). The values used for DMOS are

available in (Sheikh et al., 2005). The details of such

a calculation can be obtained in (H. R. Sheikh, 2006).

A nonlinear mapping function found to perform well

empirically is the cubic polynomial [9]:

DMOS

= ax

+ bx

+ cx+ d, (10)

where DMOS

is the predicted DMOS. The weight-

ings a, b and c and the constant d are obtained by

ﬁtting the function to the data [DMOS, IQR].

4.2 Performance Evaluation Metrics

The performance of IQMs is evaluated with respect to

their ability to estimate the subjective assessment of

the quality of an image, as follows: accuracy, mono-

tonicity and consistency (VQEG, 2003). Accuracy

is the ability to predict the subjective quality ratings

with low error and is determined by the Pearson

Linear Correlation Coefﬁcient (PLCC). Monotonicity

is the degree to which IQM predictions agree with

the relative magnitudes of subjective quality ratings.

This is accounted for by the Spearman Rank-Order

Correlation Coefﬁcient (SROCC). Consistency is the

degree to which the IQM maintains accuracy over the

range of image test sequences, an example of this is

whether its response is robust with respect to a vari-

ety of image impairments. The Root Mean Square

Error (RMSE) metric is used for the prediction of

consistency. A better IQM is expected to have higher

PLCC and SROCC while presenting lower RMSE

values.

RMSE is calculated by the following expression:

RMSE =

N − d

∑

(DMOS(i) − DMOS

(i))

(11)

where the index i denotes the image sample, N de-

notes the total number of images considered in the

analysis, and d is the number of degrees of freedom

of the mapping function. In this work, d = 4 because

the used mapping is a 3

-order monotonic polyno-

mial function (VQEG, 2008).

The results of SROOC, PLCC and RMSE are rep-

resented in the three sections of Table II. Each sec-

tion contains 4 lines, where the line contains results

of SROOC, PLCC and RMSE for all the predictions

of the IQMs in this study. The comparisons are al-

ways made between PSNR and FM

PSNR

and between

SSIM and FM

SSIM

. The best results are presented in

bold.

One observes that, for all metrics, the performance

of FM

PSNR

and FM

SSIM

are better than the results

obtained by the traditional PSNR and SSIM, respec-

tively. PLCC, SROCC and RMSE presented less sig-

niﬁcant results between FM

SSIM

and SSIM for the

Fast-fading distortion and all of the distortions to-

gether, but FM

SSIM

is still more efﬁcient than the

SSIM.

SIGMAP2015-InternationalConferenceonSignalProcessingandMultimediaApplications

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 3: Choice examples of the VAP and Distribution Map of Ganglion Cells (DMGC). (a), (d) and (g) are images existing

in LIVE (Sheikh et al., 2005), respectively, studentculpture, building2 and caps; (b), (e) and (h) are visual attention regions

(ROI) of the images of (a), (d) and (g), respectively, existing in VAIQ (Engelke et al., 2009); (c), (f) and (i) are foveated image

to images (a), (d) and (g), respectively, generated from a Visual Attention Point (VAP) that was selected manually according

the RoI image (b), (e) and (h).

4.3 Statistical Signiﬁcance of the Results

The statistical signiﬁcance of the results is given by

the ratio between the RMSEs of the IQMs, and has a

F-distribution with n1 and n2 degrees of freedom and

is deﬁned by:

ζ =

(RMSE

)

(RMSE

)

, (12)

where RMSE

and RMSE

are, respectively, the

RMSE of metrics A and B involved in the com-

parison. The ζ parameter is evaluated based on F-

distribution function, which has a F

critical

of 5% and

ensures a 95% signiﬁcance level. If ζ is higher than

the F

critical

, then there is a signiﬁcant difference be-

tween the values of RMSE (VQEG, 2008). Similarly,

F-distribution in percentage, F

= (ζ − 1) · 100, de-

livers the absolute signiﬁcance level. This way, two

IQMs cannot be considered statistically different for

values of ζ smaller than 1.05. On the other hand, if

ζ > 1.05 (or F

> 5%), results provided by IQMs can

be compared.

The statistical signiﬁcances of the IQMs are reg-

istered in Table III. In the ﬁrst and second part of this

table, the signiﬁcance data results from the compar-

ison of PSNR in relation to the SSIM and FM

SSIM

are presented. In the third part, the results of SSIM

in relation to FM

SSIM

are presented. The bold val-

ues present statistical signiﬁcances because they are

above the value Fcritical of 5%.

PSNR

metric is statistically different and per-

forms better than PSNR for all types of applied dis-

tortions. The foveated model is able to improve the

results of traditional PSNR by 26.28% for JPEG2000,

28.98% for JPEG, 15.93% for Gaussian Blur, 24.27%

for Fast-fading distortions and 14.30% for all distor-

tions types, respectively.

The SSIM and FM

SSIM

metrics are statistically

different and better than the PSNR. In the third part

FoveatedModelbasedontheActionPotentialofGanglionCellstoImproveObjectiveImageQualityMetrics

Table 2: Pearson Linear Correlation Coefﬁcient (PLCC), Spearman Rank-Order Correlation Coefﬁcient (SROCC),Root Mean

Square Error (RMSE) of the Absolute Prediction Error between Subjective Ratings using the LIVE Database.

Evaluation Metric Quality Metric All JPEG2000 JPEG Gaussian Blur Fast-fading

PLCC PSNR 0.8540 0.8984 0.8867 0.7841 0.8893

PSNR

0.8736 0.9205 0.9124 0.8173 0.9119

SSIM 0.9475 0.9650 0.9785 0.9452 0.9446

SSIM

0.9477 0.9681 0.9802 0.9557 0.9452

SROCC PSNR 0.8595 0.8934 0.8800 0.7823 0.8909

PSNR

0.8803 0.9159 0.9063 0.8200 0.9120

SSIM 0.9545 0.9598 0.9754 0.9474 0.9536

SSIM

0.9574 0.9624 0.9779 0.9601 0.9573

RMSE PSNR 13.9635 11.2158 14.8225 11.6254 13.1532

PSNR

13.0611 9.9808 13.0515 10.7972 11.7992

SSIM 8.5791 6.7004 6.6193 6.1138 9.4416

SSIM

8.5621 6.3955 6.3509 5.5157 9.3914

Table 3: ζ Statistic used for the signiﬁcance of the difference between the Root Mean Square Error. The results are presented

in two ways, ζ Statistic and (F

Quality Metric All JPEG2000 JPEG Gaussian Blur Fast-fading

PSNR by FM

PSNR

1.1430 1.2628 1.2898 1.1593 1.2427

(14.30%) (26.28%) (28.98%) (15.93%) (24.27%)

PSNR by SSIM 2.6491 2.8019 5.0144 3.6157 1.9408

(164.91%) (180.19%) (401.44%) (261.57%) (94.08%)

PSNR by FM

SSIM

2.6597 3.0755 5.4472 4.4424 1.9616

(165.97%) (207.55%) (444.72%) (344.24%) (96.16%)

SSIM by FM

SSIM

1.0040 1.0976 1.0863 1.2286 1.0107

(0.40%) (9.76%) (8.63%) (22.86%) (1.07%)

of Table III, one observes that our FM is able to im-

prove the SSIM result with statistical signiﬁcance for

JPEG2000, JPEG and Gaussian Blur Quality Experts

Group (VQEG), respectively, by 9.76%, 8.63% and

22.86%. The SSIM metric is improved in relation

to PSNR by 27.36%, 43.28% and 82.67%, respec-

tively, for these distortions. In this context, SSIM and

SSIM

IQMs are statistically different. Despite the

good results, the foveated model is not able to im-

prove the SSIM metric for Fast-fading distortions, be-

cause SSIM and FM

SSIM

are not statistically different

for this distortion.

5 CONCLUSIONS

In this work, the proposed foveated model (FM) based

on the visual attention point and on the action po-

tential of ganglion cells is used to improve the met-

ric evaluation. The results are encouraging because

the model proposed improve the performance of the

PSNR and SSIM metrics.

Despite the progress made, the FM still needs im-

provement. Therefore, as future work, it is suggested

that the model take into account the ROI and that it

can be automatically detected. The FM could be ad-

justed to work as a glasses where each metric would

receive a speciﬁc lens to be able to improve your

vision. Moreover, other database images could be

included in experiments as those found in TID2008

(Ponomarenko et al., 2009), that contain distortions

in ROIs. It is important to note according to ﬁgure

3.i which were not considered in multiple regions ex-

periments, and therefore, more of a challenge for fu-

ture work. Finally, after these improvements, we hope

that the proposed model serves as the basis for the de-

velopment of digital image compression applications

more efﬁciently.

ACKNOWLEDGEMENTS

The authors would like to thank the Federal Insti-

tute of Education, Science and Technology of the

Amazonas (IFAM), the Foundation for research sup-

port of the Amazonas (FAPEAM) and the Coordina-

tion of Qualiﬁcation of Personnel in Higher Educa-

tion (CAPES). The authors also thank the creators of

SIGMAP2015-InternationalConferenceonSignalProcessingandMultimediaApplications

LIVE and VAIQ databases, which provided the refer-

ence and test images used in this work.

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FoveatedModelbasedontheActionPotentialofGanglionCellstoImproveObjectiveImageQualityMetrics