A quantitative measure for the perception of sharpening and smoothing in images

in: M. Boasson, J.A. Kaandorp, J.F.M. Tonino, M.G. Vosselman (eds.), ASCI'99, Proc. 5th Annual Conference of the Advanced School for Computing and Imaging (Heijen, NL, June 15-17), ASCI, Delft,

1999, 291-298.

A quantitative measure for the perception of

sharpening and smoothing in images

Judith Dijk y , Dick de Ridder  , PietW. Verbeek  , JanWalraven y , Ian T. Young 

, and Lucas J. van Vliet 



Pattern Recognition Group, Dept. of Applied Physics, Faculty of Applied Sciences,

Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

y

Display Group, Department of Perception, TNO Human Factors Research Institute,

P.O. Box 23, 3769 ZG Soesterberg, The Netherlands

e-mail:

fjudith,dickg@ph.tn.tudelft.nl

Keywords:

perception, image quality measures, edge-preserving smoothing

Abstract

It is well-known that the mean squared error (MSE) is an inappropriate measure for the dif-ference between two images in many applications. For one such an application, edge-preserving smoothing, an alternative was developed which takes both goals into account: the preservation or sharpening of edges and the smoothing of regions. In this paper, tests on human subjects are reported which conrm that the new measures conform reasonably to visual judgement, and better than the MSE. Next to this, preliminary results are given from experiments in which the preference for sharpening and smoothing is investigated. It is found that images with a relatively low smooth-ing and a high sharpensmooth-ing are preferred.

1 Introduction

In previous work [1], neural networks were trained to perform the Kuwahara edge-preserving smoothing image ltering operation [2]. It was found that the error measure most commonly used in training neural networks, the mean squared error (MSE), did not give a good indica-tion of visual performance for this problem. This is not a new nding. Numerous others have no-ticed that, in image processing, the MSE does not conform well to visual judgement (e.g. [3]). A number of alternatives has been proposed, among which are mean absolute error (MAE), Pratt's Figure of Merit (FOM) for edge detection [4] and Average Risk [5].

For edge-preserving smoothing lters,

how-ever, these measures oer no viable alternative. The main cause of the problem is that the most interesting areas, the edges, are very poorly repre-sented in terms of the number of pixels. Hence, a small number of signicant errors in edge preser-vation will not be represented well in the over-all error measure. However, the latter eect has great impact on human judgement of lter qual-ity. Therefore, neural networks approximating an edge-preserving smoothing lter with more or less the same MSE may produce visually very dier-ent results. A performance measure trying to capture both eects in a single number will, in general, like the MSE, fail to conform to visual judgement.

This observation led to a formulation of two new measures to estimate the smoothing and sharpening eect of a lter. Since these measures worked satisfactory in the neural network prob-lem, the question arose as to what extent they conform to human judgement of lter quality. To this end, subjects were asked to indicate relative smoothing and/or sharpening on a number of l-tered images. As an edge-preserving smoothing lter, an anisotropic diusion lter was used. The results show that the measures are related to hu-man judgement, at least for moderately sharpen-ing/smoothing lters, and that the MSE is less related to human judgement.

2 Sharpening vs. smoothing

In order to devise an informative performance measure for both sharpening and smoothing in-duced by a lter, the two eects have to be sep-arated. To this end, a scattergram is plotted of

0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 |∇ I| | ∇ f(I)|

Gradient magnitude scattergram of Kuwahara filter

A B + b y =a_Ax y = x A y =a_Bx+ b_B

Figure 1: Scattergram of gradient magnitude im-ages of original image (x-axis) and a Kuwahara ltered version (y-axis).

the pixels of the gradient magnitude of the origi-nal image versus those of the gradient magnitude of the ltered version. Figure 1 (a) shows an ex-ample. Note that a scattergram approach has been proposed (and denounced) before [6]; how-ever, the use of the gradient magnitude is novel.

Pixels are classied as either being sharpened or smoothed. In the rst case, the gradient will have increased; i.e. the pixel is plotted above the line y = x in the scattergram. Pixels which are smoothed will end up below this line. All sharp-ened and smoothed pixels are grouped into sets

AandB, respectively:

A = f(jrI(i;j)j;jrf(I)(i;j)j)

jrI(i;j)jjrf(I)(i;j)jg (1) B = f(jrI(i;j)j;jrf(I)(i;j)j)

jrI(i;j)j<jrf(I)(i;j)jg (2)

Note that in generaljBj<<jAj, since fewer

pix-els lie on edges than in smooth regions. Lines

y = ax +b can be tted through both sets using a robust estimation technique (medfit),

minimising the absolute deviation [7], to get a density-independentestimate of the factors with which edges are sharpened and at regions are smoothed: (aA;bA) = argmin (a;b) X (x;y)2A jy;(ax+b)j(3) (aB;bB) = argmin (a;b) X (x;y)2B jy;(ax+b)j(4)

The slope of the lower line found,aA, will give an

indication of the smoothing induced by the lter

f. Likewise,aB gives an indication of the

sharp-ening eect of the lter. The osets bA and bB

are discarded, although it is necessary to estimate them to avoid biasing the estimate ofaAandaB.

Note that a demand is that aA

1 anda B

1,

so the values are clipped at 1 if necessary. To account for the number of pixels actually used to estimate these values, the slopes found are weighted with the relative number of points used for the estimate. Therefore, the numbers

Smoothing(f;I) = (a0 A ;1) jAj jAj+jBj (5) Sharpening(f;I) = (aB ;1) jBj jAj+jBj (6) are used, where a0

A=

1

a

A was substituted to

ob-tain numbers in the same range [0;1i. These

two values can be considered to be an amplica-tion factor of edges and an attenuaamplica-tion factor of at regions, respectively. Note that these mea-sures depend on:

 image content;  the lter used;

 any intermediate or afterward processing

such as scaling or contrast stretching. Given a certain image and using no further pro-cessing, they can therefore be used to compare lter operation.

3 Edge-preserving smoothing

To judge the correspondence between the mea-sures proposed in section 2 and human judge-ment, one can do experiments with, in principle, any edge-preserving smoothing lter. However, one obvious demand is that the algorithm used has parameters which allow small dierences in sharpening and smoothing to be created. This is necessary to be able to create a large number of images which span the sharpening-smoothing space. Therefore, the Kuwahara lter mentioned before is not applicable as the only parameter is the window width (3, 5, 7, ...) which gives too coarse a spacing.

The lters used in this paper are:

Gaussian:

a purely smoothing Gaussian

fG(I;), with= 0:0;0:1;:::;2:0.

Unsharp masking:

purely sharpening, it sub-tracts from an image I the Laplacian-of-Gaussian ltered version [8]:

fU(I;k) =I

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Sharpening Smoothing Measures for σ₁ = 1.0, σ₂ = 5.0, k = 0.25 ... 2.0, N = 5 ... 80 Unsharp masking N k Kuwahara anisotropic diffusion Unsharp masking & Gaussian fG fU fA (a) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Selected images on grid

Sharpening Smoothing 0.0 0.1 0.3 0.5 0.5 0.3 0.1 0.0 Sm Sm Sm Sm Sh Sh Sh Sh (b)

Figure 2: (a) Sharpening/smoothing values for a number of dierent lters on theportraitimage. Note

that only a small subset of the lters is plotted, and that forfAsome lters have been omitted for clarity.

(b) Images selected along a grid: along each of the lines indicated by the arrows, a range of images was chosen.

The eect is that edges are enhanced. How-ever, noise is also amplied. The parame-terk controls the amount of sharpening. In the experiments it was varied in the range 0:0;0:1;:::;2:0. The parameter  was xed to 1.0.

Anisotropic diusion with unsharp masking:

The diusion equation proposed by Perona and Malik [9] is given by

I

t = 12r
(C(x;y)rI) (8)

where Cis a function indicating the absence of an edge. Clearly, the image is smoothed in places where no edges are present (C= 1) but not changed near the edges. Since the location of the edges is not exactly known, a function of the gradient magnitude is usually used: C(x;y) = exp ; I2 x+I 2 y 2₂₁ ! (9) which goes to zero for large values of the gra-dient. The parameter1 decides how large a

gradient has to be in order to be considered an edge.

In practice, the ux between two pixelsaand

b is approximated by t(a;b) = 1 2
t12(Ct(xa;ya) +Ct(xb;yb))
(It(xa;ya) ;I t(xb;yb)) (10)

so that the update rule (one iteration) for one pixelpbecomes

It+1(xp;yp) = X

n2N

4

t(p;n) (11)

where N4 denotes the 4-connected

neigh-bourhood of pixel p. The time step
t in eqn. 10 is xed to 0.25, giving updates as large as possible but keeping the scheme nu-merically stable [10]. The number of itera-tions is a parameter,N.

In the experiments described below, a mod-ication due to Catte [11] was used. They proposed calculating the gradient magnitude in eqn. 9 with a Gaussian derivative:

J = I 1 p 2₂₂exp  ; (x+y)2 222  C(x;y) = exp ; J2 x+J 2 y 221 ! (12) This introduces a second parameter 2,

which can be used to suppress noise. The diusion operation described here has a purely smoothing eect1_{. To make the}

l-ter both sharpening and smoothing, images were pre-ltered with the unsharp mask-ing lter fU(I;k) described above. This

introduces another parameter, k. The to-tal lter therefore is fA(fU(I;k);1;2;N).

In the experiments, the parameters were varied thus: k = 0:0;1:0;:::;5:0; 1 =

1:0;2:0;:::;5:0; 2 = 0:0;0:25;:::;2:0 and

N = 5;7;10;14;20;28;40;56;80.

Figure 2 (a) shows an example of how vari-ous ltered versions of an image end up in the sharpening-smoothing space.

1It can sharpen edges due to the smoothing of the

4 Experiments

4.1 Images

In the experiments, two images were used as base images, shown in gure 3. They are ISO standard images taken from their CD-ROM 12640:1997 and are originally 300 dpi, in CMYK format. The images were converted to RGB rst, using Adobe Photoshop. Next, the images were converted to 32-bit greyscale oating point im-ages. Following ITU [12], the luminance Y was dened as: Y = 0:222R+ 0:707G+ 0:071B. To reduce the amount of computation time needed, the images were reduced to 3_{8of their original size}

in both thex andy direction, by pre-smoothing with a Gaussian (= 2:4) and interpolating lin-early.

For both images, fG, fU and fA were

calcu-lated with the parameter settings described in section 3, resulting in a large number of image points in sharpening-smoothing space. Finally, the images were printed on a 600 dpi HP Laser-Jet 4000N. Print size was 12:816 cm.; dithering

was done by the printer.

(a)bicycle (b)portrait

1 4 5 6 2 3 (c)bicycle(parts) 3 5 444 2 1 (d) portrait (parts)

Figure 3: The two images (a,b) and parts thereof (c,d) used in the experiments. In (c) the parts are called (1) bike (the part with only the

bi-cycle), (2)clock, (3)test pattern, (4) plant,

(5)fruitand (6)lobster. In (d) the parts are

called (1) right hand, (2) face, (3) hair, (4)

left handand (5)sweater.

4.2 Experiment A

The goal of this experiment was to see if the proposed measures, as dened in section 2, con-form to human vision, i.e. whether subjects can discriminate levels of sharpening and smoothing. The subjects were given a range of prints and asked to order them by perceived sharpening or smoothing.

In the instruction to subjects, sharpening was explained as the sharpening of edges and smooth-ing as the smoothsmooth-ing of regions. Although this might introduce a bias in the outcome of the ex-periments, it was deemed necessary since some of the subjects had no clear concept of sharpening or smoothing.

From the two dimensional feature space, one dimensional ranges were drawn containing images with constant smoothing or sharpening. Four dif-ferent sharpenings and smoothings were used for this: 0.0, 0.1, 0.3 and 0.5. These values were used for constructing series Smx (Shy),

consist-ing of { at most { 8 images with xed smoothconsist-ing

x (sharpening y). Sharpening (smoothing) was varied in steps of 0.1. The ranges used are shown in gure 2 (b).

Since the various grades in smoothing and sharpening had to be selected from a limited sam-ple (see gure 2 (a))), the specied values of 0.0 to 0.7 could only be approximated. This was done by selecting the nearest value to the desired value. However, the dierences were always less than 0.05. Some ranges consisted of less than 8 im-ages, so for some desired grid locations no nearby images could be found. Figure 2 (b) shows an example of the resulting tiling.

4.3 Experiment B

In the second experiment, subjective prefer-ence for a particular sharpening or smoothing value was tested. The subject was given a range of prints, asked to select three prints that she/he considered best and to order these three by qual-ity. Since our research concerns the subjective preference of an \average" observer for printed images, quality here means the impression a sub-ject has of an image, without reference to any specic task.

All ranges used in experiment A were also used in this experiment. In addition, an extra range was used in which both sharpening and smooth-ing were varied between 0.0 and 0.2, in steps of 0.1. Except for this last two-dimensional range, the prints were ordered by sharpening or smooth-ing in order to not unnecessarily complicate the preference experiment for the subjects.

4.4 The experimental environment

The experiments were performed in a test booth in which the prints were presented on a counter for sorting. The light source was a stu-dio lamp, which provided homogeneous, indirect lighting of the prints. The luminance on the counter was approximately 600 lux. The prints were put into transparent plastic covers to pre-vent smudges. A window was cut in the centre to see the image on the print directly and not through plastic. Four subjects participated in the experiments, all having some experience in the eld of image analysis.

5 Results

5.1 Experiment A

The results for two of the eight ranges used in experiment A are given in gure 4. In the rst range (portrait, Sm₀:5) it can be seen that the

orderings given by subjects mostly follow the or-dering given by the measures: there are only 3 de-viations. In the second range (bicycle, Sm₀:5),

there are many deviations. Furthermore, the re-sults are very dierent per subject, indicating that ordering this range is quite dicult.

The correlation between the dened sharpen-ing and smoothsharpen-ing measures on the one hand and the perceived sharpening and smoothing on the other, is measured with the Spearman rank-order correlation coecientrs[13]. With this value, the

null hypothesisH0, i.e. the dened and perceived

sharpening and smoothing are not associated (are independent) can be tested against the hypothe-sisH1, i.e. there is an association. The Spearman

rank-order coecient is dened as

rs= 1 ; 6P N i=1d i 2 N3;N (13) in whichN is the number of prints in the range anddiis the dierence in rank for the dened and

perceived sharpening/smoothing for each image in the range.

For N = 8, with an error of 5%, the critical value above which the two-tailed H0 hypothesis

can be rejected is 0:736 (forN = 7 this value is 0:786; for N= 6, 0:886).

The rank-order coecients for each subject are given in tables 1 (a) and (b). It can be seen that for most subjects and ranges the null hypothesis can be rejected. For four ranges this is not the case:



Subject 3 and 4,

portrait

, Sm

0 :1: we

suspect this to be coincidental. More exper-iments can clarify this.



Subject 1,

bicycle

, Sh

0

:5: sincebicycle

is an articial mix of many dierent images, with dierent scales of detail, we suspected subjects to base their judgements on dierent parts of the image.

To verify this, sharpening and smoothing val-ues of parts of the two images (shown in g-ure 3 (c) and (d)) were calculated. The parts were selected manually, in such a way that all parts of the images subjects claimed to have looked at were represented. When cor-relating the sharpening and smoothing val-ues of the parts with the results for sub-ject 1, it is clear that for the partsfruitand

lobsterH₀can be rejected. After the

exper-iments, the subject stated that he had looked mostly at the pineapple (fruit), lobster

and clock image parts. The conclusion is

that the large variations in the sharpening and smoothing values of various parts of the images are the reason for the results of sub-ject 1 in this range.



Subjects 1 and 3,

bicycle

, Sm

0 :3

and

Sm

0:5: in highly smoothed images, the

ef-fect of the sharpening operation is only pre-served for large-scale, high edges. Small de-tails and less prominent edges are smoothed away. While subjects tend to place emphasis on this loss of detail, the proposed sharpen-ing measure is not heavily in uenced by it. This would also explain why the portrait

ranges do not show these deviations: there is far less detail present in this image, all im-portant edges present are on more or less the same scale.

To validate these results the MSE's for the im-ages used were calculated. These MSE's also had a rank order in the ranges that were presented to the subjects, and the Spearman rank order coef-cient between the rank ordering of the subjects and the ordering in MSE was determined. The resulting coecients are given in tables 1 (c) and (d). It can be seen that they are mostly lower than for the sharpening and smoothing measures and more ranges have to be rejected. This in-dicates that the MSE conforms less to visual judgement than the sharpening and smoothing measures. It can be seen that smoothing corre-lates more to the MSE than sharpening. Because the smoothing is determined in smooth regions, which contain by far the largest number of pixels, this is not unexpected.

It can be observed that for thebicycleimage,

the ordering given by the subjects was more often dierent from the ordering by the measures than

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Presented sharpening Chosen sharpening Subject 1 Subject 2 Subject 3 Subject 4 Average (a)portrait, Sm 0:5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Presented sharpening

Chosen sharpening Subject 1_{Subject 2}

Subject 3 Average

(b)bicycle, Sm 0:5

Figure 4: The results of the ordering of two of the eight ranges. Both ranges are the ranges where the smoothing is kept constant at 0.5 and the sharpening varies. In (a) it can be seen that subjective judgement conforms to the proposed measure for sharpening. In (b) illustrates that for certain ranges, subjects do not consistently order the images and that the orderings are dierent from those given by the measures.

was the case for theportraitimage. As was

dis-cussed above, this is likely due to the diverse tent of the former image. A second general con-clusion is that dierent levels of smoothing seem to be more easily discriminated by subjects than levels of sharpening.

5.2 Experiment B

In this second experiment, subjects were asked to give a rst, second and third preference per range. These preferences were averaged with a certain weight: the rst preference had a weight of 4, the second of 2 and the third of 1. This is an arbitrary choice, but probably not worse than any other. The results are shown in gure 5.

The two left images (gures 5 (a) and (c)) show that, for smoothed images, subjects tend to prefer high sharpening to compensate for the smoothing away of the edges. Clearly, edges play an impor-tant role in subject appreciation of an image. For

portrait, however, the leftmost value, indicating

a preference for high sharpening at low smooth-ing, is hard to explain.

The ranges in which subjects were asked for smoothing preference, gures 5 (b) and (d), show that subjects prefer little smoothing. For highly sharpened images, some smoothing is preferred to reduce the artefacts introduced by the sharpening operation.

These conclusions are validated by the results for the two dimensional range, given in table 2. Note that the maximum sharpening and smooth-ing were much lower than those of the one di-mensional ranges, to keep the size of the set of images presented to subjects reasonable. Never-theless, in general, subjects seem to prefer a little

smoothing and much sharpening.

For comparison, the preferred mean MSE per subject was determined for each range in the same way as the preferred smoothing/sharpening. If the MSE is a good measure for the quality of the images, the preferred MSE should be almost con-stant over the dierent ranges. We see that the preferred MSE increases with the sharpening of the ranges, and slightly with the smoothing of the ranges. This conrms that the MSE is an in-appropiate measure for the quality of the images. The results of this experiment may not apply to noisy images, as smoothing is often used (and appreciated) on such images to reduce the noise. Some experiments in which noise is added to these images could give more insight.

6 Conclusions

Two new measures for the amount of sharpen-ing and smoothsharpen-ing induced by a lter were intro-duced. Some preliminary results of experiments relating these measures to human perception were discussed. In general, these measures correlate well with human perception. Problems arise for ranges in which parts of an image have sharping and smoothsharping values dierent from the en-tire image { such as the complexbicycleimage,

in which details at a large number of scales are present. Subjects tend to look at dierent parts and combine their judgement (nonlinearly) into an overall decision. One possible future approach is to nd these dierent image parts (perhaps using the measures themselves) and treat them seperately.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Preferred sharpening Subject 1 Subject 2 Subject 3 Subject 4 Average Sm0.0 Sm0.1 Sm0.3 Sm0.5 Presented range

(a)portraitsharpening preference

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Preferred smoothing Subject 1 Subject 2 Subject 3 Subject 4 Average Sh Sh Sh Sh_{0.0 0.1 0.3 0.5} Presented range

(b)portraitsmoothing preference

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Preferred sharpening Subject 1

Subject 2 Subject 3 Average

Sm_0.0 Sm_0.1 Sm_0.3 Sm_0.5

Presented range

(c)bicyclesharpening preference

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Preferred smoothing Subject 1 Subject 2 Subject 3 Average Sh0.0 Sh0.1 Sh0.3 Sh0.5 Presented range

(d)bicyclesmoothing preference

Figure 5: Results of the preference experiment B. tend to have much less problems in discerning

various levels of smoothing than they have with levels of sharpening. This indicates that the two measures proposed are not equivalently spaced: the just noticeable dierence of smoothing is smaller than that of sharpening.

The results of the preference experiment look promising. One can say that subjects prefer im-ages in which the smoothing is low and the sharp-ening is high. However, this may not be the case for noisy images, in which a certain amount of smoothing will likely be appreciated.

To validate the results reported here, the work should obviously be extended by performing ex-periments with more subjects. Furthermore, these subjects should be naive with respect to image analysis. The next step will then be to investigate the nature of the relation between the physical image attributes measured and the at-tributes perceived by subjects, i.e. to nd a model describing this relation. This model can then be used, in combination with a model for sharpen-ing/smoothing preference, for predicting optimal lter settings.

Acknowledgements

This research is partly supported by the IOP Beeldverwerkings project of Senter, Agency of the Ministry of Economic Aairs of the Nether-lands, the Foundation for Computer Science in the Netherlands (SION), the Dutch Organisa-tion for Scientic Research (NWO) and the Royal Dutch Academy of Sciences (KNAW).

References

[1] D. de Ridder, R.P.W. Duin, P.W. Verbeek, and L.J. van Vliet. On the application of neural networks to non-linear image pro-cessing tasks. In Proceedings International Conference on Neural Information Process-ing 1998 vol. I, pages 161{165, 1998. [2] M. Kuwahara, K. Hachimura, S. Eiho, and

M. Kinoshita. Digital processing of biomed-ical images, pages 187{203. Plenum Press, New York, NY, 1976.

[3] H. Marmolin. Subjective MSE measures. IEEE Transactions on Systems, Man and Cybernetics, 16(3):486{489, 1986.

Table 1: The Spearman rank-order coecients for the ranges used in experiment A, per subject. For the values printed in boldface, the null hy-pothesis cannot be rejected; that is, in these cases perceived sharpening and smoothing are indepen-dent of the sharpening and smoothing measures (a, b) or the MSE (c, d); CV stands for critical value. Note that subject 4 did not participate in

thebicycleexperiment.

Subject Range 1 2 3 4 Avg. N CV Sh0:0 0.98 1.00 0.95 0.81 0.98 8 0.74 Sh0:1 0.96 1.00 0.91 0.98 1.00 8 0.74 Sh0:3 0.88 0.91 1.00 0.91 1.00 8 0.74 Sh0:5 0.89 0.94 0.94 0.94 0.93 6 0.89 Sm0:0 0.98 0.98 0.88 0.91 0.95 8 0.74 Sm0:1 1.00 0.98 0.69 0.17 0.90 8 0.74 Sm0:3 1.00 0.98 0.76 0.98 0.96 8 0.74 Sm0:5 1.00 0.97 0.92 1.00 0.99 7 0.79

(a)portrait, sharpening/smoothing

Subject Range 1 2 3 Avg. N CV Sh0:0 0.98 0.83 0.93 0.97 8 0.74 Sh0:1 0.98 0.95 0.98 0.98 8 0.74 Sh0:3 0.93 1.00 0.95 0.99 8 0.74 Sh0:5 0.69 0.88 0.91 0.93 8 0.74 Sm0:0 0.95 0.88 0.83 0.96 8 0.74 Sm0:1 0.98 0.93 0.91 0.98 8 0.74 Sm0:3 0.43 0.98 0.79 0.78 8 0.74 Sm0:5 0.61 0.93 0.25 0.98 7 0.79 (b)bicycle, sharpening/smoothing Subject Range 1 2 3 4 N CV Sh0:0 0.98 1.00 0.95 0.81 8 0.74 Sh0:1 0.90 0.90 0.86 0.83 8 0.74 Sh0:3 0.98 0.79 0.95 0.83 8 0.74 Sh0:5 0.89 0.94 0.94 0.94 6 0.89 Sm0:0 0.90 0.88 0.76 0.93 8 0.74 Sm0:1 0.81 0.88 0.55 0.07 8 0.74 Sm0:3 0.93 0.90 0.60 0.90 8 0.74 Sm0:5 0.82 0.71 0.61 0.82 7 0.79 (c)portrait, MSE Subject Range 1 2 3 N CV Sh0:0 0.79 0.83 0.69 8 0.74 Sh0:1 0.98 0.95 0.98 8 0.74 Sh0:3 0.86 1.00 0.93 8 0.74 Sh0:5 0.43 0.88 0.38 8 0.74 Sm0:0 0.86 0.67 0.76 8 0.74 Sm0:1 0.93 0.76 0.83 8 0.74 Sm0:3 0.48 0.69 0.76 8 0.74 Sm0:5 0.89 0.79 -0.04 7 0.79 (d)bicycle, MSE

[4] W. K. Pratt. Digital image processing. John Wiley & Sons, New York, NY, 2nd edition,

1991.

[5] L. J. Spreeuwers. Image ltering with neu-ral networks, applications and performance evaluation. PhD thesis, Universiteit Twente, Enschede, october 1992.

[6] H. Katsulai and N. Arimizu. Evaluation of image delity by means of the delogram and level mean-square error. IEEE

Transac-Table 2: Results (Sh,Sm) of the preference exper-iment B with the two dimensional range. Note that subject 4 did not participate in thebicycle

experiment. Subject Pref. 1 2 3 4 1st (0.2,0.1) (0.2,0.0) (0.2,0.0) (0.2,0.2) 2nd (0.2,0.0) (0.2,0.1) (0.2,0.1) (0.2,0.0) 3r d (0.1,0.1) (0.1,0.1) (0.1,0.1) (0.1,0.2) (a)portrait Subject Pref. 1 2 3 1st (0.1,0.0) (0.2,0.0) (0.2,0.0) 2nd (0.2,0.0) (0.1,0.0) (0.1,0.0) 3r d (0.0,0.0) (0.0,0.0) (0.0,0.0) (b)bicycle

tions on Pattern Analysis and Machine In-telligence, 3(3):337{347, 1981.

[7] W. H. Press, B. P. Flannery, S. A. Taukolsky, and W. T. Vetterling. Numerical recipes in C. Cambridge University Press, Cambridge, 1988.

[8] I.T. Young, J.J. Gerbrands, and L.J. Van Vliet. The digital signal processing handbook, chapter Image processing fun-damentals, pages 51/1 { 51/81. CRC Press/IEEE Press, Boca Raton, FL, 1998. [9] P. Perona, T. Shiota, and J. Malik.

Anisotropic diusion. In B.M. ter Haar Romeny, editor, Geometry-driven diusion in computer vision, pages 73{ 92, Dordrecht, 1994. Kluwer Academic Publishers.

[10] W.J. Niessen, B.M. ter Haar Romeny, and M.A. Viergever. Numerical analysis of geometry-driven diusion equations. In B.M. ter Haar Romeny, editor, Geometry-driven diusion in computer vision, pages 393{410, Dordrecht, 1994. Kluwer Academic Publish-ers.

[11] F. Catte, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge detection by nonlinear diusion. SIAM Jour-nal on Numerical AJour-nalysis, 29(1):182{193, 1992.

[12] D. Bourgin. Color spaces faq. http://www.cc.iastate.edu/olc answers/ packages/graphics/color-space.faq.html, May 1998.

[13] S. Siegel and N.J. Castellan. Non para-metric statistics for the behavioral sciences. McGraw-Hill, New York, NY, 1988.