A new measure for the effect of sharpening and smoothing filters on images

in: B.K. Ersboll, P. Johansen (eds.), SCIA'99, Proc. 11th Scandinavian Conference on Image Analysis (Kangerlussuaq, Greenland, June 7-11), Pattern Recognition Society of Denmark, Lyngby, 1999, 213-220

A new measure for the eect of sharpening

and smoothing lters on images

Judith Dijky, Dick de Ridder, Piet W. Verbeek, Jan Walraveny,

Ian T. Young, Robert P.W. Duinand 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

yDisplay 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 dierence between two images in many applications. For one such an applica-tion, edge-preserving smoothing, an alternative was de-veloped which takes both goals into account: the preser-vation or sharpening of edges and the smoothing of gions. In this paper, tests on human subjects are re-ported which conrm that the new measures conform reasonably to visual judgement. Next to this, prelim-inary results are given from experiments in which the preference for sharpening and smoothing is investigated. It is found that images with a relatively low smoothing and a high sharpening are preferred.

1 Introduction

In previous work [1], neural networks were trained to perform the Kuwahara edge-preserving smoothing im-age ltering operation [2]. It was found that the error measure most commonly used in training neural net-works, the mean squared error (MSE), did not give a good indication 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 con-form 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, however, these measures oer no viable alternative. The main cause of the problem is that the most interesting areas, the edges, are very poorly represented in terms of the num-ber of pixels. Hence, a small numnum-ber of signicant er-rors in edge preservation will not be represented well in the overall 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 dierent results. A per-formance measure trying to capture all eects into a sin-gle number will, in general, fail to do signicantly better than the MSE.

This observation led to a formulation of two new mea-sures to estimate the smoothing and sharpening eect of a lter. Since these measures worked satisfactory in the neural network problem, 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 ltered images. As an edge-preserving smoothing lter, an anisotropic diusion lter was used. The results show that the measures are related to human judgement, at least for moderately sharpening/smoothing lters.

Finally, subjects were asked to give an indication of their appreciation of the ltered image, that is, of the perceived quality of the image. The outcome of this ex-periment shows that the subjects preferred moderately smoothed yet highly sharpened images.

2 Sharpening vs. smoothing

In order to devise an informative performance measure for both sharpening and smoothing induced by a lter, the two eects have to be separated. To this end, a scattergram is plotted of the pixels of the gradient mag-nitude of the original image versus those of the gradient magnitude of the ltered version. Figure 1 (a) shows an example. Note that a scattergram approach has been proposed (and denounced) before [6]; however, 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

in-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 images of original image (x-axis) and a Kuwahara ltered version (y-axis).

creased; i.e. the pixel is plotted above the line y=xin the scattergram. Pixels which are smoothed will end up below this line. All sharpened and smoothed pixels are grouped into setsAandB, 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 general jBj<< jAj, since fewer pixels lie on edges than in smooth regions. Lines y = ax+b

can be tted through both sets using a robust estima-tion technique (medfit), minimising the absolute

devi-ation [7], to get a density-independent estimate 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 indica-tion of the smoothing induced by the lterf. Likewise,

aB gives an indication of the sharpening eect of the lter. The osets bA andbB are discarded, although it is necessary to estimate them to avoid biasing the esti-mate ofaAandaB. Note that a demand is thataA

1 and aB

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 obtain numbers in the same range [0;1i. These two values can be considered to be an amplication factor of edges and an attenuation factor of at regions, respectively. Note that these measures 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 processing, they can therefore be used to compare lter operation.

3 Edge-preserving smoothing

To judge the correspondence between the measures pro-posed in section 2 and human judgement, 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 GaussianfG(I;), with

= 0:0;0:1;:::;2:0.

Unsharp masking:

purely sharpening, it subtracts from an imageI the Laplacian-of-Gaussian ltered version [8]:

fU(I;k) =I

;kLoG(I;) (7) The eect is that edges are enhanced. However, noise is also amplied. The parameter k controls the amount of sharpening. In the experiments it was varied in the range 0:0;0:1;:::;2:0. The param-eter was xed to 1.0.

Anisotropic diusion with unsharp masking:

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

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 f_G f_U f_A (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 the portrait image. Note that

only a small subset of the lters is plotted, and that forfA some 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.

where C is 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 mag-nitude is usually used:

C(x;y) = exp ; I2 x+I 2 y 2₂₁ ! (9) which goes to zero for large values of the gradient. The parameter1 decides how large a gradient has

to be in order to be considered an edge.

In practice, the ux between two pixels aand 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 pixel

pbecomes

It+1(xp;yp) = X

n2N4

t(p;n) (11) where N4 denotes the 4-connected neighbourhood

of pixelp. The time step
tin eqn. 10 is xed to 0.25, giving updates as large as possible but keeping the scheme numerically stable [10]. The number of iterations is a parameter,N.

In the experiments described below, a modication due to Catte [11] was used. They proposed cal-culating the gradient magnitude in eqn. 9 with a

Gaussian derivative: J = I 1 p 2₂₂ exp  ; (x+y)2 2₂₂  C(x;y) = exp ; J2 x+J 2 y 2₂₁ ! (12) This introduces a second parameter2, 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 masking l-ter fU(I;k) described above. This introduces an-other parameter, k. The total lter therefore is

fA(fU(I;k);1;2;N). In the experiments, the pa-rameters 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 various ltered versions of an image end up in the sharpening-smoothing space.

1It can sharpen edges due to the smoothing of the regions the

(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 bicycle), (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 Experiments

4.1 Images

In the experiments, two images were used as base im-ages, 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 im-ages were converted to 32-bit greyscale oating point images. 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_{8 of their original size in both the x and y}

direction, by pre-smoothing with a Gaussian ( = 2:4) and interpolating linearly.

For both images,fG,fU andfAwere calculated with the parameter settings described in section 3, result-ing in a large number of image points in sharpenresult-ing-

sharpening-smoothing space. Finally, the images were printed on a 600 dpi HP LaserJet 4000N. Print size was 12:816 cm.; dithering was done by the printer.

4.2 Experiment A

The goal of this experiment was to see whether subjects can discriminate levels of sharpening and smoothing as dened in the previous sections. 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 ex-plained as the sharpening of edges and smoothing as the smoothing of regions. Although this might introduce a bias in the outcome of the experiments, it was deemed necessary since some of the subjects had no clear con-cept of sharpening or smoothing.

From the two dimensional feature space, one dimen-sional ranges were drawn containing images with con-stant smoothing or sharpening. Four dierent sharpen-ings and smoothsharpen-ings were used for this: 0.0, 0.1, 0.3 and 0.5. These values were used for constructing series Smx (Shy), consisting of { at most { 8 images with xed smoothing 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 sample (see gure 2a) the specied values of 0.0 to 0.7 typically could only be approximated. This was done by selecting the nearest value to the desired value. However, as can be seen in table 1, which shows the actual values used, the dier-ences were always less than 0.05. Some ranges consisted of less than 8 images, 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 preference 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 quality. 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 smoothing in order to not unnecessarily complicate the preference experiment for the subjects.

4.4 The experimental environment

A room was used containing a special, somewhat tilted table on which the subject could sort the prints. The

Table 1: The grid location and actual sharpening (Sh) and smoothing (Sm) values of the image ranges used in experiment A. A \-" indicates no image could be found near the grid location. Ranges are indicated by what is constant (Sh/Sm) and at what value.

Range(s) Grid portrait bicycle

Sh Sm Sh Sm Sh Sm Sh0:0, Sm0:0 0.00 0.00 0.00 0.00 0.00 0.00 Sh0:0, Sm0:1 0.00 0.10 0.00 0.10 0.00 0.10 Sh0:0, 0.00 0.20 0.00 0.21 0.01 0.21 Sh0:0, Sm0:3 0.00 0.30 0.01 0.30 0.01 0.31 Sh0:0, 0.00 0.40 0.01 0.39 0.01 0.38 Sh0:0, Sm0:5 0.00 0.50 0.01 0.52 0.02 0.51 Sh0:0, 0.00 0.60 0.02 0.60 0.01 0.62 Sh0:0, 0.00 0.70 0.02 0.70 0.04 0.69 Sh0:1, Sm0:0 0.10 0.00 0.09 0.04 0.08 0.04 Sh0:1, Sm0:1 0.10 0.10 0.12 0.10 0.10 0.09 Sh0:1, 0.10 0.20 0.10 0.20 0.10 0.20 Sh0:1, Sm0:3 0.10 0.30 0.11 0.29 0.10 0.30 Sh0:1, 0.10 0.40 0.09 0.41 0.10 0.39 Sh0:1, Sm0:5 0.10 0.50 0.09 0.49 0.09 0.50 Sh0:1, 0.10 0.60 0.10 0.60 0.09 0.61 Sh0:1, 0.10 0.70 0.10 0.69 0.10 0.69 Sm0:0 0.20 0.00 0.21 0.05 0.23 0.04 Sm0:1 0.20 0.10 0.21 0.11 0.20 0.10 Sm0:3 0.20 0.30 0.20 0.31 0.20 0.30 Sm0:5 0.20 0.50 0.21 0.50 0.19 0.50 Sh0:3, Sm0:0 0.30 0.00 0.27 0.02 0.30 0.04 Sh0:3, Sm0:1 0.30 0.10 0.31 0.12 0.30 0.10 Sh0:3, 0.30 0.20 0.30 0.19 0.30 0.18 Sh0:3, Sm0:1 0.30 0.30 0.29 0.30 0.29 0.30 Sh0:3, 0.30 0.40 0.31 0.40 0.28 0.41 Sh0:3, Sm0:1 0.30 0.50 0.30 0.49 0.28 0.51 Sh0:3, 0.30 0.60 0.31 0.60 0.34 0.59 Sh0:3, 0.30 0.70 0.25 0.69 0.33 0.73 Sm0:0 0.40 0.00 - - 0.39 0.05 Sm0:1 0.40 0.10 0.40 0.10 0.40 0.09 Sm0:3 0.40 0.30 0.42 0.29 0.41 0.31 Sm0:5 0.40 0.50 0.41 0.49 0.40 0.50 Sh0:5, Sm0:0 0.50 0.00 0.52 0.04 0.5 0.04 Sh0:5, Sm0:1 0.50 0.10 0.49 0.11 0.50 0.10 Sh0:5, 0.50 0.20 0.49 0.19 0.49 0.19 Sh0:5, Sm0:3 0.50 0.30 0.48 0.33 0.50 0.29 Sh0:5, 0.50 0.40 0.49 0.40 0.50 0.41 Sh0:5, Sm0:5 0.50 0.50 0.49 0.40 0.48 0.48 Sh0:5, 0.50 0.70 - - 0.50 0.68 Sm0:0 0.60 0.00 0.56 0.03 0.59 0.03 Sm0:1 0.60 0.10 0.61 0.10 0.60 0.09 Sm0:3 0.60 0.30 0.58 0.31 0.61 0.30 Sm0:5 0.60 0.50 0.52 0.50 - -Sm0:0 0.70 0.00 - - 0.71 0.03 Sm0:1 0.70 0.10 0.70 0.11 0.71 0.10 Sm0:3 0.70 0.30 0.70 0.29 0.69 0.27 Sm0:0 0.80 0.00 0.81 0.04 - -Sm0:0 0.90 0.00 0.86 0.03 -

-light source was a studio lamp, which provided homoge-neous, indirect lightning of the prints. The luminance on the table was approximately 600 lux. The prints were put in plastic covers to prevent them from becoming dirty. A window was cut in the centre to see the image on the print directly and not through plastic. Four sub-jects 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 ex-periment A are given in gure 4. In the rst range (portrait, Sm₀:5) it can be seen that subjects are quite capable of ordering the prints: only 3 mistakes (wrong orderings) are made. In the second range (bicycle,

Sm0:5) it can be seen that the subjects are not capable of ordering the prints well; too many mistakes are made. The correlation between the dened sharpening and smoothing measures on the one hand and the perceived sharpening and smoothing on the other, is measured with the Spearman rank-order correlation coecient

rs [13]. With this value, the null hypothesis H0, i.e. the dened and perceived sharpening and smoothing are not associated (are independent) can be tested against the hypothesis H1, 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 which N is the number of prints in the range and di is 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

re-jected is 0:736 (forN = 7 this value is 0:786; forN = 6, 0:886).

The rank-order coecients for each subject are given in table 2. 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,

portrait

, Sm

0

:1: we suspect this to be coincidental. More experiments can clarify this. 

Subject 1,

bicycle

, Sh

0

:5: since bicycle is an articial mix of many dierent images, with dier-ent scales of detail, we suspected subjects to base their judgements on dierent parts of the image. To verify this, sharpening and smoothing values of parts of the two images (shown in gure 3 (c) and (d)) were calculated. The parts were selected man-ually, in such a way that all parts of the images sub-jects claimed to have looked at were represented. When correlating the sharpening and smoothing values of the parts with the results for subject 1, it is clear that for the partsfruitandlobsterH₀

can be rejected. After the experiments, the subject stated that he had looked mostly at the pineap-ple (fruit),lobsterand clockimage parts. The

conclusion is that the large variations in the sharp-ening and smoothing values of various parts of the images are the reason for the results of subject 1 in this range.

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 the subjects are capable of ordering the images in the same order as given by the sharpening measure, in (b) it can be seen that the subjects are not able to order the prints in the same order.



Subjects 1 and 3,

bicycle

, Sm

0

:3

and Sm

0:5: in highly smoothed images, the eect of the sharpen-ing operation is only preserved for large-scale, high edges. Small details and less prominent edges are smoothed away. While subjects tend to place em-phasis 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 important edges present are on more or less the same scale.

It can be observed that subjects had much more di-culty in ordering thebicycleimage than in performing

the same task on theportraitimage. As was discussed

above, this is likely due to the diverse content of the for-mer image. A second general conclusion 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. 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 sharp-ening to compensate for the smoothing away of the edges. Clearly, edges play an important role in subject appreciation of an image. For portrait, however, the

leftmost value, indicating a preference for high sharpen-ing at low smoothsharpen-ing, is hard to explain.

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

These conclusions are validated by the results for the two dimensional range, given in table 3. Note that the maximum sharpening and smoothing were much lower than those of the one dimensional ranges, to keep the size of the set of images presented to subjects reasonable. Nevertheless, in general, subjects seem to prefer a little smoothing and much sharpening.

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 sharpening and smoothing induced by a lter were introduced. Some preliminary results of experiments relating these mea-sures 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 sharpening and smoothing values dierent from the entire image { such as the complex bicycle image, in

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 Sm_0.0 Sm_0.1 Sm_0.3 Sm_0.5 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 Sh_0.0 Sh_0.1 Sh_0.3 Sh_0.5 Presented range (d)bicyclesmoothing preference Figure 5: Results of the preference experiment B.

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.

Our experiments also showed that subjects tend to have much less problems in discerning various levels of smoothing than they have with levels of sharpen-ing. 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 promis-ing. One can say that subjects prefer images in which the smoothing is low and the sharpening is high.

How-ever, 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 experiments 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 attributes perceived by subjects, i.e. to nd a model describing this relation. This model can then be used, in combination with a model for sharpening/smoothing preference, for predicting optimal lter settings.

Table 2: The Spearman rank-order coecients for the ranges used in experiment A, per subject. For the val-ues printed in boldface, the null hypothesis cannot be rejected; that is, in these cases perceived sharpening and smoothing are independent of the measures. CV stands for critical value. Note that subject 4 did not participate in the bicycleexperiment.

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 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

Table 3: Results (Sh,Sm) of the preference experiment B with the two dimensional range. Note that subject 4 did not participate in the bicycleexperiment.

Subject Pref. 1 2 3 4 Avg. 1st (0.2,0.1) (0.2,0.0) (0.2,0.0) (0.2,0.2) (0.20,0.08) 2nd (0.2,0.0) (0.2,0.1) (0.2,0.1) (0.2,0.0) (0.20,0.05) 3r d (0.1,0.1) (0.1,0.1) (0.1,0.1) (0.1,0.2) (0.10,0.13) (a)portrait Subject Pref. 1 2 3 Avg. 1st (0.1,0.0) (0.2,0.0) (0.2,0.0) (0.17,0.00) 2nd (0.2,0.0) (0.1,0.0) (0.1,0.0) (0.13,0.00) 3r d (0.0,0.0) (0.0,0.0) (0.0,0.0) (0.00,0.00) (b)bicycle

Acknowledgements

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

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