Chantler, M

Drbohlav, O

Green, Patrick Richey

Padilla, S

English

In this paper we present an investigation into visually perceived surface roughness. First we present psychophysical evidence that suggests that there is a simple relationship between perceived roughness and two well known surface parameters:fractal dimension and rms roughness. And that neither are good estimators, on there own, of perceived roughness. Second we present a measurement modelfor deriving the perceived roughness of a surface from its height function which ismotivated by the spatial frequency channel model of the human visual system

Heriot Watt Pure

Padilla, Drbohlav, Green, Chantler, Measurement of Perceptual Roughness  1 MEASUREMENT OF PERCEPTUAL ROUGHNESS                                      IN FRACTAL SURFACES Stefano Padilla1, Ondrej Drbohlav3, Patrick Green2 and Mike Chantler11School of Mathematical and Computer Sciences 2School of Life Sciences Heriot-Watt University, Edinburgh, UK 3Faculty of Computer and Information Science  University of Ljubljana, Slovenia ABSTRACT  In this paper we present an investigation into visually perceived surface roughness. First we present psychophysical evidence that suggests that there is a simple relationship between perceived roughness and two well known surface parameters: fractal dimension and rms roughness. And that neither are good estimators, on there own, of perceived roughness. Second we present a measurement model for deriving the perceived roughness of a surface from its height function which is motivated by the spatial frequency channel model of the human visual system. 1. INTRODUCTION  Our long-term goal is to establish perceptually relevant measurements for surface texture. By surface texture we understand a stochastic surface which is described by its three-dimensional surface relief and reflectance properties (see Fig. 1(a) and Fig. 2). ‘Sand ripples’ and ‘animal skin’ can serve as examples of natural surface textures, while ‘textile’ and ‘wallpaper’ are two man-made ones. To start with a problem of manageable complexity we constrain the study to measuring the perceived roughness of artificially generated fractal surfaces.  − Fractal surfaces. Surface textures investigated in this article are constrained to unit-albedo Lambertian surfaces whose geometry is modelled as 1/ frequencyβ noise. They are parameterised by just two terms: β the magnitude roll-off factor, and σ the surface RMS roughness (see Fig. 1(a) for examples). − Perceived roughness. We select perceived roughness (ξ PR), as the only perceptual dimension to be studied.      (a)         (b) Figure 1. (a) Examples of fractal surfaces obtained for different values of β (the magnitude spectrum roll-off factor) and σ (the RMS roughness). The surfaces are generated for points as indicated in (b), which is the β − σ space. The contours illustrate the possible form of lines of equal perceived roughness (ξ). 2. PREVIOUS WORK  There has been surprisingly little work published on experiments that have sort to determine the mapping between the physical description of a surface texture and its perceived characteristics. Most researchers have tried to identify perceptual dimensions by using collections of still Padilla, Drbohlav, Green, Chantler, Measurement of Perceptual Roughness   2 images of natural textures such as the Brodatz album [4]. To our knowledge only Ho et al [8] has used surface models. We will therefore divide this survey into two parts: research using image texture, and research using surface models. 2.1 Research using Image Texture Two broad methods have been used to establish a perceptual space of texture using collections of single still images of texture samples. One method has been to ask observers to judge texture similarity along pre-defined dimensions [17, 1]. While these experiments achieved some agreement in identifying perceptual dimensions, they did not translate well to digital analysis of textures for content-based retrieval. In other experiments [7, 15, 16], multi-dimensional scaling was applied to results from observers asked to sort image textures freely. These authors concluded that visual texture has three major orthogonal dimensions. Long and Leow pointed out that previous authors did not normalise for orientation or scale and argued that such variations would affect texture perception. After normalising image textures in this way, they established a four-dimensional perceptual space which they mapped onto Gabor features using a variety of non-linear functions [11, 12]. Balas [2] manipulated images of natural textures in more sophisticated ways, using Portilla and Simoncelli’s algorithm [14] to alter specific statistical properties of synthesised grey-scale images of texture. 2.2 Research using Surface Texture A characteristic of the above experiments is that they have used image texture. However, our goal is to characterise perception of surface texture. It is well known that images of surface texture, and features derived from such images, are fundamentally affected by illumination and viewing conditions (see Fig. 2) [13, 6]. Moreover, single still images provide relatively poor sensory stimuli – multiple images obtained while moving our heads, the sample orientation, or the illumination greatly enhance our perceptions of surface characteristics. Koenderink et al [9] used sets of still images of natural surfaces captured under precisely controlled conditions of illumination in order to test observers’ ability to estimate the direction of illumination from the images. More relevant to the topic of our work however, Ho et al [8] synthesised surface representations and rendered these under varying conditions of illumination in order to test observers’ perception of roughness as a function of illumination angle. They concluded that the perceived roughness of texture patches did not remain constant under varying illumination slant angle. However, the surfaces were obviously artificial (20×20 vertices were used) and the single, still, fronto-planar images subsequently generated provided limited stimuli for observers.       Figure 2. Effect of illumination variation on images of surface texture. (The two images demonstrate the effect of illumination variation on resulting image texture: both images are of the same physical surface; only the illumination has been changed between photographs.) 3. EXPERIMENTAL PROCEDURE In developing our procedure for investigating the perceptual nature and mappings of surface textures we wanted to use stimuli similar to those typically experienced by humans when visually inspecting a surface, but under totally controlled and reproducible experimental conditions. We have therefore used fast computer graphics techniques to render photorealistic imagery of synthesised surfaces in real-time. This provides: 1. Rich real-time stimuli (up to the resolution of the human eye) using self and cast shadowing of Lambertian surfaces, 2. Natural appearing surface textures (very similar to those produced by shattering plaster blocks), 3. Real-time interactive (or pre-programmed) variation of illumination and surface orientation, and Padilla, Drbohlav, Green, Chantler, Measurement of Perceptual Roughness   3 4. Real-time interactive variation of surface characteristics.  Exp. 1 Constant Roughness Using the methods described above we sought to establish a series of contours of constant perceived roughness in the β-σ space of surfaces. We did this by: 1. Generating a ‘reference’ fractal surface at a given β and σ, which we plot on a β-σ scatter plot, 2. Generating a second ‘test’ surface at a different β and a random σ, 3. Presenting the observer with visualisations of both surfaces, during which time the orientations of both surfaces simultaneously follow the same predefined wobbling motion, 4. Asking the observer to interactively adjust the σ of the ‘test’ surface so its perceived roughness matches that of the reference. Observers were instructed to consider how the surfaces would feel if touched when making these matches. 5. We then plot the final β-σ of the ‘test’ surface on a scatter plot. 6. We repeat 1–5 with ‘test’ surfaces of differing β, each time randomising the phase of the ‘reference’ and ‘test’ surfaces. This provides one set of iso-roughness points (see Fig. 3). 7. Finally we repeat 1-6 for four other ‘reference’ surfaces for which we choose a reference β-σ to provide a total of five iso-roughness lines at different perceptual roughnesses.  Exp. 2 Roughness Scaling Later in a second set of experiments the scaling relationship was analysed by: 1. Generating two ‘reference’ fractal surfaces at given β and σ values based on the successive contours found in the previous experiments.  2. Generating a third ‘test’ surface at a similar β and a random σ, 3. Presenting the observer with the three surfaces, during which time the orientations of the surfaces follow the same motion, 4. Asking the observer to adjust the σ of the ‘test’ surface until it was perceived as being equidistant to the two ‘reference’ surfaces, 5. Repeat 1-4 with different β, σ and phase values for all possible iso-roughness lines found previously.  Figure 3. The principle of identifying the isocontours of perceived roughness. An observer is presented with a pair of textures at a time: the reference texture (the dark point) and a test texture (a light point), and is asked to adjust the RMS of the test texture such that it matches the perceived roughness of the reference. Doing this for several test textures (light points) is a key to obtaining an isocontour corresponding to the reference, ξ = ξ ref.  The same methods can of course be extended to study the effects of varying any parameters of surface texture on any perceptual judgements. 4 RESULTS AND ANALYSIS Exp. 1 Constant Roughness Five observers completed the constant roughness experiments (Exp. 1). The scatter plot of the resulting contour lines is shown in Fig. 4. The data is displayed with a logarithmic σ-axis, as it is natural for human observers to appreciate surface height scaling in that way. The plots show evidence of a linear relationship between log rms roughness and roll-off factor for a constant perceived roughness.  Padilla, Drbohlav, Green, Chantler, Measurement of Perceptual Roughness   4 Straight lines were therefore fitted to each of the five sets of results (one for each reference surface roughness). Note the lines were fitted independently to each reference roughness.  We believe that these results clearly indicate a linear relationship between log σ and β for a constant perceived roughness.  1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.510-1100101Roll-off factorlog RMS1.41.21.00.80.6 Figure 4. The results of L1 linear regression of experimental data. The five fitted lines in each graph correspond to reference surfaces whose β’s were set to 2, while the reference RMS’s (in cm) were as shown in the plot.  Exp. 2 Roughness Scaling For the second set of experiments the resulting isocontours are plotted in Fig(5). Again, this shows evidence of the linear relationship, but more importantly gives us the scaling behaviour with which to investigate a measurement model.  5 A MEASUREMENT MODEL OF PERCEIVED ROUGHNESS  In this section we propose a model for obtaining numerical estimates of the perceived roughness ( PRξ ) of a surface from its height function. Our proposal was inspired by the common frequency channel model of V1 (the first part of the human visual system). It comprises a number of FRF stages tuned to different frequencies. For the purposes of this modelling, we express the frequency domain description of the fractal surfaces as cycles per degree of visual angle at the experimental viewing distance of 90 cm.  1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.510-1100101Roll-off Factorlog RMS             ISO Roughness Contours             Equidistant Roughness Lines Figure 5. The results of the experimental data from the second set of experiments. The three solid lines correspond to the perceptual middle contour between the adjacent isocontours from the previous set of experiments.  Similarly our model comprises of a linear filter stage (F) followed by a non-linear (integrating) stage (RF). It is expressed below in the frequency domain for simplicity. θωθωθωξ ddSFPR ),(),(∫∫=        (2) where  ),( θωS is the surface height function expressed in the frequency domain, and   ),( θωF is the linear filter.  We have found that using a Gaussian function as the linear frequency-domain filter provides a good fit to the psychophysical data. We parameterised it with its width (Gaussian variance) and its weight at 30 cycles/degree.   We optimised this model’s parameters to minimise the variation in predicted PRξ  along the lines of constant roughness Padilla, Drbohlav, Green, Chantler, Measurement of Perceptual Roughness   5 estimated from experiments Ex.1 & 2. The shape of these optimisation spaces are shown in Figs 6 & 7 respectively.  Filter weight at 30 cycles per degreeGaussian Variance0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.522.53 Figure 6. Fit of the measurement model PRξ  as a function of its parameters for Ex. 1.   Filter weight at 30 cycles per degreeGaussian Variance0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.522.53 Figure 7. Fit of the measurement model PRξ as a function of its parameters for Ex. 2.  From the above it can be seen that both of the optimisation surfaces follow the same valley shape. The error is not terribly sensitive to traversing along the bottom of the valley and this gives a range of possible filter shapes as shown in Fig. 8.  Contour lines of constant roughness PRξ  predicted by the measurement model (shown in bold in Fig 8) are plotted together with the original psychophysical data in figure 9.  10-1 100 10110-210-1100Cycles per degreeFilter weight Figure 8. Possible Gaussian distributions. All the filters have almost similar minimum variances. The bold filter is the most likely filter, which will be used in figure 9 to plot the fitting of the model to the real data.  6. SUMMARY AND CONCLUSIONS We have demonstrated that for fractal surfaces of constant perceptual roughness a linear relationship exists between surface roll-off factor and rms roughness.  Thus neither rms roughness or fractal dimension (which is directly and simply related to the surface roll-off factor) are good measures of perceived roughness on their own. Finally we have proposed a measurement model for perceptual roughness which is based upon a simple frequency channel of V1 and which we have shown can derive the perceived roughness of a surface from its height function.    Figure 8. Fit of the most likely model to the original psychophysical data from Ex. 1. Padilla, Drbohlav, Green, Chantler, Measurement of Perceptual Roughness   6 REFERENCES [1] Amadasun M. and King R. Textural features corresponding to textural properties. IEE Trans. On SMC, 19, 1264–1274, 1989. [2] Balas B. Texture synthesis and perception: Using computational models to study texture representations in the human visual system. Vision Research, 46, 299–309, 2006. [3] Belhumeur Peter N., Kriegman David J., and Yuille Alan L. The bas-relief ambiguity. International Journal of Computer Vision, 35(1), 33–44, November 1999. [4] Brodatz P., Textures: A Photographic Album for Art and Designers. Dover Publications, Inc., New York, NY, 1966. [5] Campbell F.W.  and Robson J.G. Application of fourier analysis to the visibility of gratings. Journal of Physiology, 197, 551–566, 1968. [6] Chantler M. J. Why illuminant direction is fundamental to texture analysis. IEE Proc. Vision, Image and Signal Processing, 142(4), 199–206, 1995. [7] Harvey L.O.  and Gervais M.J. Internal representation of visual texture as the basis for judgements of similarity. Journal of Experimental Psychology: Human Perception and Performance, 7, 741–753, 1981. [8] Ho Y.-X, Landy M. S., and Maloney L. T.. How illuminant direction affects perceived visual roughness. Journal of Vision, 6, 634-648, 2006. [9] Koenderink J.J.  and Pont S.C. Irradiation direction from texture. Journal of the Optical Society of America, 20, 2003. [10] Landy M. S. and Oruc P. Properties of second-order spatial frequency channels. Vision Research, 42(19), 2311–2329, 2002. [11] Long H. and Leow W. Perceptual texture space improves perceptual consistency of computer features. IJCAI 2001, 1391–1396, August 2001. [12] Long H. and Leow W. A hybrid model for invariant and perceptual texture mapping. In Proc. ICPR, volume 1, 135–138, 2002. [13] Pentland A.P. Fractal based description of natural scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 1984. [14] Portilla J. and Simoncelli E.P. A parametric texture model based on joint statistics and complex wavelet coefficient. International Journal of Computer Vision, 40, 2000. [15] Rao A.R. and Lohse G.L. Towards a texture naming system: Identifying relevant dimensions of texture. In IEEE Visualization 93, 220–227, October 1993. [16] Rao A.R. and Lohse G.L. Towards a texture naming system: Identifying relevant dimensions of texture. Vision Research, 35(11), 1649–1669, 1996. [17] Tamura H., Mori S., and Yamawaki T. Texture features corresponding to visual perception. IEEE Trans. Sys. Man, and Cybernetics, 8, 460–473, 1978.    ACKNOWLEDGEMENTS Stefano Padilla1, Ondrej Drbohlav3, Patrick Green2 and Mike Chantler1  1School of Mathematical and Computer Sciences 2School of Life Sciences Heriot-Watt University Riccarton Edinburgh - EH14 4AS - UK  +44(0) 131-451-4166 ceesmp@macs.hw.ac.uk P.R.Green@hw.ac.uk M.J.Chantler@hw.ac.uk  3Faculty of Computer and Information Science Visual Cognitive Systems Laboratory Trzaska 25, SI-1001 - University of Ljubljana – Slovenia ondrej.drbohlav@fri.uni-lj.si  This work was funded in part by EPSRC grants EP/D059364/1 and GR/S12395/01.  

Measurement of perceptual roughness in fractal surfaces

https://pureapps2.hw.ac.uk/ws/files/4405911/2006_Measurement_Roughness.pdf

Measurement of perceptual roughness in fractal surfaces

Abstract

Similar works

Full text

Available Versions

Heriot Watt Pure

Heriot Watt Pure