Surface roughness image analysis using fractal methods.

Vesselenyi, Tiberiu ; Moga, Ioan ; Mudura, Pavel 等

Abstract: In this paper the authors describe the results of experiments for surface roughness image acquisition and processing in order to develop an automated roughness control system. This implies the finding of a characteristic roughness parameter (for example Ra) on the bases of information contained in the image of the surface.

Keywords: image processing, surface roughness, fractal parameters.

1. INTRODUCTION

Surface roughness of manufactured products is defined in SR ISO 4287/2001 standard and other international standards. Simple and complex characterization parameters are explained in works like (Costa, 2000), which are considering the use of stylus devices to measure roughness after a linear or curved path. Although these devices had been continuously upgraded in order to increase measuring precision (Leach, 2001), they are not efficient enough used in automated measuring systems, due to the fact that the stylus have to contact the measured surface and also due to the very long time of measurement. A newer technique in surface roughness measurement is the employment of digital image acquisition and processing (Lee & Tang, 2001). In this case the camera is coupled to a microscope (bellow x100) and the acquisitioned images are processed with specially designed computer programs.

2. ACQUISITION AND PREPROCESSING OF SURFACE IMAGES

For image acquisition purposes several manufactured roughness probes were used (STALI DOVODCA--GOST 9378-80 E15718) obtained by manufacturing operations as: cylindrical milling, plane milling, shaping, frontal grinding, plane grinding. Several non-overlapping images, of every probe's surface were taken using a CCD camera mounted on a CITIVAL microscope at scale of x10 and x25. The resolution of the images was 640x480 pixel. The correlation between surface roughness and surface image had been studied in a large number of papers (Lee & Tang, 2001) showing a certain functional dependency between asperity height and image intensity. During experiments however, we observed that this correlation is more complex and depends in a very high degree on the illumination conditions of the probe.

After the image acquisition phase, a number of preprocessing operations had to be made in order to obtain better image quality. The used preprocessing methods were as follows:

--filtering--eliminate inherent image noises;

--establishing region of interest--keep only high information regions of the image;

--uneven illumination effects elimination--eliminate effects of higher intensity in the middle of the image;

--correction of probe rotation and position variations

as the images are an-isotropic, rotation of the probe can alter the analysis results. Here 2D Fast Fourier Transforms described in (Jiang et al., 2001) or oriented Gabor filters described in (Tsai et al., 2000) can be used.

On the base of tested preprocessing methods a program module had been generated, which was finally included in the automated quality control system. After preprocessing, the image quality was fair enough to perform the next step of image processing. Studying recent researches in texture analysis and image processing a number of statistical methods (co-occurrence, statistical moments) and frequency domain methods (Gabor filters, wavelet analysis), had been tested in order to obtain automated recognition of surface roughness parameters, but these methods didn't yield the wanted results. So we focused our research on fractal methods.

3. FRACTAL IMAGE PROCESSING METHODS

Computation of fractal dimension is less important from a practical point of view. It's more important to use fractal parameters in order to discriminate surfaces with different roughness characteristics. Fractal dimension computation of rough surfaces using the Weirstrass-Mandelbrot function is described in (Jiang et al., 2001) and others. When this function is correlated to power spectral density, the fractal dimension is correlated to the slope of the spectrum represented in logarithmic scale. The Weirstrass-Mandelbrot function is difficult to apply in practice. That is why we had to use methods, which are easier to implement as computer algorithms. These methods are the box counting method (BC) and the frequency domain fractal parameter (FDFP). Both methods had been tested on the roughness probes images. The box counting method (BC) had been derived from the "compass dimension" and is closely related to fractal dimension as it has been stated by Mandelbrot with the relation:

D = logN/log(1/r) (1)

The compass dimension is obtained measuring a curve with decreasing measuring units ([r.sub.i], i=1 ... k) and storing the number of measures [N.sub.i] for each [r.sub.i]. The diagram of log([N.sub.i]) as function of log(1/[r.sub.i]) is drawn obtaining a so called Richardson plot. If the Richardson plot is a straight line then the measured object is fractal and the slope of the plot is it's compass dimension. The BC method uses rectangular boxes of decreasing edges instead the linear measure [r.sub.i]. Fractal dimension can also be computed on the bases of power spectral density (PSD), as it is stated in (Costa, 2000). If the PSD amplitude is represented as a function of spatial frequency (f) in a logarithmic diagram then the fractal parameter can be considered as the slope ([p.sub.1]') of the log(PSD) approximation line and the ([p.sub.2]') as the intersection of this line with the ordinate axis.

(2)

First we have developed a 2D box counting algorithm and then a 3D algorithm both yielding satisfactory results. The experiments showed that is better to use a [p.sub.3]' parameter defined as [p.sub.3]'=[p.sub.2]'/[p.sub.1]' instead of [p.sub.2]'. Although the obtained results show that the analyzed images do not have true fractal behavior (the resulted Richardson plot is not a rigorously straight line), the goal is to find correlations between parameters [p.sub.1]' and [p.sub.3]' on one hand and the surface roughness on the other hand.

4. EXPERIMENTAL RESULTS

In order to have a good sight of the results we defined a Pf (fractal parameter) diagram to plot the values of [p.sub.3]' versus [p.sub.1]'. An example of such a diagram is shown in figure 1, for surfaces machined with a cylindrical mill, and for a magnification of x10. In these diagrams for each roughness we have assigned a certain marker. The goal was to obtain linearly separable clusters for different roughness. In figure 1 we have squares (S) of [R.sub.a] = 6.3; upward triangles (UT) of [R.sub.a] =3.2 and down pointing triangles (DT) of [R.sub.a] =1.6. It is clear that in the diagram in figure 1 we have obtained a good separation of S from UT and DT but a bad separation of UT and DT. Analyzing then the Pf diagram for a magnification of x25 (figure 2) we can see that the UT marked probes are well separated from the others.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Using the fractal parameter method all the probes could be classified with a good precision. In figures 3 and 4 the diagrams obtained by plane grinding are presented. In figure 3 (magnification of x10) we can observe a clear separation of probes of Ra = 1.6 (squares) from the rest of the probes. Then in the x25 magnification diagram we obtain the separation of the other probes.

[FIGURE 3 OMITTED]

Establishing of discrimination sub-domains can be made automatically by a series of clustering methods. like fuzzy reasoning or artificial neural networks. Good separation of probes with different surface roughness is possible only using analysis with multiple magnifications.

[FIGURE 4 OMITTED]

The selection of optimum magnifications to be used needs to be experimented for the sets of images involved in the study. The establishing of box dimension range is also an issue, but this can be solved with experiments on large sets of calibration images. The authors plan to present algorithms for these issues in a future works.

We had mentioned before that there is a closed link between fractal dimension and power spectral density parameters (Jiang et al., 2001) and (Costa, 2000).

The authors had made experiments with the PSD method too, in order to compare the two methods. For the PSD method the same probes were used as in the first case. The obtained results were very close to results obtained with the box counting method. Here an issue to solve is the automated selection of the analysis frequency range.

5. CONCLUSIONS

Based on earlier research results, in this paper the authors experimented two fractal methods (BC and PSD) in order to recognize surface roughness of machined surfaces from their images. Both method had produced good results and it can be concluded that the PSD method is much faster and can be successfully applied in automated quality control systems.

In this paper new fractal parameters ([p.sub.2]' and [p.sub.3]') were defined and a new type of diagram ([P.sub.f]) diagram had been proposed to enhance fractal image processing methods. As further developments the selection of box dimension range for BC method and frequency range for PSD method will be studied. Automated interpretation of results can also be the subject of future works.

6. REFERENCES

Costa M., A.; (2000) Fractal Description of Rough Surfaces for Haptic Display--PhD Thesis, Stanford University.

Jiang, Z.; Wang, H.; Fei B. (2001), Research into the application of fractal geometry in characterising machined surfaces, Intenational Journal of Machine tools & Manufacture, Elsevier Science Ltd.

Leach, R.K. (2001), NanoSurf IV: traceable measurement of surface texture at the National Physical Laboratory, Intenational Journal of Machine tools & Manufacture, Elsevier Science Ltd.

Lee, B.Y.; Tang, Y.S. (2001) Surface roughness inspection by computer vision in turning operations, Intenational Journal of Machine tools & Manufacture, Elsevier Science Ltd.

Tsai, D.M.;Wu, S.K.;Chen, M.C. (2000) Optimal Gabor filter design for texture segmentation using stochastic optimization, Image and Vision Computing, Elsevier Science.

Table 1. Sub-domains and roughness correlation.

Subdomain Subdomain Roughness
[P.sub.f] x 10 [P.sub.f] x25 [R.sub.a]

SD1 SD2 6,3
SD2 SD1 3,2
SD2 SD2 1,6