Metal microstructure recognition using image processing methods.

Moga, Ioan ; Vesselenyi, Tiberiu ; Tarca, Radu Catalin 等

Abstract: Microstructure identification tasks were studied using texture recognition, statistical, fractal and spatial frequency domain analysis methods, from which fractal methods had produced good results Determination of phase percentage had also been tried with fractal methods but with less success. Therefore the authors tried to solve this kind of tasks with spatial frequency methods. An application of this type of method is presented in this paper. Keywords: microstructure identification, spatial frequency, phase percentage determination

1. INTRODUCTION.

Metallography analysis, as it is currently made, implies a large variety of analysis methods each of them being a result of practically tested knowledge.

That is the reason why, automation of metallography analysis, cannot be made developing a single generally applicable algorithm, but a collection of algorithms, gathered in an expert system.

From the large amount of metallography tasks, for this study, we had selected two important categories:

--microstructure identification task;

--determination of microstructure phase percentage (PP), which can be represented by a series of numbers, i.e. from 0 to 5, correlated with the percentage of a component or phase of the microstructure.

Microstructure identification tasks were mainly studied using texture recognition, statistical, fractal and spatial frequency domain analysis methods, from which fractal methods had produced good results (Vesselenyi, 2005).

Determination of phase percentage had also been tried with fractal methods but with less success. Therefore we tried to solve this kind of tasks with spatial frequency methods. An application of this type of method is presented in this paper.

2. ANALYSIS METODS FOR METALLOGRAPHY TASKS

Images for algorithm testing had been taken from metallography album (Radulescu et al., 1972), but similar collections of images are given also in (METALLOROM, 2004) and (METADEX, 2004) or in SR 5000:1997 standard. For every studied microstructure four, 512x512 pixel, non-overlapping images had been taken. For image analysis a computer program had been developed which is using a 2D fast Fourier transform (2DFFT) based algorithm adapted for spatial frequencies. All the selected images had been processed with the help of this algorithm.

Similar algorithms were used for surface roughness characterization (Vesselenyi & Mudura, 2001). A graphical representation of the result of 2DFFT processing is given in figure 1.

The amplitude of 2D power spectral density represented in the diagram from figure 1 is named PSD. The middle point of spatial frequency plane represents the 0 frequency and the frequency is increasing to the margins.

[FIGURE 1 OMITTED]

If we define [parallel]k[parallel] = [square root of [f.sup.2.sub.x] + [f.sup.2.sub.y]] as the spatial frequency, on any direction from the center to the margin, (where fx is the spatial frequency on lines and fy is the spatial frequency on colons) we can consider circles with the center in origin and of radius

[parallel][k.sub.n][parallel], n = 1 ... (N - 1)/2, (for an image matrix of N x N). For every circle a mean value can be defined PSDmed (kn), given by the relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where mn represents the number of points on the circle of radius kn.

The obtained PSDmed values can be plot versus kn obtaining a 2D diagram which can be approximated by a line of equation:

log([DSP.sup.med]([k.sub.n])) = [p".sub.1](log)([k.sub.n])) + [p".sub.2] (2)

By computing parameters [p.sub.1]" and [p.sub.2]" for every tested image and then representing them on a diagram we can study if the ([p.sub.1]", [p.sub.2]") points representing the same type of structure are grouped together or not. If yes, it means that the parameters [p.sub.1]" and [p.sub.2]" can be used to identify that particular type of structure. In microstructure identification tasks a large number of images were successfully identified but there were still some that were not. In order to enhance the identification success rate, a third statistical parameter had been introduced which was defined as

[p.sub.h] = [i.sub.max] (3)

where imax is the image intensity corresponding to the maximum of the image histogram:

h([i.sub.max])=max(h(i)), i=1 ... 256. (4)

So a 3D space had been defined in which the coordinates are (p1", p2", imax) each set of parameters corresponding to an analyzed image (Prf-Ph diagrams). After performing the computations for all the selected images we can conclude that every microstructure from the studied set could be identified with a good precision (figure 2).

For the determination of phase percentage task, although the discrimination of images was good, the algorithm could not establish an ordering of the parameters, which should correspond with the PP. So, for PP tasks we had defined other different algorithms, which could solve this issue. In this paper we present an example of such an algorithm used for the determination of phase percentage of ferrite in ferrite-pearlite microstructures.

3. APPLICATION OF FERITE PERCENTAGE DETERMINATION IN A FERITE-PERLITE STRUCTURE.

For this purpose we had defined a quantity Emax also derived from the 2D PSD diagram computed with the relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where iPSD=(n ... k) and jPSD=(m ... l) represents the spatial frequencies in the domains n-k and m-l. Limiting the spatial domain frequency is the same as to define a band pass filter for which the Emax value is maximal.

Once the Emax values computed for all the image sets representing groups of different microstructures (with the same phase percentage within a group), we can represent these values versus phase percentage, as it is shown in figure 3. As we can see the correlation works only in two domains from 0 - 2 and 3 - 5. Here the following spatial frequency ranges were selected: [i.sub.PSD]=(248 ... 264), [j.sub.PSD]=(1 ... 64).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Now we can recall that in the Prf-Ph diagrams these two domains are well separated so we can establish a heuristic rule to obtain a modified Emax diagram called Emax', given by the relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where [i.sub.hmedp] = 42,5; [k.sub.p] = 1,15;

Representing the newly obtained characteristic Emax' as a function of phase percentage we will obtain the diagram presented in figure 4. To obtain a mathematical expression of these experimental points we had interpolate them using a third degree polynomial and obtaining:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where pfp is the phase percentage and the coefficient values are as follows.:

a = -0,0006; b = 0,0115; c = -0,0053; d = 0,7537;

4. CONCLUSIONS

Automated microstructure identification and phase percentage determination needs an expert system approach based on a large number of experimental studies. For both tasks we had presented some methods, which gave satisfactory results, in order to be applicable in automated microstructure control systems. We had defined a number of parameters (p1", p2", ph, Emax and Emax') and some diagrams (Prf-Ph and Emax'), which can be used with good results in the studied field of applications.

5. REFERENCES

METADEX, CSA, Avaiable from: http: www.csa.com Accessed: 12-03-2007.

MetalloROM, HDH Thermal, Dr. Sommer Werkstofftechnik, Avaiable from: http: www.werkstofftechnik.com Accessed: 12.03.2007.

Radulescu M.; Dragan N.; Hubert H.; Opris C. (1972) Metallography Atlas, Editura Tehnica, Bucuresti.

Vesselenyi, T.; Mudura, P. (2001) Metallography image, FFT characteristics analysis, (in Romanian) Simpozion materiale avansate, tratamente termice si calitatea managementului, Zilele Academice Timisene, ISBN 973-8247-32-2.

Vesselenyi, T., (2005) Metallography image analysis automation, (in Romanian)PHD Thesis, University "Politehnica" Timisoara.