Filtering of Signals with Defectograms
Abstract Generated abstract
This paper addresses the automation of decoding radiographic defectograms, motivated by the high information volume of film images and the impracticality of direct full-resolution input into electronic computers. The authors argue for an intermediate, non-machine preprocessing stage that filters and reduces measurement information by retaining only coordinates associated with useful defect signals, such as contours and extrema. Using estimates for X-ray film input and a simplified model of pore-like defects, they show that such reduction can make computer processing feasible, and they formulate a signal model based on pulse sequences, modulation, and noise outliers. The proposed primary filtering structure combines matched filters, threshold decision devices, approximation, and phase-based secondary filtering, with experimental results reported to support the approach.
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PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
NAMED AFTER S. M. KIROV, HOLDER OF THE ORDER OF THE OCTOBER REVOLUTION AND THE ORDER OF THE RED BANNER OF LABOR
Volume 248
1975
FILTERING OF SIGNALS FROM DEFECTOGRAMS
V. I. GORBUNOV, B. N. EPIFANTSEV, Yu. P. ZABASHTA
The ever-increasing number of photo images obtained in various areas of application of human thought, and the high labor intensity of deciphering them, have led to the formulation of the problem of automating the process of decoding photographic images. With some delay, the problem of transferring decision-making functions to an automatic device has also arisen in radiography. The reasons for this are as follows.
First, even in the event of the successful completion of research on the creation of systems that make it possible to obtain, practically instantaneously, a two-dimensional image of the structure of an object—moreover with the accuracy and resolving power of these systems being at the same level as that of X-ray film—the contradiction between the desire to intensify technological processes and the potential need to spend time on inspection would still not be eliminated. Indeed, the magnitude of the “operator time” in a closed-loop control system limits the speed of inspected items moving along the line to 0.14 m/sec [1]. This is clearly insufficient to satisfy modern production. Therefore, a qualitatively new effect in defectoscopy will be obtained only when the “inspection time” and the rate of change of the structure of the inspected objects or media prove to be coordinated. And this, in turn, leads to the transfer of decision-making functions to an automatic device.
Second, X-ray and gamma inspection currently account for no less than 80% of the total volume of physical nondestructive testing methods used in industry, and radiography predominates over the other methods [2]. Therefore, automation of the process of deciphering negatives is relevant in itself.
Third, in order to obtain statistically reliable conclusions, it is necessary to construct laws of distribution of features on representative statistics. Setting up experiments to simulate possible situations, however, is an expensive and time-consuming process; from this point of view, the use of photographic images that are the product of experiments already carried out and that, with still unsurpassed quality, reflect the structures under investigation is not only desirable, but also necessary.
The second point that should be considered here is the choice of a research model, which in the classical version reduces to three stages.
a) A sensor is selected by means of which the state of the objects under investigation is transformed into a signal, usually of electrical origin, convenient for subsequent use.
b) The electrical signal obtained is brought into a form with which an electronic computer (EC) operates. In other words, at this stage the problem is solved of matching the characteristics of the information source with the information-processing instrument.
c) The signal entered into the EC, by means of a previously compiled system of rules (an algorithm for solving the problem), is transformed first into feature space and then into decision space. On the set of algorithms, an optimal system of transformations is determined in accordance with specified criteria (for example, minimum average risk). The result obtained is analyzed from the point of view of whether it satisfies the consumer. In the case of a positive decision, one proceeds to the stage of designing an automaton operating according to the algorithm found; otherwise, either the search for new solutions is continued, or a conclusion is drawn that it is inexpedient to replace a human being by an automaton in this sphere of transformed information.
Let us analyze the scheme considered, a→b→c, in the plane of the problem posed. Obviously, automation of the decoding of defectograms (photographic images of the defectiveness of the structures under study) will be logically fully justified only if the parameters of the automaton are, at the very least, no worse than the corresponding parameters of a human being. If we take the contrast-sensitivity threshold to be 0.01, and the resolving power to be 10 lines/mm [2], then it is possible to estimate the amount of information obtained from the area of an elementary frame (Fig. 1). Then, using the obvious formula
\[ T\;(\text{minutes})= \frac{10^{4}\;(\text{numbers}/\text{cm}^{2})\cdot S\;(\text{cm}^{2})} {60\cdot V\;(\text{numbers}/\text{sec})}, \]
where
\(V\) is the maximum permissible rate of information input, determined by the method of matching the information source with the machine. We obtain that input into the EC of the description of the optical-density structure from 30 meters of X-ray film 12 cm wide, using a PL-80/8 perforator, will take 5 months without interruption; when magnetic tape is used as an intermediate carrier, it will take about 6 hours.
Fig. 1. Dependence of the output amount of information on the area of the defectogram
The figures given cast doubt on the expediency of carrying out studies according to the scheme a→b→c and require a search for ways of preliminary (non-machine) reduction of the amount of measurement information (introduction into the model of the intermediate transformation a¹). The meaning of this transformation is obvious: to enter into the EC only the coordinates of readings that belong to the image of the useful signal.
As an example, let us estimate the amount of information at the input of the machine if only the coordinates of defect contours are entered. Let us denote the area of the defectogram by \(S\), and the area occupied by defects by
\[ S_g=\sum_i s_{ig}. \]
where
\(S_{ig}\) is the area of one defect.
Assuming, for simplicity, that all defects have the form of gas pores, we find
\[ S_g=\sum_i \pi R_i^2, \qquad \overline{S}_g=\frac{1}{N}\sum_{i=1}^{N}\pi R_i^2, \]
\[ P_g=\sum_i 2\pi R_i, \qquad \overline{P}_g=\frac{1}{N}\sum_{i=1}^{N}2\pi R_i \]
and the reduction coefficient
\[ \gamma=\frac{S}{2S_g}\,\overline{R}, \]
where
\(\overline{R}\) is the mean value of the defect radius. For \(\overline{R}=5\) mm, \(S/S_g=20\), the reduction in the volume of information reaches 400, so that to input information from 30 m of film 12 cm wide, in principle only 9 hours will be required when using PL-80/8 perforators, and less than a minute for magnetic tape. These are already acceptable figures.
Thus, the model of the study should be represented in the form \(a \to a^1 \to b \to c\). The transformation \(a^1\) includes various kinds of signal-filtering operations, whose essence may be judged from [3].
Any filtering narrows the space of measurements. Therefore, before introducing an intermediate transformation, one should make sure that useful coordinates in the feature space will not be lost. Two points should be noted here.
First, the section of any defect in the amplitude–time plane is a pulse, the form of which is not important, for the reason that the statistical description of the densities of a gas pore, slag inclusions, lack of fusion, and cracks is, on average, an approximation to a bell-shaped or trapezoidal form. Rather, the duration of the pulse at the base and, to some extent, the position and magnitude of its extremum should be regarded as the distinguishing feature.
Second, the extrema and contour points of defects, unlike film noise, are characterized by rectilinearity in an elementary space (defined by the measurement accuracy). This gives grounds for speaking of the appearance of a deterministic component in a stationary pulse stream
\[ z(t_i)=\sum_{\kappa=1}^{M_i}\int_a^b f(t)\cdot \delta(t-\kappa T_i-t_i)\,dt, \]
where \(\delta(\ldots)\) is the delta function, the integral over the \(\xi\)-neighborhood of which is
\[ \int_{-\xi}^{\xi}\delta(t)\,dt=1 \quad \text{for any } \xi>0, \]
\[ \int_{t_0-\xi}^{t_0+\xi}\delta(t-t_0)f(t)\,dt=f(t_0), \]
\[ a=\kappa T_i-t_i-\xi,\qquad b=\kappa T_i-t_i+\xi, \]
\(t_i\) is the initial phase of the sequence of \(\delta\)-pulses with period \(T_i\),
\(K\) is an integer \((1,2,\ldots,M_i)\),
\(M_i\) is the number of pulses in the \(\delta\)-sequence with number \(i\).
This means that, under line-by-line scanning, the defects can be modeled by a one-dimensional signal representing a sum of the form
\[ u(t_i)=\sum_{i=1}^{N}\sum_{\kappa=1}^{M_i} f(t)\int_a^b \delta(t-\kappa T_i-t_i)\,dt . \]
Any “waviness” of the contour leads to modulation
\[ z(t_i)=\sum_{\kappa=1}^{M_i}\int_a^b f(t)\delta(t-\kappa T_i+f_i(t)-t_i)\,dt, \]
which, for two-tone images, is expressed as
\[ u(t_i)=\sum_{i=1}^{N}\sum_{\kappa=1}^{M_i}\int_a^b f(t)\delta(t-\kappa T_i+f_i(t)-t_i)\,dt, \]
and, taking noise outliers into account,
\[ F(t_i)=u(t_i)+\sum_j f(t)\int_c^d \delta(t-t_j)\,dt, \]
where
\[ c=t_j-\xi,\qquad d=t_j+\xi . \]
Analyzing the considerations presented in terms of the posed problem, one can determine the block diagram of the intermediate transformation \(a'\) (primary filtering). From the output of the photoelectric converter the signal is fed to a bank of matched filters covering the range of useful signals. The useful signals and interferences that have entered the filter passband are fed to a decision device, which cleans the signal of interferences whose level is below the controllable constant component of the decision threshold, found from the condition of minimizing the average risk. The signals and the remaining part of the interferences are fed through an approximation block to the second filtering stage, which uses the phase information of the formed \(\delta\)-pulses.
In conclusion, we note that the validity of the considerations set forth here, in terms of posing the problem of determining the structure of the automaton, has been confirmed experimentally.
REFERENCES
- V. I. Gorbunov, B. N. Epifantsev. On the improvement of nondestructive testing systems. Izv. TPI (in press).
- S. V. Rumyantsev. Radiation Defectoscopy. Atomizdat, Moscow, 1968.
- I. I. Tsukerman. On the introduction of information into the brain and into a computer. In: Information and Cybernetics, Sov. Radio, 1967.