- Email: [email protected]
Teseo: A vectoriser of historical seismograms
ARTICLE IN PRESS
Computers & Geosciences 31 (2005) 1277–1285 www.elsevier.com/locate/cageo
Teseo: A vectoriser of historical seismograms$ Stefano Pintore, Matteo Quintiliani, Diego Franceschi Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy Received 15 October 2004; accepted 1 April 2005
Abstract Historical seismograms contain a rich harvest of information useful for the study of past earthquakes. It is necessary to extract this information by digitising the analogue records if modern analysis is required. Teseo has been developed for quick and accurate digitisation of seismogram traces from raster files, introducing a vectorisation step based on piecewise cubic Be´zier curves. The vectoriser can handle greyscale images stored in a suitable file format and it offers three concurrent vectorisation methods: manual, automatic by colour selection, and automatic by neural networks. The software that implements the methods described is distributed with open source license. r 2005 Published by Elsevier Ltd. Keywords: Historical seismogram; Vectorisation; Digitisation
1. Introduction The use of modern techniques to recover seismological information contained in historical seismograms can supply additional knowledge on past seismicity and ongoing tectonic processes. This important goal is widely acknowledged (Kanamori, 1988; Stein et al., 1988), but it presents some difficulties, since data recorded by early instruments on paper media must be properly processed to obtain numerical data usable for modern analysis. The Sismos Project1 is aimed at preserving the heritage of historical seismograms owned by all the Italian observatories. For this purpose, an acquisition of the raster images from approximately one million recordings is planned. Data access will be ensured through a dedicated web portal. Digitisation will be performed on a number of the most important $
Source code is available from server at http://sismos.ingv.it
Corresponding author. Tel.: +39 06 51860671;
fax: +39 06 5041303. E-mail address: [email protected] (M. Quintiliani). 1 Istituto Nazionale di Geofisica e Vulcanologia. 0098-3004/$ - see front matter r 2005 Published by Elsevier Ltd. doi:10.1016/j.cageo.2005.04.001
events. All this requires a fast and accurate digitisation procedure that is usable on images of large dimensions and independent of the original paper type or recording instrument. In the digitisation process, seismograms can be classified based on the similarity of the raster images used. Common problems encountered in automatic digitisation of seismic traces are well described by Trifunac et al. (1999). Other recent work on seismogram digitisation includes that by Samardjieva et al. (1998), who created a digital database for historical earthquakes using a manual digitisation process whereby the original records were enlarged by a projector on a screen. TevesCosta et al. (1999) presented an example of the recovery of source parameters from historical records and developed a semi-automatic method using commercial software on images of 200 dpi resolution. Baskoutas et al. (2000) digitised 1852 seismograms obtained from the Mainka and Wiechert seismographs in the National Observatory of Athens during the period 1911–1960. They developed software usable on black and white images with 1600, or 500 dpi if the image was too large.
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The digitisation procedure usually involves: (i) extraction of the sample sequence directly from the image, in a manual or automatic way, (ii) correct mapping from the ðx; yÞ image coordinates to the amplitude and time of the samples. We present here a different method that relies on an intermediate parametric vectorial representation of the seismogram trace using piecewise cubic Be´zier curves. To implement this method, a software tool named Teseo has been developed. It offers one manual and two automatic modes of operation. The first automatic mode is analytical and the second is based on neural networks.
Fig. 1. Example of seismogram curvature derived from use of a tracing needle mounted on a finite-length pivoting arm.
2. Data Analogue seismograms recorded on paper result from the response of a seismometer and a recording system to ground motion. The main classes of traditional seismometers include short-, intermediate- and long-period instruments. The recording system for analogue instruments is characterised by several mechanisms, the most important being the kind of support used (smoked, photographic, thermal), the type of tracing device (needle, light beam) and the paper speed. The digitisation of traces contained in such seismograms is the final objective. The Sismos Project has set scanning specifications to ensure that all information contained in the paper seismograms are preserved, while considering both the characteristics of the support and the expected digital output. To this end, it has been found that the raster images must be acquired using very high-quality A0 scanners, at a resolution of 1016 dpi with 256 grey levels for the raster images containing the earthquake traces. The standard format used to store these images is plain TIFF2 (Adobe Developers Association, 1992). This choice requires approximately 400–500 MB for a sheet of paper measuring 120 cm 40 cm and it guarantees integrity and consistency of the information contained in the raster image. Teseo software is designed to offer a tool for vectorisation of all classes of seismograms acquired by the Sismos project. Obvious difficulties, however, follow from the different types of seismogram objects for the vectorisation. Most problems are related to the quality of the trace recorded on the paper. It is possible to delimit various main blocks of problems or cases. Fig. 1 shows a seismogram produced by a Wiechert seismograph on smoked paper. The curvature of the trace resulting from the needle mechanism is evident. In 2
Tagged Image File Format.
Fig. 2. Example of a seismogram trace crossing on a photographic record. Trace crossing occurs in any type of drum recording medium.
this case, there is a loss of correspondence between the abscissa and time, because the trace at its maximum amplitude is somewhat ahead of the zero crossing at the same time. This justifies the use of a parametric representation of the seismogram trace. Crossing traces as shown in Fig. 2 are another problem when digitising. In fact, digitisation systems based only on the determination of trace colour are not able to distinguish between points belonging to one trace rather than the another. Sometimes this task can be very difficult, even for a skilled seismologist. When digitising, it is also important to consider the thickness of the traces in relation to the frequency of the signal. An algorithm calculating the weighted mean of
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the trace shown in Fig. 3 will easily miss the true trace and will return a smoother, incorrect trace. The example in Fig. 4 shows a blurred trace. In this case it is hard to determine the middle of the trace because of the overall lack of contrast. All the above types of problem make it difficult to find the best general solution and suggest that the use of artificial intelligence techniques can be of value, in addition to standard image elaboration. This document describes the operating mode and the strategies adopted within the Teseo vectoriser in order to solve the problems outlined here.
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3. Teseo vectoriser The standard seismogram digitisation process is shown in a flow chart in Fig. 5. The Image process produces a pixel coordinate sequence for the trace (rough digital) and the Correction process transforms it in a time domain to a seismic signal (final digital). This latter stage needs some instrumental parameters, either known a priori or obtainable from the seismogram image. Within the Image process, we have introduced an intermediate step that produces a vectorial representation of the seismic trace on the image (Fig. 6). Vectorial representation is more compact than the pixel coordinate sequence and allows more interactivity with the graphic software. One of the most important vectorial representations in computer graphics consists of Be´zier, 1974 curves. They can be defined as follows. Given n þ 1 points Pi , the Bernstein form of the Be´zier curve is PðtÞ ¼
n X
Bni ðtÞPi ,
i¼0
Bni ðtÞ ¼
n ti ð1 tÞni . i
For four points Fig. 3. Example of seismogram traces recorded on a shortperiod instrument. Digitisation of this type of seismogram record is extremely cumbersome and difficult.
PðtÞ ¼
3 X
B3i ðtÞPi
i¼0
which gives the cubic Be´zier curve PðtÞ ¼ P0 ð1 tÞ3 þ 3P1 tð1 tÞ2 þ 3P2 t2 ð1 tÞ þ P3 t3
for 0ptp1.
Fig. 5. Flow diagram for standard digitisation process.
Fig. 4. Example of an out-of-focus photographic record trace.
Fig. 6. Flow diagram of Teseo image process. Note that this approach introduces vector transformation phase before obtaining rough digital output.
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3.1. Manual trace vectorisation
Fig. 7. Example of a cubic Be´zier curve with its anchor and control points.
A graphical representation of a cubic Be´zier curve is shown in Fig. 7. P0 and P3 are named anchor points, and P1 and P2 are named control points. The seismic trace can be represented by a piecewise cubic Be´zier curve, that is, a sequence of cubic Be´zier segments. This vectorial description of the curve requires the definition of four points for each Be´zier curve. It also allows an unlimited level of detail in resampling. Using Be´zier curves to vectorise images is quite common, e.g. for shape description (Cinque et al., 1998) or for vectorisation of hand-drawn images (Chang and Yan, 1998). A very common problem in seismogram images is the lack of a trace, but Be´zier curves are well suited to resolve this issue (Atzori and De Natale, 2000). Usually the raster seismogram needs some enhancement, such as contrast adjustment or more sophisticated filtering. For these reasons, vectorisation of seismograms needs a software tool able to manage large seismogram images, to apply the desired raster filter for enhancement, and to interactively represent cubic Be´zier curves. We have chosen a powerful graphics software developed by Spencer Kimball, Peter Mattis et al. named GIMP3 (Kylander and Kylander, 1999; Bunks, 2000). It can manage images of any dimension and is potentially limited only by the hardware available. Furthermore, it already includes a cubic Be´zier curve representation. We have developed Teseo, a plug-in for GIMP 1.2, that interacts with it by carrying out seismic trace vectorisation, resampling and saving of the rough digital trace. The Teseo vectoriser system has been designed to offer several methods to vectorise seismic traces on a raster image while featuring different levels of automation. The trace vectorisation methods implemented are manual, automatic by colour selection, and automatic based on neural networks. To generate these neural networks, we have developed two programs: another GIMP plug-in named neuronexamples and a stand-alone program named neuronlearn. All programs are compiled for the Linux operating system. 3
GNU Image Manipulation Program.
Most simple vectorisation methods are manual: the user picks out a sequence of points connected by straight lines or spline curves. In the manual mode of Teseo, the user can create the curve directly on the seismogram image using the mouse pointer to reproduce the shape of the trace by choosing the position of the control and the anchor points. Fig. 8 shows a vectorisation carried out manually by choosing a few Be´zier points, but covering a large part of the trace. Unfortunately, the accuracy of the result is dependent entirely on the skill of the operator and, if this work is extended through long digitising sessions, the overall quality tends to decrease. Otherwise, Teseo offers some vectorising modalities whereby the operator has only a controlling function on the results obtained from the automatic procedure adopted. 3.2. Automatic trace vectorisation The automatic method determines a polygonal line or a piecewise cubic Be´zier curve that starts from the last point of a pre-existing curve. The latter is the output of either the manual or the automatic method applied previously. In this mode, the operator can either accept, modify or reject the solution suggested by the automatic method. What effectively takes place is an iterative procedure, whereby at each single iteration step the next point is found by submitting to an ‘‘oracle’’ a rectangular portion of the image centred at the current
Fig. 8. Example of manual vectorisation using Teseo. Note that with a few Be´zier points it is possible to represent a long trace segment.
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point and the information regarding the closest previous points. The operator can either set automatic Be´zier fitting of the point sequence produced by the last n iterations, or refine the whole final digital trace at the end, as described in Section 3.5. Two different algorithms are presented here to evaluate the next digitisation point. The first is based on colour selection, while the second is based on neural networks. 3.3. Colour trace weighted mean vectorisation Vectorisation based on the colour weighted mean applies to greyscale images, where the values of the pixel colour are between Black, the lowermost bound value, and White, the uppermost bound value. We define a pixel array as a linear array in which each item contains a value for pixel colour. In Fig. 9(A), the two pixel arrays used in the following algorithm are shown. Given the parameters I, a, b, ðxk ; yk Þ, s, G, a, b, where 0osp b2:
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(4) Let w be the weight function of item i belonging to a pixel array V: wðV ; i; GÞ ¼
ðWhite jV ½i GjÞa ðj jV2 j ijÞb
ðaX0; bX0Þ,
where the numerator represents the degree of similarity between colour V ½i and the base colour G biased by the a exponent, and the denominator is the distance between i and the central item of V biased by b. (5) Let F be the weighted mean function of a pixel array V and the base colour G PjVj iwðV ; i; GÞ F ðV ; GÞ ¼ Pi¼1 . jV j i¼1 wðV ; i; GÞ (6) The algorithm calculates the next point ðxkþ1 ; ykþ1 Þ in the following way: (a) Let Bs be the pixel array corresponding to the column at abscissa xs ¼ xk þ s, with height a and centred in yk ; then, ykþ1 ¼ F ðBs ; GÞ.
(1) Let I be the seismogram raster image. (2) Let xk ; yk be the coordinates of the starting point. (3) Let G 2 fBlack; Whiteg be the base colour of the trace.
(b) Let At be the pixel array extracted from the row ykþ1 , with width ðb 2sÞ and centred in xs ; then, xkþ1 ¼ FðAt ; GÞ. The parameters a, b and s depend on the thickness and slope of the trace, and the user can set them at run-time. Good results occur when using b values of one or two times the trace thickness, abb and s ¼ 1. a and b were experimentally determined and are hard-coded with values a ¼ 4 and b ¼ 14. 3.4. Neural network vectorisation
Fig. 9. Input and output specifications of automatic methods. Both methods share following parameters: rectangular portion of the image, with height a and width b, and centre at current point ðxk ; yk Þ. A schema of application of vectorisation algorithm based on colour trace is shown in panel (A). Next point ðxkþ1 ; ykþ1 Þ is found through a weighted mean function that is applied first to pixel array Bs , and then to pixel array At . Panel (B) shows input data for neural network execution: rectangular ‘‘view’’ R of the image and three points ðxk2 ; yk2 Þ; ðxk1 ; yk1 Þ; ðxk ; yk Þ calculated previously. Neural network seeks next point ðxkþ1 ; ykþ1 Þ. Note that ðxk ; yk Þ is on a trace crossing and next points calculated by two algorithms are different. The first algorithm does not consider previous points and returns the same result whatever they were. The second one, a trained neural network gives the correct next point.
The input of the following algorithm based on neural networks is shown in Fig. 9(B). Given the parameters I, a, b, ðxk ; yk Þ, ðxk2 ; yk2 Þ, ðxk1 ; yk1 Þ, the algorithm calculates the next point ðxkþ1 ; ykþ1 Þ in the following way: (1) Let I be the seismogram raster image. (2) Let R be the bi-dimensional pixel array extracted from the rectangular portion in the image I, with height a and width b, centred at the current point (xk ; yk ). (3) Let (xkn ; ykn ) be the nth previous point coordinates. (4) Neural network execution then computes the next point: ðxkþ1 ; ykþ1 Þ ¼ NðR; ðxk2 ; yk2 Þ; ðxk1 ; yk1 ÞÞ.
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Previous studies related to image recognition have suggested the use of neural networks. A review of important cases can be found in Egmont-Petersen et al. (2002). For example, there is some affinity between vectorising seismograms and the problem of autonomous land vehicles tackled by the ALVINN project Pomerleau (1989), or the robot end-effector of Baek et al. (1999). According to these problems, the type of neural network chosen is multi-layered with two hidden layers, the neurons are all connected and feed-forward. Each neural network is characterised by its input and output. The input information is logically made up of two parts: the first is the rectangular portion of the image, which represents the field of vision, and the second part is the two preceding points on the trace. The rectangle shown in Fig. 9(B) represents the ‘‘view’’ of the neural network; the two points that precede the centre of the rectangle are extremely useful for determining the direction in which to advance if crossover or overlap of traces occurs. 3.4.1. Neural network generation The additional program neuronlearn allows the generation and training of neural networks through a user friendly graphics interface. The learning algorithm used by supervised training is Error Back Propagation, which is extensively described in the literature (Khanna, 1990; Mitchell, 1997). The GIMP plug-in neuronexamples allows the creation of examples that can be undertaken by either using real seismic traces from the seismogram images, or by drawing new synthetic wave images that have the desired characteristics. Also note that before building the training set it is possible to modify each raster image using appropriate filters, for example, by highlighting the background or using edge detection. The examples are created using vectorial information from the traces, which can be the result of manual vectorisation or the corrected result from a neural network. Two essential characteristics of examples that must be defined for each neural network are the dimensions of the field vision and the step used to fix the average distance from one point to the next. In spite of the ease of creation of a neural network, the user must be aware that increasing the network dimensions and the number of examples will result in an increase in learning time, but not necessarily in improved performance. Some suggestions for these choices can be found in (Mitchell, 1997; Masters, 1993). 3.5. Refinement of the output The use of several types of vectorisation procedures in a unique trace will result in a path consisting of a mixed sequence of Be´zier curves and a succession of unevenly spaced samples. For this purpose, the operator can fit the sequence of samples with piecewise cubic Be´zier
curves using the Be´zier fitting algorithm implemented in Teseo. In general, the objective of the curve fitting algorithm is to use a minimum number of cubic curve pieces to approximate the data with minimum distortion. There are several ways to identify the anchor and control points reported in the literature (Shao and Zhou, 1996; Huang and Tai, 2000; Pavlidis, 1983; Plass and Stone, 1983; Piegl, 1987; Schneider, 1990). Our algorithm selects the anchor points at the maximum and minimum of the sample sequence. The sample sequence between a maximum and minimum is fitted to a single cubic Be´zier curve, thus leading to the control points. For fitting, we have used some least-squares fitting functions from Numerical Recipes in C (Press et al., 1992). A single piecewise cubic Be´zier curve is then created, sequencing the various segments. It is still possible to interactively alter the curve once the operation has been completed, because the curve is already in vectorial format. Once the desired results have been achieved, it is possible to resample the curve and the sequence of samples can be saved in various standard formats, such as DXF4 polylines (Autodesk, 1992), SAC5 (Goldstein et al., 2003), or in plain ASCII.
4. Vectorising with Teseo In this section, some examples of vectorisation with the various automatic systems illustrated here are shown. Fig. 10(A) shows an example of automatic vectorisation of a smoked paper seismogram image. This image presents little curvature distortion and some crossings. Vectorisation was successfully obtained using the weighted mean colour algorithm. Fig. 10(B) shows the vectorisation during the first stage, in which many Be´zier segments were found. The resulting Be´zier path after least-squares fitting is shown in Fig. 10(C). The last example is shown in Fig. 11(A), for which vectorisation was carried out using a neural network. The original photographic record is badly focused and some crossings are present. In Fig. 11(B) the vectorisation was post-processed by applying least-squares fitting.
5. Comments and conclusions A vectorisation method for seismic records is presented, together with the software used. The vectorisation output is a piecewise cubic Be´zier curve that can be resampled. A feature of Teseo is that it adopts both higher dpi images and long greyscale depth. Two 4
Drawing Interchange File Format. Seismic Analysis Code.
5
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Fig. 10. Example of trace colour weighted mean vectorisation: Panel (A) shows algorithm results for a smoked paper seismogram image, and panel (B) shows in detail the Be´zier segments found. Panel (C) shows piecewise Be´zier curve that resulted from least-squares fitting.
characteristics distinguish this system from previous work. A manual and two semi-automatic vectorisation methods have been described. Manual vectorisation is accurate but time-consuming. The colour trace algorithm is well suited in many instances, but needs human intervention for critical points such as the crossing of traces. Neural networks have displayed fair results in a few cases, and this warrants further development of the technique. For example, future extension of the Teseo vectoriser could be a complex architecture in which the choice of neural networks takes place automatically while exploiting another neural network, or through a decision tree located at a hierarchically superior level. More features are currently under development: a Be´zier fitting procedure optimisation, as suggested in Shao and
Zhou (1996) and Huang and Tai (2000), and integration of the correction phase to complete the digitisation process. These and other improvements can be made by anyone interested, because Teseo is distributed with an open-source license while the use of the C routine in Numeral Recipes is under license to Press et al. (1992). Teseo software and its updates are available on the Sismos site at http://sismos.ingv.it.
Acknowledgements The authors would like to thank A. Michelini for his useful and constructive suggestions and for his continuous encouragement. They are also grateful to B. De
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Fig. 11. Example of neural network vectorisation shown on a poorly focused photographic seismogram. In panel (A) sample sequence output of repeated neural network execution, and in panel (B) Be´zier fitting result.
Simoni for giving them the opportunity to start this work. Further thanks are addressed to B. Palombo, who uses Teseo for her studies, and to L. Arcoraci, who was a dedicated beta tester.
References Adobe Developers Association, 1992. TIFF 6.0. Adobe Systems Incorporated—1585 Charleston Road—P.O. Box 7900— Mountain View, CA 94039-7900, URL ftp://ftp.adobe.com/ pub/adobe/DeveloperSupport/TechNotes/PDFfiles. Atzori, L., De Natale, F.G.B., 2000. Reconstruction of missing or occluded contour segments using Bezie´r interpolations. Signal Processing 80 (8), 1691–1694. Autodesk, 1992. AutoCAD Release 12 DXF Format. Adobe Systems Incorporated—1585 Charleston Road—P.O. Box
7900—Mountain View, CA 94039-7900, Drawing Interchange and File Formats Release 12. Baek, S., Park, D., Cho, J., Lee, Y., 1999. A robot endeffector tracking system based on feedforward neural networks. Robotics and Autonomous Systems 28 (1), 43–52. Baskoutas, I.G., Kalogeras, I.S., Kourouzidis, M., Panopoulou, G., 2000. A modern technique for the retrieval and processing of historical seismograms in Greece. Natural Hazards 21 (1), 55–64. Be´zier, P.E., 1974. Mathematical and practical possibilities of unisurf. In: Barnhill, R.E., Riesenfeld, R.F. (Eds.), Computer Aided Geometric Design. Academic Press, New York, pp. 127–152. Bunks, C., 2000. Grokking the GIMP. New Riders Publishing, Thousand Oaks, CA 352pp. Chang, H., Yan, H., 1998. Vectorization of hand-drawn image using piecewise cubic Be´zier curves fitting. Pattern Recognition 31 (11), 1747–1755. Cinque, L., Levialdi, S., Malizia, A., 1998. Shape description using cubic polynomial Bezie´r curves. Pattern Recognition Letters 19 (9), 821–828. Egmont-Petersen, M., de Ridder, D., Handels, H., 2002. Image processing with neural networks-a review. Pattern Recognition 35 (10), 2279–2301. Goldstein, P., Dodge, D., Firpo, M., 2003. SAC2000: signal processing and analysis tools for seismologists and engineers. In: Lee, W., Kanamori, H., Jennings, P., Kisslinger, C. (Eds.), International Handbook of Earthquake & Engineering Seismology, Part B. Academic Press, New York, pp. 1613–1614. Huang, M., Tai, C., 2000. The pre-processing of data points for curve fitting in reverse engineering. International Journal of Advanced Manufacturing Technology 16, 635–642. Kanamori, H., 1988. Importance of historical seismograms for geophysical research. In: Lee, W.H.K., Meyers, H., Shimazaki, K. (Eds.), Historical Seismograms and Earthquakes of the World. Academic Press, Inc., San Diego, CA, pp. 16–36. Khanna, T., 1990. Foundations of Neural Networks. AddisonWesley Longman Publishing, Co., Inc., Boston, MA 196pp. Kylander, O., Kylander, K., 1999. Gimp the Official Handbook with Cdrom. Coriolis Value 895pp. Masters, T., 1993. Practical Neural Network Recipes in C++. Academic Press Professional, Inc., San Diego, CA 493pp. Mitchell, T., 1997. Machine Learning. McGraw Hill, New York 432pp. Pavlidis, T., 1983. Curve fitting with conic splines. ACM Transactions on Graphics 2 (1), 1–31. Piegl, L., 1987. Interactive data interpolation by rational Be´zier curves. IEEE Computer Graphics and Applications 7, 45–57. Plass, M., Stone, M., 1983. Curve-fitting with piecewise parametric cubics. Computer Graphics 17, 229–239. Pomerleau, D., 1989. ALVINN: an autonomous land vehicle in a neural network. In: Tovretzky, D.S. (Ed.), Advances in Neural Information Processing Systems 1. Morgan Kaufmann Publishers Inc., San Francisco, CA, pp. 305–313. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA 1035pp.
ARTICLE IN PRESS S. Pintore et al. / Computers & Geosciences 31 (2005) 1277–1285 Samardjieva, E., Payo, G., Badal, J., Lopez, C., 1998. Creation of a digital database for XXth century historical earthquakes occurred in the Iberian area. Pure and Applied Geophysics 152, 139–163. Schneider, P.J., 1990. An algorithm for automatically fitting digitized curves. In: Glassner, A.S. (Ed.), Graphics Gems. Academic Press, Inc., San Diego, CA, pp. 612–625. Shao, L., Zhou, H., 1996. Curve fitting with Be´zier cubics. Graphical Models and Image Processing 58 (3), 223–232. Stein, S., Okal, E.A., Wiens, D.A., 1988. Application of modern techniques to analysis of historical earthquakes. In: Lee,
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W.H.K., Meyers, H., Shimazaki, K. (Eds.), Historical Seismograms and Earthquakes of the World. Academic Press, Inc., San Diego, CA, pp. 85–104. Teves-Costa, P., Borges, J.F., Rio, I., Ribeiro, R., Marreiros, C., 1999. Source parameters of old earthquakes: semiautomatic digitization of analog records and seismic moment assessment. Natural Hazards 19, 205–220. Trifunac, M.D., Lee, V., Todorovska, M., 1999. Common problems in automatic digitization of strong motion accelerograms. Soil Dynamics and Earthquake Engineering 18 (7), 519–530.
Computers & Geosciences 31 (2005) 1277–1285 www.elsevier.com/locate/cageo
Teseo: A vectoriser of historical seismograms$ Stefano Pintore, Matteo Quintiliani, Diego Franceschi Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy Received 15 October 2004; accepted 1 April 2005
Abstract Historical seismograms contain a rich harvest of information useful for the study of past earthquakes. It is necessary to extract this information by digitising the analogue records if modern analysis is required. Teseo has been developed for quick and accurate digitisation of seismogram traces from raster files, introducing a vectorisation step based on piecewise cubic Be´zier curves. The vectoriser can handle greyscale images stored in a suitable file format and it offers three concurrent vectorisation methods: manual, automatic by colour selection, and automatic by neural networks. The software that implements the methods described is distributed with open source license. r 2005 Published by Elsevier Ltd. Keywords: Historical seismogram; Vectorisation; Digitisation
1. Introduction The use of modern techniques to recover seismological information contained in historical seismograms can supply additional knowledge on past seismicity and ongoing tectonic processes. This important goal is widely acknowledged (Kanamori, 1988; Stein et al., 1988), but it presents some difficulties, since data recorded by early instruments on paper media must be properly processed to obtain numerical data usable for modern analysis. The Sismos Project1 is aimed at preserving the heritage of historical seismograms owned by all the Italian observatories. For this purpose, an acquisition of the raster images from approximately one million recordings is planned. Data access will be ensured through a dedicated web portal. Digitisation will be performed on a number of the most important $
Source code is available from server at http://sismos.ingv.it
Corresponding author. Tel.: +39 06 51860671;
fax: +39 06 5041303. E-mail address: [email protected] (M. Quintiliani). 1 Istituto Nazionale di Geofisica e Vulcanologia. 0098-3004/$ - see front matter r 2005 Published by Elsevier Ltd. doi:10.1016/j.cageo.2005.04.001
events. All this requires a fast and accurate digitisation procedure that is usable on images of large dimensions and independent of the original paper type or recording instrument. In the digitisation process, seismograms can be classified based on the similarity of the raster images used. Common problems encountered in automatic digitisation of seismic traces are well described by Trifunac et al. (1999). Other recent work on seismogram digitisation includes that by Samardjieva et al. (1998), who created a digital database for historical earthquakes using a manual digitisation process whereby the original records were enlarged by a projector on a screen. TevesCosta et al. (1999) presented an example of the recovery of source parameters from historical records and developed a semi-automatic method using commercial software on images of 200 dpi resolution. Baskoutas et al. (2000) digitised 1852 seismograms obtained from the Mainka and Wiechert seismographs in the National Observatory of Athens during the period 1911–1960. They developed software usable on black and white images with 1600, or 500 dpi if the image was too large.
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The digitisation procedure usually involves: (i) extraction of the sample sequence directly from the image, in a manual or automatic way, (ii) correct mapping from the ðx; yÞ image coordinates to the amplitude and time of the samples. We present here a different method that relies on an intermediate parametric vectorial representation of the seismogram trace using piecewise cubic Be´zier curves. To implement this method, a software tool named Teseo has been developed. It offers one manual and two automatic modes of operation. The first automatic mode is analytical and the second is based on neural networks.
Fig. 1. Example of seismogram curvature derived from use of a tracing needle mounted on a finite-length pivoting arm.
2. Data Analogue seismograms recorded on paper result from the response of a seismometer and a recording system to ground motion. The main classes of traditional seismometers include short-, intermediate- and long-period instruments. The recording system for analogue instruments is characterised by several mechanisms, the most important being the kind of support used (smoked, photographic, thermal), the type of tracing device (needle, light beam) and the paper speed. The digitisation of traces contained in such seismograms is the final objective. The Sismos Project has set scanning specifications to ensure that all information contained in the paper seismograms are preserved, while considering both the characteristics of the support and the expected digital output. To this end, it has been found that the raster images must be acquired using very high-quality A0 scanners, at a resolution of 1016 dpi with 256 grey levels for the raster images containing the earthquake traces. The standard format used to store these images is plain TIFF2 (Adobe Developers Association, 1992). This choice requires approximately 400–500 MB for a sheet of paper measuring 120 cm 40 cm and it guarantees integrity and consistency of the information contained in the raster image. Teseo software is designed to offer a tool for vectorisation of all classes of seismograms acquired by the Sismos project. Obvious difficulties, however, follow from the different types of seismogram objects for the vectorisation. Most problems are related to the quality of the trace recorded on the paper. It is possible to delimit various main blocks of problems or cases. Fig. 1 shows a seismogram produced by a Wiechert seismograph on smoked paper. The curvature of the trace resulting from the needle mechanism is evident. In 2
Tagged Image File Format.
Fig. 2. Example of a seismogram trace crossing on a photographic record. Trace crossing occurs in any type of drum recording medium.
this case, there is a loss of correspondence between the abscissa and time, because the trace at its maximum amplitude is somewhat ahead of the zero crossing at the same time. This justifies the use of a parametric representation of the seismogram trace. Crossing traces as shown in Fig. 2 are another problem when digitising. In fact, digitisation systems based only on the determination of trace colour are not able to distinguish between points belonging to one trace rather than the another. Sometimes this task can be very difficult, even for a skilled seismologist. When digitising, it is also important to consider the thickness of the traces in relation to the frequency of the signal. An algorithm calculating the weighted mean of
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the trace shown in Fig. 3 will easily miss the true trace and will return a smoother, incorrect trace. The example in Fig. 4 shows a blurred trace. In this case it is hard to determine the middle of the trace because of the overall lack of contrast. All the above types of problem make it difficult to find the best general solution and suggest that the use of artificial intelligence techniques can be of value, in addition to standard image elaboration. This document describes the operating mode and the strategies adopted within the Teseo vectoriser in order to solve the problems outlined here.
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3. Teseo vectoriser The standard seismogram digitisation process is shown in a flow chart in Fig. 5. The Image process produces a pixel coordinate sequence for the trace (rough digital) and the Correction process transforms it in a time domain to a seismic signal (final digital). This latter stage needs some instrumental parameters, either known a priori or obtainable from the seismogram image. Within the Image process, we have introduced an intermediate step that produces a vectorial representation of the seismic trace on the image (Fig. 6). Vectorial representation is more compact than the pixel coordinate sequence and allows more interactivity with the graphic software. One of the most important vectorial representations in computer graphics consists of Be´zier, 1974 curves. They can be defined as follows. Given n þ 1 points Pi , the Bernstein form of the Be´zier curve is PðtÞ ¼
n X
Bni ðtÞPi ,
i¼0
Bni ðtÞ ¼
n ti ð1 tÞni . i
For four points Fig. 3. Example of seismogram traces recorded on a shortperiod instrument. Digitisation of this type of seismogram record is extremely cumbersome and difficult.
PðtÞ ¼
3 X
B3i ðtÞPi
i¼0
which gives the cubic Be´zier curve PðtÞ ¼ P0 ð1 tÞ3 þ 3P1 tð1 tÞ2 þ 3P2 t2 ð1 tÞ þ P3 t3
for 0ptp1.
Fig. 5. Flow diagram for standard digitisation process.
Fig. 4. Example of an out-of-focus photographic record trace.
Fig. 6. Flow diagram of Teseo image process. Note that this approach introduces vector transformation phase before obtaining rough digital output.
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3.1. Manual trace vectorisation
Fig. 7. Example of a cubic Be´zier curve with its anchor and control points.
A graphical representation of a cubic Be´zier curve is shown in Fig. 7. P0 and P3 are named anchor points, and P1 and P2 are named control points. The seismic trace can be represented by a piecewise cubic Be´zier curve, that is, a sequence of cubic Be´zier segments. This vectorial description of the curve requires the definition of four points for each Be´zier curve. It also allows an unlimited level of detail in resampling. Using Be´zier curves to vectorise images is quite common, e.g. for shape description (Cinque et al., 1998) or for vectorisation of hand-drawn images (Chang and Yan, 1998). A very common problem in seismogram images is the lack of a trace, but Be´zier curves are well suited to resolve this issue (Atzori and De Natale, 2000). Usually the raster seismogram needs some enhancement, such as contrast adjustment or more sophisticated filtering. For these reasons, vectorisation of seismograms needs a software tool able to manage large seismogram images, to apply the desired raster filter for enhancement, and to interactively represent cubic Be´zier curves. We have chosen a powerful graphics software developed by Spencer Kimball, Peter Mattis et al. named GIMP3 (Kylander and Kylander, 1999; Bunks, 2000). It can manage images of any dimension and is potentially limited only by the hardware available. Furthermore, it already includes a cubic Be´zier curve representation. We have developed Teseo, a plug-in for GIMP 1.2, that interacts with it by carrying out seismic trace vectorisation, resampling and saving of the rough digital trace. The Teseo vectoriser system has been designed to offer several methods to vectorise seismic traces on a raster image while featuring different levels of automation. The trace vectorisation methods implemented are manual, automatic by colour selection, and automatic based on neural networks. To generate these neural networks, we have developed two programs: another GIMP plug-in named neuronexamples and a stand-alone program named neuronlearn. All programs are compiled for the Linux operating system. 3
GNU Image Manipulation Program.
Most simple vectorisation methods are manual: the user picks out a sequence of points connected by straight lines or spline curves. In the manual mode of Teseo, the user can create the curve directly on the seismogram image using the mouse pointer to reproduce the shape of the trace by choosing the position of the control and the anchor points. Fig. 8 shows a vectorisation carried out manually by choosing a few Be´zier points, but covering a large part of the trace. Unfortunately, the accuracy of the result is dependent entirely on the skill of the operator and, if this work is extended through long digitising sessions, the overall quality tends to decrease. Otherwise, Teseo offers some vectorising modalities whereby the operator has only a controlling function on the results obtained from the automatic procedure adopted. 3.2. Automatic trace vectorisation The automatic method determines a polygonal line or a piecewise cubic Be´zier curve that starts from the last point of a pre-existing curve. The latter is the output of either the manual or the automatic method applied previously. In this mode, the operator can either accept, modify or reject the solution suggested by the automatic method. What effectively takes place is an iterative procedure, whereby at each single iteration step the next point is found by submitting to an ‘‘oracle’’ a rectangular portion of the image centred at the current
Fig. 8. Example of manual vectorisation using Teseo. Note that with a few Be´zier points it is possible to represent a long trace segment.
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point and the information regarding the closest previous points. The operator can either set automatic Be´zier fitting of the point sequence produced by the last n iterations, or refine the whole final digital trace at the end, as described in Section 3.5. Two different algorithms are presented here to evaluate the next digitisation point. The first is based on colour selection, while the second is based on neural networks. 3.3. Colour trace weighted mean vectorisation Vectorisation based on the colour weighted mean applies to greyscale images, where the values of the pixel colour are between Black, the lowermost bound value, and White, the uppermost bound value. We define a pixel array as a linear array in which each item contains a value for pixel colour. In Fig. 9(A), the two pixel arrays used in the following algorithm are shown. Given the parameters I, a, b, ðxk ; yk Þ, s, G, a, b, where 0osp b2:
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(4) Let w be the weight function of item i belonging to a pixel array V: wðV ; i; GÞ ¼
ðWhite jV ½i GjÞa ðj jV2 j ijÞb
ðaX0; bX0Þ,
where the numerator represents the degree of similarity between colour V ½i and the base colour G biased by the a exponent, and the denominator is the distance between i and the central item of V biased by b. (5) Let F be the weighted mean function of a pixel array V and the base colour G PjVj iwðV ; i; GÞ F ðV ; GÞ ¼ Pi¼1 . jV j i¼1 wðV ; i; GÞ (6) The algorithm calculates the next point ðxkþ1 ; ykþ1 Þ in the following way: (a) Let Bs be the pixel array corresponding to the column at abscissa xs ¼ xk þ s, with height a and centred in yk ; then, ykþ1 ¼ F ðBs ; GÞ.
(1) Let I be the seismogram raster image. (2) Let xk ; yk be the coordinates of the starting point. (3) Let G 2 fBlack; Whiteg be the base colour of the trace.
(b) Let At be the pixel array extracted from the row ykþ1 , with width ðb 2sÞ and centred in xs ; then, xkþ1 ¼ FðAt ; GÞ. The parameters a, b and s depend on the thickness and slope of the trace, and the user can set them at run-time. Good results occur when using b values of one or two times the trace thickness, abb and s ¼ 1. a and b were experimentally determined and are hard-coded with values a ¼ 4 and b ¼ 14. 3.4. Neural network vectorisation
Fig. 9. Input and output specifications of automatic methods. Both methods share following parameters: rectangular portion of the image, with height a and width b, and centre at current point ðxk ; yk Þ. A schema of application of vectorisation algorithm based on colour trace is shown in panel (A). Next point ðxkþ1 ; ykþ1 Þ is found through a weighted mean function that is applied first to pixel array Bs , and then to pixel array At . Panel (B) shows input data for neural network execution: rectangular ‘‘view’’ R of the image and three points ðxk2 ; yk2 Þ; ðxk1 ; yk1 Þ; ðxk ; yk Þ calculated previously. Neural network seeks next point ðxkþ1 ; ykþ1 Þ. Note that ðxk ; yk Þ is on a trace crossing and next points calculated by two algorithms are different. The first algorithm does not consider previous points and returns the same result whatever they were. The second one, a trained neural network gives the correct next point.
The input of the following algorithm based on neural networks is shown in Fig. 9(B). Given the parameters I, a, b, ðxk ; yk Þ, ðxk2 ; yk2 Þ, ðxk1 ; yk1 Þ, the algorithm calculates the next point ðxkþ1 ; ykþ1 Þ in the following way: (1) Let I be the seismogram raster image. (2) Let R be the bi-dimensional pixel array extracted from the rectangular portion in the image I, with height a and width b, centred at the current point (xk ; yk ). (3) Let (xkn ; ykn ) be the nth previous point coordinates. (4) Neural network execution then computes the next point: ðxkþ1 ; ykþ1 Þ ¼ NðR; ðxk2 ; yk2 Þ; ðxk1 ; yk1 ÞÞ.
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Previous studies related to image recognition have suggested the use of neural networks. A review of important cases can be found in Egmont-Petersen et al. (2002). For example, there is some affinity between vectorising seismograms and the problem of autonomous land vehicles tackled by the ALVINN project Pomerleau (1989), or the robot end-effector of Baek et al. (1999). According to these problems, the type of neural network chosen is multi-layered with two hidden layers, the neurons are all connected and feed-forward. Each neural network is characterised by its input and output. The input information is logically made up of two parts: the first is the rectangular portion of the image, which represents the field of vision, and the second part is the two preceding points on the trace. The rectangle shown in Fig. 9(B) represents the ‘‘view’’ of the neural network; the two points that precede the centre of the rectangle are extremely useful for determining the direction in which to advance if crossover or overlap of traces occurs. 3.4.1. Neural network generation The additional program neuronlearn allows the generation and training of neural networks through a user friendly graphics interface. The learning algorithm used by supervised training is Error Back Propagation, which is extensively described in the literature (Khanna, 1990; Mitchell, 1997). The GIMP plug-in neuronexamples allows the creation of examples that can be undertaken by either using real seismic traces from the seismogram images, or by drawing new synthetic wave images that have the desired characteristics. Also note that before building the training set it is possible to modify each raster image using appropriate filters, for example, by highlighting the background or using edge detection. The examples are created using vectorial information from the traces, which can be the result of manual vectorisation or the corrected result from a neural network. Two essential characteristics of examples that must be defined for each neural network are the dimensions of the field vision and the step used to fix the average distance from one point to the next. In spite of the ease of creation of a neural network, the user must be aware that increasing the network dimensions and the number of examples will result in an increase in learning time, but not necessarily in improved performance. Some suggestions for these choices can be found in (Mitchell, 1997; Masters, 1993). 3.5. Refinement of the output The use of several types of vectorisation procedures in a unique trace will result in a path consisting of a mixed sequence of Be´zier curves and a succession of unevenly spaced samples. For this purpose, the operator can fit the sequence of samples with piecewise cubic Be´zier
curves using the Be´zier fitting algorithm implemented in Teseo. In general, the objective of the curve fitting algorithm is to use a minimum number of cubic curve pieces to approximate the data with minimum distortion. There are several ways to identify the anchor and control points reported in the literature (Shao and Zhou, 1996; Huang and Tai, 2000; Pavlidis, 1983; Plass and Stone, 1983; Piegl, 1987; Schneider, 1990). Our algorithm selects the anchor points at the maximum and minimum of the sample sequence. The sample sequence between a maximum and minimum is fitted to a single cubic Be´zier curve, thus leading to the control points. For fitting, we have used some least-squares fitting functions from Numerical Recipes in C (Press et al., 1992). A single piecewise cubic Be´zier curve is then created, sequencing the various segments. It is still possible to interactively alter the curve once the operation has been completed, because the curve is already in vectorial format. Once the desired results have been achieved, it is possible to resample the curve and the sequence of samples can be saved in various standard formats, such as DXF4 polylines (Autodesk, 1992), SAC5 (Goldstein et al., 2003), or in plain ASCII.
4. Vectorising with Teseo In this section, some examples of vectorisation with the various automatic systems illustrated here are shown. Fig. 10(A) shows an example of automatic vectorisation of a smoked paper seismogram image. This image presents little curvature distortion and some crossings. Vectorisation was successfully obtained using the weighted mean colour algorithm. Fig. 10(B) shows the vectorisation during the first stage, in which many Be´zier segments were found. The resulting Be´zier path after least-squares fitting is shown in Fig. 10(C). The last example is shown in Fig. 11(A), for which vectorisation was carried out using a neural network. The original photographic record is badly focused and some crossings are present. In Fig. 11(B) the vectorisation was post-processed by applying least-squares fitting.
5. Comments and conclusions A vectorisation method for seismic records is presented, together with the software used. The vectorisation output is a piecewise cubic Be´zier curve that can be resampled. A feature of Teseo is that it adopts both higher dpi images and long greyscale depth. Two 4
Drawing Interchange File Format. Seismic Analysis Code.
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Fig. 10. Example of trace colour weighted mean vectorisation: Panel (A) shows algorithm results for a smoked paper seismogram image, and panel (B) shows in detail the Be´zier segments found. Panel (C) shows piecewise Be´zier curve that resulted from least-squares fitting.
characteristics distinguish this system from previous work. A manual and two semi-automatic vectorisation methods have been described. Manual vectorisation is accurate but time-consuming. The colour trace algorithm is well suited in many instances, but needs human intervention for critical points such as the crossing of traces. Neural networks have displayed fair results in a few cases, and this warrants further development of the technique. For example, future extension of the Teseo vectoriser could be a complex architecture in which the choice of neural networks takes place automatically while exploiting another neural network, or through a decision tree located at a hierarchically superior level. More features are currently under development: a Be´zier fitting procedure optimisation, as suggested in Shao and
Zhou (1996) and Huang and Tai (2000), and integration of the correction phase to complete the digitisation process. These and other improvements can be made by anyone interested, because Teseo is distributed with an open-source license while the use of the C routine in Numeral Recipes is under license to Press et al. (1992). Teseo software and its updates are available on the Sismos site at http://sismos.ingv.it.
Acknowledgements The authors would like to thank A. Michelini for his useful and constructive suggestions and for his continuous encouragement. They are also grateful to B. De
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Fig. 11. Example of neural network vectorisation shown on a poorly focused photographic seismogram. In panel (A) sample sequence output of repeated neural network execution, and in panel (B) Be´zier fitting result.
Simoni for giving them the opportunity to start this work. Further thanks are addressed to B. Palombo, who uses Teseo for her studies, and to L. Arcoraci, who was a dedicated beta tester.
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