The Description of Craquelure Patterns

The Description and Classification of Craquelure Spike Bucklow Studies in Conservation, Vol. 44, No. 4. (1999), pp. 233-244. Stable URL: http://links.jstor.org/sici?sici=0039-3630%281999%2944%3A4%3C233%3ATDACOC%3E2.0.CO%3B2-%23 Studies in Conservation is currently published by International Institute for Conservation of Historic and Artistic Works. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/iich.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Mon Sep 24 05:44:01 2007 THE DESCRIPTION AND CLASSIFICATION OF CRAQUELURE Spike Bucklow Summary--The priper provicies the stutisticul context of research to rfejne sinzple ciichotonzous terms ,for the ciescription of crrzquelure. The valiciity of the proposed set of eight descr@tors of cruquelure is established by reference to the results of various clussiJicution tusks. These include the unassisted rissi'qnnr~lentof craqztelure to spec& categories by experienced subjects, the same task undertaken by ine.xperiencet1 subjects assisted by rules, the c.la.rsification of repres~ntationsof craquelure by a neurul network, ant1 61- discriminant anulysis. Tu.o vpe.s qf repres~ntutionare c,or?lpareci;one based upon the Repertory Grid technique and t h other ~ based upon Brzier c.urves. Introduction A recent paper offered a number of simple dichotomous terms for the description of craquelure [I]. It also presented some 'rules of thumb' which related particular descriptive terms to particular technical traditions of painting or art historical categories. Those rules of thumb were derived from a statistical analysis of numerical representations of crack patterns generated by 31 subjects judging 40 crack patterns against a series of scales defined by the dichotomous terms. This paper offers comparisons between various ways of describing craquelure. Two activities, in which individuals classified photographs of crack patterns, are compared. The computational classifications of two types of numerical representation of craquelure are also compared. The human activities both involved the sorting of 40 photographs into four sets of 10 photographs. One group of individuals (including experienced conservators) received no assistance in this task. The other group of individuals (inexperienced students. for example) were guided in their task by the rules of thumb. The computational routines (involving neural networks and discriminant analysis) were applied to two numerical representations of the 40 photographs. One set of numerical representations was derived heuristically from the data provided by 31 subjects from which the rules of thumb were also derived. The other set of numerical representations was generated algorithmically from the data obtained by scanning and digitizing the 40 photographs. Unassisted sorting Subjects were presented with a set of 40 photographs. 10 examples each of: fifteenth century Studies in Conservution 44 (1999) 233-244 Italian panels (It), sixteenth century Flemish panels (Fl), seventeenth century Dutch canvas (Du) and eighteenth century French canvas paintings (Fr). The 4 x 6 inch black and white photographs showed areas of craquelure of between c. 3 x 5 and c. 13 x 20cm. A scale bar was printed in the margin of the photograph to indicate the degree of magnification and orientation with respect to the wood grain or the maximum stretcher dimension. Subjects were asked to sort the 40 photographs into four groups of 10 and identify the groups as Italian, Flemish. Dutch or French. One subject with little experience of the variety of crack patterns had a success rate of little better than chance when sorting the 40 photographs. Ten experienced subjects (eight conservators, a conservation scientist and a curator) sorted the 40 photographs. They were given no assistance in this task and analysis of the groups they created revealed a success rate in classification of between 25 and 35 out of 40. This represents 62.5 to 87.5% correct attribution of crack patterns. The average score was 73.0%. Rule-based sorting Twenty-one subjects with little o r no experience of crack patterns undertook the same task of sorting 40 photographs into four groups of 10. They were assisted in this task by four sets of rules which correlated pattern characteristics and painting categories [I]. Analysis of the groups they created revealed a success rate in classification of between 27 and 32 out of 40. This represents 67.5 to 80.0% correct attribution of crack patterns. The average score was 74.0%. Although the average scores for both sets of subjects were effectively the same, the range of scores was significantly different. The range of scores 233 S. Bucklow among those assisted by rules ( i 6.25%) was half that of those who undertook the task unassisted ( i 12.5%). This indicates that the rules enable a better level of performance than the least successful unassisted subject but d o not allow the novice to emulate the performance of the expert. The 10 subjects who undertook the task unassisted represented a range of experience: one professed a degree of expertise, two had formally studied craquelure as part of their training and the remaining seven had no particular interest in cracks. The time taken to complete the task (c. 3 0 4 5 minutes) was similar for the two groups and the most successful subjects took the least time. In view of the speed of execution and range of results, it is most unlikely that the connoisseurship of craquelure relies upon a mental representation of patterns such as the one developed in this research. Its value lies not in the emulation of connoisseurship, but in demonstrating that complex visual phenomena may be described simply, and that simple descriptions nonetheless possess potential for rigorous analysis in terms of the material structure of paintings. Heuristic representation The rules correlating pattern descriptions with painting categories were derived from the eight numerical scores given to each of the 40 photographs by all 31 subjects. The mean value and standard deviations of these numerical scores were calculated to determine rules such as: that Italian panels usually displayed cracks perpendicular to the grain, cracks in Flemish paintings were parallel to the grain, and that cracks in French paintings had no particular direction, etc. A method known as the Repertory Grid technique was employed to convert perceptual judgments into numerical scores. A critical evaluation of the acquisition stage that generated the data for subsequent analysis is given elsewhere [2], but arteTable 1 Neural network classijcation of one subject's heuristic representution of 40 patterns Neural net It F1 Du Fr as if It as if F1 as if Du as if Fr Total 6 1 3 0 10 0 10 0 0 10 0 1 0 0 7 2 10 3 Group total 1 7 10 6 12 3 9 30140=75.0% facts which may have influenced the statistical evaluation of the data, such as crack patterns due to specific localized damages or stresses, were avoided. Some pre-selection of the data presented to subjects was therefore undertaken. This did not, however, influence the statistical evaluation of the crack patterns as the criteria for selection were independent of the classification categories. The resultant numerical representations of crack patterns were classified directly using a computer. This classification of the heuristic representation enabled a quantitative assessment of the validity of the dichotomous descriptions underlying the rules. Each subject's responses were classified individually using a 'neural network'. In a typical example, the neural network created four groups which can be identified as mainly Italian, mainly Flemish, mainly Dutch and mainly French, containing 6, 12, 13 and 9 crack patterns in total, respectively. As it was not possible to specify to the neural network that there were 10 examples of each category, this task is not exactly equivalent to the human sorting tasks reported above. A summary of the assignments is presented in Table 1. The neural network classified 30 (6 Italian, 10 Flemish, 7 Dutch and 7 French) out of 40 correctly. This represents a success rate of 75.0%, effectively the same as the average performance of the 31 subjects who directly sorted the same 40 photographs. This suggests that the rules given to the 21 less experienced subjects, if not actually responsible for their enhanced level of performance, were at least not inconsistent with their judgments. The set of eight dichotomous descriptions classified by computer and the heuristic rules available to novices both resulted in approximately the same level of discrimination between patterns as the average achieved by experienced conservators. However, the neural network classification of 40 sets of eight numbers, the sorting of 40 photographs by novices using rules and the unassisted sorting of 40 photographs by experts are all equally artificial tasks. To the extent that craquelure has attributive significance, it is judged in terms of the conformity of an individual example to a class of examples. The neural net separately judged representations of individual unclassified photographs against representations of the other, already classified, photographs. The inexperienced subjects judged individual photographs against the rules representing each class. The experienced subjects judged individual photographs against their previous experience of craquelure patterns in general. These tasks are artificial as, in each case, the class of the photograph is unknown. To the extent that craquelure is used in the attribution of a painting, it is used to confirm or refute an existing proStudies in Conservution 44 (1999) 233-244 The description and classification of craquelure posed attribution. In other words, before we judge a crack pattern in terms of the technical tradition which produced it, we already know (or think we know) the identity of that tradition. With the computational classification of the numerical representations of crack patterns, this prior knowledge of the origin of the pattern can be emulated by using discriminant analysis instead of a neural network. Discriminant analysis classified examples not only on the strength of the eight numerical scores describing the crack pattern, but also with reference to the art historic category of the painting. Using the same data that illustrated the neural network classification above, Table 2 shows the assignments made by discriminant analysis. That discriminant analysis produced four groups with 10 examples in each was fortuitous and did not happen with every subject's data. However, the heuristic representations of the 40 crack patterns appear to cluster together in a manner which accurately reflects the art historic categories of the paintings. This suggests two things: first, that crack patterns are indeed related to technical traditions, and second, that the eight descriptive terms capture sufficient information about the pattern to enable discrimination between categories. The heuristic representation is, however, provided by a human being, and by analysing the data provided from only one subject we d o not know whether or not their description is idiosyncratic. A heuristic representation is only valid if it is used consistently [3]. T o check whether the representations were consistent, discriminant analysis was undertaken for the data provided by all 31 subjects. Analysis of the groups created revealed a success rate in classification of between 30 and 39 out of 40. This represents 75.0 to 97.5% correct attribution of crack patterns with an average score of 91.4%. The range of results ( 2 11.25%) is similar to the range of results in the direct sorting task undertaken by unassisted experienced subjects. This suggests that the insertion of a (simple) mediating Table 2 Discriminant analysis of one subject's heuristic representation of 40 patterns Discriminant analysis It as if It as if F1 as if Du as if Fr Total FI Du Fr Group total 9 0 0 1 0 1 0 0 0 10 10 1 0 8 1 10 0 0 1 9 10 10 10 10 10 36140 = 90% Studies in Conservation 44 (1999) 233-244 Table 3 Discriminant analysis of the author's heuristic representution of 386 putterns Discriminant analysis It FI Du Fr Group totul as if It as if F1 asifDu as if Fr Total 2 80 4 0 86 0 1 92 6 99 0 2 3 99 104 86 86 109 105 3551386 = 92% 84 3 10 0 97 description does not exaggerate the variation across subjects in classifying what are, after all, complex perceptual stimuli. Having demonstrated that the representations were related to the categories and that they were generated consistently by a significant number of subjects, it remained to demonstrate consistency across a larger sample of paintings. The author judged a set of 528 photographs of craquelure in terms of the eight dichotomous descriptors to create heuristic numerical representations. Discriminant analysis was then applied to a statistically significant number of examples of each of the technical traditions. The results are presented in Table 3. The author's representation of 386 examples produced effectively the same level of success as an inexperienced subject's representation of 40 examples. This indicated that the method of representation was robust; it could be applied equally well by different individuals and it was applicable to large numbers of crack patterns with considerable variation across categories. The 92% correct attribution of 386 examples results from simultaneously comparing each example with four potential categories. When using attribution to an art historical category as a means of assessing the validity of a representation of craquelure, it is more realistic to compare pairs of categories. In attribution, the craquelure pattern is Table 4 Pair-wise discriminant analysis of the author's heuristic representation of Italian and Flemish crack patterns Discriminant analysis It FI Group total as if It as if F1 Total 84 3 87 2 80 82 86 83 1641169 = 97% S. Bucklow considered in concert with numerous other features of the painting to confirm or refute an impression derived from, for example, iconographic or stylistic data. Those features will suggest one particular category and the crack pattern either will, or will not, be consistent with the patterns typically associated with that category. We should therefore consider the level of success in attributing to individual pairs of categories. This can be done by reducing the 4 x 4 data in Table 3 into a number of 2 x 2 tables. Table 4 is one example of the six possible tables (ItalianIFlemish, ItalianIDutch, ItalianIFrench, Flemish/Dutch, FlemisWFrench and DutcWFrench) which can be derived from Table 3. These 2 x 2 tables are summarized in Table 5, which shows, for example, 97% success in distinguishing between Italian and Flemish panels, 95% success in distinguishing between Italian panels and Dutch 'paintings on canvas and 100% success in distinguishing between Italian panels and French paintings on canvas. The least accurate discrimination (95%) was effected between the Italian and Dutch categories and the Dutch and French categories. In the first case, discrimination between Italian and Dutch craquelure would be improved by reference to global patterns. These could include 'keying out' cracks on Dutch canvases (see Figure 10 in reference [I]). Global patterns were, however, beyond the scope of this study. The distinction could also be improved by reference to local patterns due to the canvas weave. However, in order to ensure that this study was statistically verifiable, such patterns were not included. Also, the effects of impact on paintings from different categories are significantly different (see Figure 1). Such local patterns were avoided in this survey but would obviously aid discrimination between the Italian and Dutch categories. Improvement in discrimination between the Dutch and French categories is more complex. They are both on canvas, so the kinds of features referred to above are of little help. Differences will Figure I Impact cracks on ( a ) a French painting on canvas (Francois Boucher, 'Venus asks Vulcan for the arms of Aeneas', Louvre, Paris) and ( b ) a Dutch painting on canvas (Abraham de Verwer, 'The Battle of Zuderzee ,' Rijksmuseum, Amsterdam). 236 Studies in Conservation 44 (1999) 233-244 The description and classijication of craquelure Table 5 Level of success in discriminating between individual categories using data presented in Table 3 % It It F1 DU Fr pair-wise average FI Du Fr Averages - 97 - 95 97 100 97 95 100 97.3% 97.7% 95.7% 98.0% 97 99 - 99 95 95 - 97.2% exist which are not evident in a study based upon only approximately 100 examples of each, but there is an inherent relationship between categories which must manifest itself in the craquelure pattern. The general pattern of misattribution throws light upon the variations within each category and the ability of the eight descriptive terms to characterize each category. There are two types of possible error: false rejection or false acceptance of the null hypothesis [4]. The erroneous classifications reported in Table 3 are summarized in Table 6. Table 6 shows that most incorrect inclusions occurred in the Dutch category. This indicates that Dutch craquelure is the category least well represented by the eight descriptors. It also shows that the Italian category suffered the most incorrect exclusions. This indicates that the greatest variation within any category was found amongst Italian examples of craquelure. Craquelure from other categories of painting was also examined to determine the applicability of the method beyond the above four categories. For example, 65 samples of crack patterns from early German panel paintings made evident the difficulties associated with any attempt at making general statements about a technically heterogeneous category of painting. In this case, what became apparent from analysis of the data was the influence of other technical traditions upon individuals and workshops across a broadly defined region. That technical traditions do not arise and flourish in isolation is evident in, for example, the craquelure of early German panels, and in the overlap between Dutch and French craquelure. Consequently, in this context, attribution to a Table 6 False inclusions and exclusions in the classijication of 386 examples presented in Table 3 It Fl Du Fr Error type 2 13 6 6 17 7 6 5 Type I: false inclusions Type 11: false exclusions Studies in Conservation 44 (1999) 233-244 Figure 2 Impact pattern in drying cracks in a nineteenth century British painting (unknown artist, 'Portrait of Bishop Moore ', Bishop's Palace, Ely). broad school or period has limited validity. The study reported here is presented in terms of such attributions for the sole reason that they enable large numbers of examples to be encompassed while remaining concise. Although incomplete, the framework of attribution nonetheless demonstrates the validity of a causal connection between the material structure of a physical object and subtle variations in the visible image. The contribution of craquelure to the conservator is not primarily as an indicator of the probable art historic category of a painting but as a method of non destructive testing. As such, craquelure can be considered independent of any category [5]. For example, Figure 2 displays some 'drying crack' characteristics and some 'aging crack' characteristics, but neither of these generally accepted categories is, on its own, sufficient to characterize the pattern. In this case, the overall configuration of cracks is determined by brittle failure ('aging cracks' in the ground layer as a result of an impact) S. Bucklow that has developed, and become visible, by ductile failure ('drying cracks' in the immature paint layer). ,! . / / / Nondestructive testing Craquelure is determined by the material properties of the object under study. For example, in mediaeval altar frontals, craquelure can indicate whether the seasoning of wood occurred before or after the panel was painted [6], while in geological specimens, the pattern of surface cracks can indicate the particular internal mode of degradation, alerting the conservator to alterations within the fossil [7]. In this survey of paintings, misattributions (the overlap between categories) can throw light upon the mechanisms of crack formation. This in turn may provide information about the materials or methods employed in a painting. Figures 3 and 4 are both from areas of sky in paintings by Dutch artists. Figure 3 displays a typical seventeenth-century Dutch crack pattern Johannes Augustus Knip, 'Jardin de Figure 4 bagatelle, Paris ', Rijksmuseum, Amsterdam. t Figure 3 Frederik de Moucheron, 'Figures in an Italian garden', National Gallery, London. 238 whereas the cracks in Figure 4 appear characteristically French. One reason for the discrepancy between these two paintings is suggested by their titles. Figure 3 shows the cracks associated with a painting which uses Dutch materials and methods. The painting is an Italianate fantasy which was almost certainly executed in the Low Countries; indeed, it is not even certain that Moucheron visited Italy [8]. Figure 4, on the other hand, appears from the crack pattern to have been painted on a canvas with a typically resilient French ground layer. This suggests that Knip bought the pre-prepared canvas whilst working in Paris. Figures 5 and 6 are both from areas of sky in paintings by Italian artists. Both of these examples are anomalous in that subjects perceived them, and discriminant analysis classified them, as Flemish panels (see Figure 7). One reason for the misattribution of these two paintings is suggested by the identity of the artists. Antonello da Messina is generally accredited, Studies in Conservation 44 (1999) 233-244 The description and classification of craquelure Figure 5 Antonello da Messina, 'Christ crucified', National Gallery, London. Figure 6 Giovanni Bellini, 'Agony in the garden', National Gallery, London. through his contact with Petrus Christus, with bringing Northern painting techniques to Italy [9]. Giovanni Bellini was also influenced by Flemish painting. In his case there is some controversy about whether he arrived at his Northern influenced technique independently [lo] or whether it was due to his contact with da Messina [ll]. One could speculate whether a survey of craquelure across Bellini's oeuvre may help clarify the date at which his method of painting became influenced by Northern techniques. Such a survey would be easier to undertake than any study based upon destructive techniques such as medium analysis or cross-sections. The interpretation of such a survey would, however, be complicated by the observation that, in many paintings, craquelure patterns vary between paint passages. As Figure 2 graphically demonstrates, the final crack pattern is a consequence of the behaviours of all members of the laminar structure of the painting. Figure 4 is the result of stresses within the painting where the mechanical properties of the ground layer predominate. In such a painting, there is little variation in crack pattern between paint passages. If, however, the paint and ground layers Studies in Conservation 44 (1999) 233-244 Canonical Discriminant Functions GROUP D - , Gw+Catdh -5 MESSINA 6 BEWNI a0194 FRENCH - Cl8 a0193 DUTCH-Cl7 ' 0 G,W2 FLEMISH Cl5 / 14 2 4 -1 ITAWN-CI4Il5 n 4 4 . 2 0 2 1 - 4 FuMb1 Figure 7 Discriminant analysis of selected areas of craquelure from the paintings by da Messina and Bellini in relation to the four categories. 239 Figure 8 Master of Liesborn, 'Presentation in the temple', National Gallery, London: crack pattern in an area ofjlesh paint. Figure 9 Master of Liesborn, 'Presentation in the temple', National Gallery, London: crack pattern in an area of green paint. are of comparable strength, then some significant variation between passages may occur. It was for this reason that the areas of craquelure surveyed in this study were predominantly rich in lead white. Figures 8 and 9 are both from the same panel from an altarpiece by the Master of Liesborn. Figure 8 shows the crack pattern found on areas of flesh and Figure 9 shows the pattern found in a green garment. One would not expect any significant variations in the support and ground layer between adjacent paint passages. The difference between the cracks in the flesh and in the green garment must therefore be due to differences in paint layer structure, pigments and/or media in those passages. The full interpretation of the crack pattern is dependent upon the results of other forms of analysis. Apparent anomalies illuminate differences in technique, either in the use of particular materials or methods. The heuristic representation, although simple and incomplete, is sufficiently comprehensive to alert the observer to technical nuances in the structure of the painting. A more complex and complete representation of craquelure has, however, been developed by Dr Peter Rayner and Dr Andrew Varley [12]. 240 Algorithmic representation The above heuristic representations were generated by humans and could be expressed in a form which was immediately accessible to humans (the rules of thumb). The involvement of a computer in the study was merely as a means of validating the relationship between human response to craquelure and technical traditions in an unambiguous and objective manner. If the heuristic part of the research was a systematic study of the human response to craquelure, then the algorithmic part of the research is a systematic study of the craquelure itself. For this, a computer was required not only to classify, but also to generate, the representation. The computational Studies in Conservation 44 (1999) 233-244 The description and class@cation of craquelure Table 7 Neural net~jorkclassification of the algoritlzmic representation of 200 patterns Table 9 Level of success in discriminating between individual categories using data presented in Table 8 Neural net It F1 Du Fr Group totals % as if It as if F1 as if D u as if Fr Totals 19 20 9 2 50 6 34 9 1 50 4 2 39 5 50 6 0 14 30 50 35 56 71 38 1221200=61~10/0 It F1 83 DU 94 Fr 99 pair-wise average It FI 83 - 99 100 Du Fr Averages 94 99 - 99 100 87 87 - 92.01%) 94.11%) 93.4%) 95.4% 93 7% methods of classification were the same as those utilized in the heuristic part of the research. The algorithmic representation of crack patterns depended upon converting the digitized images of craquelure from pixels into lines. Lines were extracted from the images using Markov chains [13]. The lines were then characterized as Bezier curves [14]. An approximate model of the original image was then recreated with Bezier curves of known specification. Crack patterns were represented by the statistical parameters which summarized these collections of Bezier curves. The parameters included data on the length of curves. the junctions between curves. the ends of curves, the tangents of curves within a specified range of angles to a reference direction, and the averages and standard deviations of these measures. Twenty such parameters were extracted from the sets of Bezier curves and these 20 parameters formed the basis for a representation of the crack patterns. The classification of these algorithmic representations by a neural network is presented in Table 7. For logistic reasons. the classification was undertaken using 200 images derived from the same sub-set of 40 images used by all subjects and presented in Table 1. This compares with averages of 73 to 75% for the unassisted sorting by experts, rule-based sorting by novices and neural network classification of the heuristic representation. Comparisons are offered in the form of percentages, as opposed to more sophisticated measures of similarity, due to the minor differences between the tasks. The algorithmic representation would probably prove to be more robust if tested against a wider survey. Following the chain of reasoning outlined above, the data were then subjected to discriminant analysis. Table 8 presents the resultant attributions. Again. the 4 x 4 table was reduced to number of 2 x 2 tables, and the level of success in pair-wise discrimination was calculated. These results are summarized in Table 9. The greatest level of success is found in the discrimination between French and all other categories (95.4%). Next most successful is the discrimination between Flemish and all other categories (94.1%). In this respect, the pattern of classification of the algorithmic and heuristic representations is the same (98.0 and 97.7% respectively, see Table 5). However, where the heuristic representation was least successful for discrimination between the Dutch and all other categories (95,7%), the algorithmic representation was least successful for discrimination between the Italian and all other categories (92.0%). It can be seen from Tables 6 and 7 that the major misattributions are Italian panels classified as Flemish: 40%) of all examples in the neural network and 30% in discriminant analysis. Table 9 shows that the Italian/Flemish pair-wise discrimination (at 83%) is significantly lower than pair-wise discrimination between any other combination of categories Table 8 Discriminant analysis oj the algorithmic (87 to 100%)). It was stated above that, for logistic reasons. the repre~entationoj 200 patterns algorithmic part of the research only examined the initial sub-set of 40 photographs. These images Discriwzinant Group were each sub-divided in five to create the 200 analysis It F1 Du Fr totals images studied. The classification was therefore based upon areas of painting one fifth the area of as if It 32 1 2 1 36 the examples utilized in the heuristic classification asifF1 15 49 1 0 65 exercise and averaging only 6cm2. The smaller areas as if D u 3 0 45 10 58 and smaller sample of paintings both rendered the as if Fr 0 0 2 39 41 Totals 50 50 50 50 165/200=82.5U/~ algorithmic classification task more vulnerable to the 'anomalous' Bellini example, perhaps account- Studies in Conservation 44 (1999) 233-244 241 Table 10 Comparison oj task durations Task --- Duration - Subject sorting 40 photographs (unassisted or rule-based sorting) Subject classifying one photograph (unassisted or rule-based sorting) Computer classifying 40 photographs (heuristic or algorithmic representation) Subject heuristically representing one photograph (for classification by computer) Computer algorithmically representing one photograph (for classification by computer) ing for the relatively poor ItalianiFlemish discrimination. The reason for limiting the number and size of examples examined algorithmically was due to the computationally intensive nature of the task. Conversion of the digitized photographic image into lines, segmentation of those lines into Bezier curves and calculating statistical summaries of those curves proved to be more time-consuming and computationally intensive than expected; this is apparent from Table 10. As noted above. the sorting of 40 photographs is an unrealistic task and the time taken reflects the artificiality of the task; it represents the selection of one solution from an enormous number (8 x 10") of potential solutions. The assignment of a single crack pattern to a single category by an expert is almost instantaneous. The heuristic representation of 528 crack patterns took the author about nine hours. On the other hand, the algorithmic representation of 40 crack patterns took a computer several months. Conclusions The heuristic and algorithmic representations, based upon the Repertory Grid and Bezier curves respectively, produce comparable results upon classification. The advantage of the heuristic method of representation is that it is accessible; it can be presented informally as rules of thumb for each category. The preceding analysis of the classification of these representations demonstrates that the eight descriptive terms are, if not exhaustive, sufficient for a high level of discrimination between patterns. The eight descriptive terms are applicable to other categories of easel paintings and discrimination between paintings from diverse traditions is possible. The same eight descriptive terms also discriminate between closely related traditions, and can highlight chronological and geographical trends within traditions. Its disadvantages are that it is based upon the judgment (albeit consistent) of individuals and is a qualitative representation. <45 minutes c. 1 minute < 10 seconds < 1 minute c. 3 days The advantage of the algorithmic method of representation is that it is quantitative. Its quantitative nature means that, in theory. it could be used in the non-destructive in situ analysis of painting components such as assessment of the strength of ground layers. Unfortunately. the present research reflects the general finding that the characterization of visual texture is computationally much more complex and less tractable than the characterization of colour. However, the Bezier representation has the potential to be fine-tuned: different parameters could be extracted and computational routines could be optimized. Its disadvantages are a dependence on expensive hardware and (at present) the time taken to process images. Another form of representation which may be applicable to craquelure but which has not been explored here is Fourier analysis. This method has already been applied to the visual arts [15, 161. It may offer an advantage of speed over the Bezier representation, but the Fourier transform of a craquelure pattern would not be as explicit and as open to interrogation as Bezier curves. The information available from craquelure is limited not only by our ability to represent it, but also by the technical context of the painting. The discriminations alluded to above are all dependent upon the predictable nature of the technical traditions involved. A particular painting may be typical or atypical of a class, but we are only able to judge the particular painting if the class itself is stable. This is because the crack pattern is not only dependent upon the materials used in the construction of a painting. but also upon the way in which they are employed in the construction of the painting. The heuristic and algorithmic methods of representation outlined above are complementary: qualitative and quantitative. quick and slow. etc. The information offered by craquelure is also complementary to that offered by other methods of technical analysis. Methods such as medium analysis and the examination of cross-sections all focus on a particular aspect of a particular component of the painting and have the potential to generate unequivocal data about that component. Analysis of craquelure-by whatever means-will always Studies in Conservation 44 (1999) 233-244 The description and classiJication of craquelure produce a more equivocal result, this is a consequence of the nature of craquelure as a 'holistic' phenomenon: it is the visible product of the response of the whole painting to its whole history. Acknowledgements The author would like to acknowledge the financial support of the Queen Elizabeth Scholarship Trust. Harold Wingate Foundation, Samuel H . Kress Foundation and Girton College, Cambridge. He would also like to thank the staff of the Fitzwilliam Museum. Cambridge, National Gallery. Tate Gallery. Courtauld Institute of Art and Wallace Collection, London, Rijksmuseum, Amsterdam and Louvre, Paris. The author expresses his gratitude to all those individuals who acted as experimental subjects. especially Bronwyn Ormsby. He extends thanks to Dr Peter Rayner and Dr Andrew Varley for their contribution to the project and for permission to quote the results of their research here. Equipment A standard 35mm lens and SLR camera (supported on a tripod under ambient light) were used in the photographic survey. All statistical routines were undertaken in SPSS for Windows, Version 6.1.3 (Professional and Advanced Statistics Options). The neural network was emulated within SPSS. The algorithmic representation was undertaken on a SUN Sparc 20. SPSS Inc., 444 N Michigan Avenue, Chicago, IL 6061 1, USA. SUN Microsystems Inc., 2550 Garcia Avenue. Mountain View, CA 94043, USA. Information Science 43(2) (1992) 115-129. 4 LEACH,C.. Introduction to Statistics, Wiley, New York (1979) 32. 5 VON BERALANFFY. L., 'An essay on the relativity of categories'. Philosophy of Science 22 (1955) 243-263. 6 PLAHTER,U., Oldsaksamlingen, University of Oslo, personal communication (1997). 7 COLLINS,C., Department of Earth Sciences, University of Cambridge, personal communication (1998). 8 National Gallery General Illustrated Catalogue, National Gallery Publications, London (1973) 495. 9 WRIGHT.J.. 'Antonello da Messina, the origins of his style and technique', Art History 3 (1980) 52. 10 GOFFEN,R., Giovanni Bellini, Yale University Press, New Haven (1989) 201. 11 ROBERTSON, G., Giovanni Bellini. Clarendon Press. Oxford (1968) 58. 12 VARLEY.A.J., 'Statistical image analysis methods for line detection', unpublished PhD dissertation, University of Cambridge (1999). 13 GREEN,P., 'Reversible jump Markov chain Monte Carlo computation and Bayesian model determination', Biometrika 82 (1996) 71 1-732. 14 VARLEY, A,, and RAYNER, P., Bezier Modelling of Cracks, ICIAP '97, Florence (1996). 15 DESSIPRIS, N.G.. and SAUNDERS, D., 'Analysing the paper texture in Van Dyck's Antwerp sketchbook'. Computers in the History of Art 5 (1995) 65-78. 16 HIGGINS,T., and LANG, J., 'Research into watermarks at the British Museum'. Conzputers in the History of Art 5 (1995) 79-86. Author References 1 BUCKLOW,S.L., 'The description of craquelure', Studies in Conservation 42 (1997) 129-140. 2 BUCKLOW,S.L., 'A stylometric analysis of craquelure', Computers and the Hunzanities 31 (1998) 505-51 7. 3 LATTA.G.F., and SWIGGER, K., 'Validation of the Repertory Grid for modeling knowledge', Journal of the American Society for SPIKEBUCKLOW holds a BSc in chemistry from the University of Southampton (1978) MSc in artificial intelligence from South Bank Polytechnic, London (1988), a diploma in the conservation of easel paintings from the Hamilton Kerr Institute, Cambridge (1994) and PhD from the University of Cambridge (1997). He is currently research scientist and teacher of theory at the Hamilton Kerr Institute. Address: Hamilton Kerr Institute, Whittlesford, Cambridge CB2 4NE, UK. RCsume-Cet article fournlt un contexte statistique de recherche pour dkfinir en termes dichotomiques simples une description des craquelures. La validitk du systkme proposk, bask sur huit descripteurs, est ktablie par rkfkrence aux resultats de diverses mkthodes de classement. Celles-ci comprennent Ie classenzent non supervisk Studies in Conservation 44 (1999) 233-244 243 des craquelures, dans des categories spCci$ques, par des sujets expPrimentPs, le mkme travail entrepris par des sujets inexpPrimentPs assistis par des instructions, la classIJicatzon des representations des craquelures par analogie avec un rCseau de neurones, et l'analyse discriminante. Deux types de representation sont compares: l'une basee sur la technzque de la 'Repertory Grid: et l'autre sur les courbes de BBeziers. Zusammenfassung-In dem vorliegenden Papier nird versucht, auf dem Hintergrund statistischer Forschungserkenntnisse mit ternzinologischen Fachbegriffen die Beschreibung von Krakelee zu ermoglichen. Die Gultigkeit der vorgeschlagenen Zahl von acht Deskriptoren von Krakeleefornzen wird mit Bezug auf die Ergebnisse verschiedener Klassi$zierungsaufgaben hergestellt. Dabei5ndet eine Zuordnung von Krakeleetypen zu spezijischen Kategorien statt ebenso wie die Klassi$zierung von Krakeleeformen mittels eines neuronalen Netznerkes und durch die Diskriminanzanalyse. Die rastergestiitzte Datendarstellung nird mit der auf dem Einsatz der Bezierkurven basierenden Darstellung verglichen. Resumen-Este articulo proporciona el context0 estadistico de investigacidn para definir terminos dicdtonzos para la descripcidn de tipos de craquelados. La validez de un grupo propuesto de ocho slstemas de descripcidn de craquelados se establece por referencia a 10s resultados de varios criterios de clasi$cacidn. Estos incluyen la asignacidn de tipos de craquelado a categorias especi$cas por profesionales cualijicados y experirnentados, lo mismo se realizd con individuos con poca experiencia ayudados por reglas tedricas de clasijicacidn, la caracterizacidn de craquelados por 'neural network' (red neural), y por analisis discriminativo. Se comparan dos tipos de representacidn: uno basado en la ticnica del Repertory Grid y la otra basada en las curvas de Bezier. Studies in Conservation 44 (1999) 233-244