Digital Environments: Design, Heritage and Architecture
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Clustering Techniques for the Analysis of the Execution of a Fresco

Luciana Bordoni, Attilio Colagrossi, Giovanna Martellotti and Claudio Seccaroni

Keywords: wall paintings, frescoes, software system, informatic application, clusters, graph processing

 

Introduction

The peculiar characteristic of a fresco painting lies in the technique of working directly on the wet plaster (intonaco). In this way, the pigments are layered on the wall before the starting of the carbonation process, which fixes them on the surface. Thus, in large paintings, in order always to have fresh plaster to work on, the intonaco needs to be applied in sections. The size of these sections depends on the painter's capacity and ability. Commonly, in the study of fresco paintings, the patch of the plaster - or so-called intonaco - applied for a day's work is called a giornata, corresponding to the Italian word for day.

The addition of a new giornata means that the plaster of the latest giornata overlaps the plaster along the border of one or more giornate executed previously. Generally these overlaps are recorded on a map, with arrows indicating the direction of the overlaps from one border to another.

The study of the plaster overlaps along the joins of the giornate allows them to be put in a chronological order. In large-scale frescoes, often found on large walls and ceilings, there may be numerous giornate. For example in the San Brizio Chapel in the Cathedral of Orvieto, the complete decoration scheme - which covers the walls and the ceiling - involves more than 800 giornate. In such cases, it is not easy to understand and work with all information concerning the overlaps. Even with ten or twenty giornate on a map, studies are limited to the mind's holding capacity and to local confrontations.

An informatic application, described in [1] and [2] has been developed in order to overcome the difficulty of managing frescoes with several hundreds of giornate. Such an application allows for the manipulation of all the binary relations involving all the pairs of adjacent giornate in an entire painting. A mathematical model, already adopted in [3] and the appropriate software described in [1]. and [2] can then be used to work out the chronological sequence of all the giornate.

In this way, the frescoes are modelled by a direct acyclic graph (DAG), as in [4]. In such a graph each node is identified by a giornata (represented in the informatic application by values of whatever ordinal types, for example by integers or characters, depending on the number of the nodes). A pair (A,B) of the graph nodes is connected by an arc from A to B, this indicates that the giornata A was laid down before the giornata B.

The model based on the DAG identifies any errors that may arise in the plotting of the direction of the overlaps. It also simulates and processes various solutions in cases where information about some overlaps may be missing, most frequently due to the difficulty in identifying the direction of the overlaps.

The program has a user-friendly interface and combines all available information, thus providing a global view of the time sequences of the giornate for the whole fresco. The sequence determined by the program can be visualised in the form of a path on the map of the giornate, or as an oriented graph in which every giornata is a single block.

This software tool can be further enhanced to simplify the interpretation of the results. This is necessary as the graph very rapidly becomes much more complicated than a simple linear model, when the number of the giornate increases and their geometry becomes more complicated. To help in the ordering of the sequences, we may also include other data about the fresco apart from the simple recording of binary data about the overlaps.

After the elimination of all the redundant information, the graph obtained is not always readable, even when it shows a more simplified situation.

A graph containing a large number of giornate is often complicated, with numerous branches. Simplifying the structure into "work phases" could allow us to have a better understanding of how the fresco actually developed. Here we will be examining one aspect of simplifying the graph, which, however, requires external input of information. The following discussion will be drawn from our work on two cases of 17th-century fresco decoration in Rome: the ceiling of the Loggia Pallavicini Rospigliosi and the ceiling with the Assumption of the Virgin in the church of San Silvestro in Capite. The present study has been made possible thanks to the recent restorations of both frescoes. The restorations have been executed for the Soprintendenza ai Beni Artistici e Storici of Rome under the direction of Dr. A. Negro.

The decoration of the vault of the Loggia Pallavicini Rospigliosi, as described in [5] and [6], was carried out between 1611 and 1612 by Paul Bril and Guido Reni. It is made up of five bays divided by pendentives and groins. The decoration depicts a pergola - an arbour of grapevines. The painting exploits its divisions into groins and pendentives to create the illusion of octagonal or circular cupolas that seem to break through the top of the vault. In the spaces in the centre of the groins and the bays are animals and birds painted by Paul Bril. On the base of each pendentive are putti painted by Guido Reni. The picture covers a surface of about 84 square metres with a total of 85 giornate. The decoration of the ceiling in the nave of the church of San Silvestro in Capite was painted during the second half of the 17th century by Giacinto Brandi. The fresco has a surface of approximately 230 square metres, on a simple vault with a wide and richly decorated frame of gilded stucco. There is a total of 198 giornate.

Clustering

The sequencing of all the giornate allows a global overview of the binary relations between the giornate; but the resulting graph can in some cases be difficult to read. The two examples just mentioned show this very well.

The structure of the graph can be simplified by clustering the giornate. However, this clustering should be carried out on the basis of certain criteria: giornate can only be included in the same cluster on the basis of their sequence in the execution of the fresco. The clusters cannot be incompatible with the overall structure of the graph and must respect the information concerning all the overlaps of all the joins. If the clustering is right, the DAG structure is respected.

Clustering can be used to slim down the graph. This occurs as all the separate arrows, which indicate the individual giornate of two different groups (clusters), are reduced to a single indication of precedence between the two clusters. Within each of these clusters, the ordering is carried out treating the group as an isolated unit. The grouping of giornate making up frames, borders, niches, different scenes or even walls can justify the use of clustering. The grouping can be applied to a very limited number (short clustering) or to an extended number (large clustering) of giornate. In each of these cases, the clustering is based on hypothesis concerning the phases of the work and the organisation of the work site. All information concerning the selected giornate of a cluster is transferred in a single giornata-cluster. For example 1, 2, 3 and 4 are the giornate to be clustered, while the relations order defined by the overlapping of the joins are (figure 1):

1 overlaps 0
2 overlaps 0, 1
3 overlaps 1 and 2
4 overlaps 0, 2 and 3
5 overlaps 1 and 3
6 overlaps 3, 4 and 5

Figure 1: Hypothesis of clustering for a simulated situation.

In this way all these data are globally collected as follows: 1, 2, 3 and 4 (taken all together) overlap 0, 1, 2 and 3.

Further, we must cancel in the second group of the relation all the giornate belonging to the cluster, because at this point, it is important to consider only the relations between the cluster and the giornate not belonging to it.

This operation involves the elimination of all relations among the giornateinside of the cluster; otherwise it would create nonsense concerning the tautology referred to the cluster: "X overlaps X". Our example can be now schematised as:

the cluster A (containing the giornate 1, 2, 3 and 4) overlaps the giornata 0,
the giornata 5 overlaps the cluster A,
the giornata 6 overlaps the cluster A and the giornata 5.

To discover the giornate not belonging to the cluster A, it is necessary to substitute the reference for each giornata belonging to the cluster A with its direct reference. If the hypothesis building the basis of the cluster definition were correct - in other words if they are not in contradiction with the information about all the joins of the fresco - the outcoming graph would still be a DAG. Otherwise it would collapse and be incompatible with the DAG structure. If the giornata 2, in the above example, had not been inserted in the cluster A, it would create a loop, generated by the two following contradictory statements:

the cluster A overlaps the giornata 2,
the giornata 2 overlaps the cluster A.

This situation is not acceptable, so the hypothesis we assumed for the definition of the cluster is wrong. One possibility to escape from the impasse is to insert in the cluster also the giornata 2 - in case this is possible from the point of view of the execution of the fresco. Otherwise we must look for a new cluster, using a new hypothesis, in which the giornate will be selected with a different logic.

The informatic application performs two main tasks:

1. 1. It accepts from the user some hypothesis concerning the possibility of grouping two or more giornate on the basis of their form, their geometrical disposition, and the logic of execution of the painted surface;
2. 2. It verifies the hypothesis formulated above (consisting in the persistence of the DAG structure).

Short clustering (first type). Union of two residual giornate

The short clustering concerns a very small group of giornate, generally two. This clustering often allows a great simplification of the graph. There are two possibilities, which can be executed.

The first one concerns a giornata divided in two (or more) parts, due to the insertion of a successive giornata. This inserted element removed a part of the plaster from a preceeding giornata. In the decoration of San Silvestro in Capite this happened often. Such situations were created by later insertion of figures in wide monochrome fields (heaven, clouds). Inserting figures in the composition could indicate a modification of the composition during the execution of the fresco (as for example, cancelling a figure), but it could also indicate a particular method of optimising the resources of the studio of Giacinto Brandi. Generally, at first, the assistants executed the ground; than the master or the specialised painters inserted the more complicated figures.

In the vault of San Silvestro in Capite, an angel executed in two giornate broke down three previous giornate. After this insertion, each of these three giornate was separated in one large and one very small part. The short clustering formed by the union of two residual giornate eliminates one or more blocks, merging two items in one. The adjunctive information, on which the clustering is based, is obviously not derived from the overlap of the plaster. It recognises the fact that two or more non-adjacent giornate are fragments of a larger one, because their forms and measures are not to be interpreted, logically, as separate giornate. In the short clustering of this first type two parallel blocks are merged into one.

Short clustering (second type). Union of two giornate forming the same figure

The second type of short clustering treats two giornate, where it is possible to do a hypothesis about a strictly consecutive execution.

Figure 2: Overlaps at the joins in the case of two adjacent figures both executed in two giornate.

For example, this happens when one figure is layered on two (or more) giornate, so we have to consider the use of only one cartoon for its execution. In this case, we have to admit that the figure was finished before the execution of a new one. In the first giornata the head of the figure - with or without the bust - is produced, while the rest of the figure is achieved in a second giornata (figure 2).

In this case the clustering operation allows us to linearise in the graph some typical rhomboid structures: one node has two exits, which have at their end a unique exit. If, in the example of two adjacent figures both executed in two giornate, the giornata with the last part of the figure executed first (Ib) and the giornata with the first part of the figure executed in a second time (IIa) are not adjacent, we have a graph with a rhomboid structure (figure 3).

Figure 3: Rhombus structure in the graph and its linearisation.

The hypothesis that the painter did not interrupt the execution of each one of those figures allows us to correlate the giornate (Ib) and (Ila). This operation simplifies the graph and linearises the rhomboid structure. Again, the supplementary information which allows clustering does not derive from the overlaps; it concerns only the strict dependence between (Ia) and (Ib) and the strict dependence between (Ila) and (IIb).

A meaningful example has been found in the fresco of San Silvestro in Capite and concerns the giornate 60, 35, 58, 59, 57 and 55¹. This example shows two rhomboid structures in a sequence (figure 4). The first rhombus is formed by the giornate 60, 35, 58 and 59, while the second rhombus is formed by the giornate 58, 59, 57 and 55. The presence of two separate figures - the first figure concerns the giornate 58 and 59, the second one the giornate 57 and 55 - allows us to make a hypothesis about a strict succession inside of each pair of these giornate. The last two giornate (60 e 35) are representing the ground with clouds. They are to be found at the beginning of the sequence, which after the clustering is completely linearised. The hypothesis that clouds were painted before the figures is reasonable and coherent with the rest of the execution of the fresco.

Figure 4: Example of a double rhombus structure and its linearisation in the graph concerning the fresco with the Assumption of the Virgin by Giacinto Brandi (Rome, church of San Silvestro in Capite).

This second type of short clustering is to fix the strict temporal succession between two non-adjacent giornate. This second type of short clustering also keeps unaltered the number of the giornate, but it linearises the structure.

Another example for the graph linearisation by short clustering of the second type can be found in the Loggia Pallavicini Rospigliosi. A rhombus structure is defined by two giornate executed by Guido Reni (33 and 34) and two other giornate by Paul Bril's studio (35 and 36). In this case the hypothesis for the clustering is that the two artists did not work contemporaneously (figure 5).

Figure 5: Linearisation of a rhombus structure in the graph concerning the decoration of the ceiling of the Loggia Pallavicini Rospigliosi (Rome) executed by Guido Reni (circles) and Paul Bril (squares).

Large clustering

Some considerations about the organisation of the work site allow us to gather additional information for the general ordering of the giornate beyond the information obtained only by the examination of the joins. It is clear, that once the borders of the eventual pontate² have been defined, analogous to what happens between two single adjacent giornate, it is possible to establish a preceding relationship between all the giornate above the scaffold-line and those below. These considerations make it possible to group together the giornate in a cluster.

The large clustering allows a better visualisation and understanding of the organisation and the phases of the work site, simplifying the graph as much as possible.

The decoration of the Loggia Pallavicini Rospigliosi is complex and required ingenious technical solutions. This is due in part to the way the architecture is painted and to the geometry of the vault. Its divisions into groins and pendentives takes advantage of illusionistic octagonal or circular cupolas that seem to break through the top of the vault. A profound study was made of the integration of this structure with the dense vegetation and animals, all rendered in a very naturalistic way. Finally, there is the verified presence of both masters, both with different technical training, but nevertheless they had to develop a rational system of cooperation.

It is evident that the order of the giornate is closely tied to the construction of the arbour and in this way the overlaps generally run on the side of a wooden support, already painted the previous day.

The graph from the output of the system is shown in fig. 5. There is a distinction between the giornate executed by Paul Bril and his collaborators, indicated by a rectangle, and the giornate painted by Guido Reni, indicated by a circle. The decoration began with the giornata number 42, in the third groin west side. In fact, the other three initial giornate, which are situated in three groins of the northern sector of the vault, have all very short and limited paths. The giornata 42 generates numerous paths either toward north or south, which reach almost the entire surface of the vault. The only exceptions are those brief paths, which start from the other three initial giornate. These three giornate can be interpreted as secondary roots. The plaster of the two pendentives adjacent to giornata 42 overlap this initial giornata. These are the pendentives depicting putti with jasmine and carnations. These are totally extraneous from that which is the norm in the rest of the decoration.

Figure 6: Resulting graph for the giornate sequence concerning the decoration of the ceiling of the Loggia Pallavicini Rospigliosi (Rome) executed by Guido Reni and Paul Bril.

The other eight groups by Reni are, in fact, always executed on final giornate, which do not overlap the intonaco of the surrounding groins, but only the intonaco of the central part of the vault. The paths going towards the rest of the surface pass from these two pendentives.

The part of the vault which includes giornata 42 and which is composed of six giornate can be easily identified. This test area was initially intended to verify the aesthetic effect of the composition and the degree of integration between the two masters. But it was also helpful in establishing the best rational system of cooperation. The first adopted rationalisation criterion was to render totally independent the work of the two masters in a way that they did not hinder one another. There are technical differences concerning the laying-on and the organisation of the two pendentives adjoining giornata 42, compared with the other eight by Reni. This choice was evidently made to render the work of the two artists independent. A loss of integration of the putti in the arbour resulted; yet, the simplification of the work derived from this choice outweighed the loss.

After the first test area, the work went ahead, completing the central bay and going on the two southern bays. As this work progressed, the system of execution was improved and then adopted in a systematic manner in the two northern bays. The logic of the planner of all the giornate in each groin is not identical in the two sectors in which the vault can be divided. The study of the groins pointed out a technical development inherent to the technique of their execution.

In the northern sector of the vault, the birds in the ovals are painted on final giornate, which end the work in each groin. In the southern sector this is true only for the eagle and the wild crow in the last bay. This way of proceeding simplified the work, making it possible for one painter to execute the large figures, while the others went ahead painting other elements of the arbour. In addition, the giornate in the northern sector are more regular and symmetrical than those on the opposite side. The construction of the arbour was solved by always placing the wooden braces of the underlying structure in the groins. These latter constantly preceded the work in the central sector of the vault. Here, the groins were finished in three giornate, instead of four or five as in the south sector. Two symmetrical giornate define the arbour, and the oval giornata with the bird overlies them.

Figure 7: Loggia Pallavicini Rospigliosi (Rome), graph after the clustering of the giornate. The clusters concerning the trial test are coloured in grey. The borders of the blocks corresponding to clusters concerning the giornate in the north sector of the vault are represented by a line, while the borders of the blocks corresponding to those in the south sector are represented by a dotted line.

A clustering was created from the two masters' giornate and on the basis of the geometric units in which the vault is laid-out. Groins and central sectors were separated from one another, and the groupings of giornate were checked one by one so that they did not in contrast with the oriented paths. In this way a simplified graph of the vault which contains the ten pendentives by Reni (R1-R10), the fourteen groins (U1-U14) and the six central sectors of the vault (V0-V5) painted by Bril³ was obtained (figure 7). As mentioned, there is a technical evolution in the organisation of the work site between the northern and southern sector. In the bays towards the south side, the development is linear and it touches one after the other the sectors represented by the clusters, corresponding to the geometrical structure of the vault. In the development of the work in this first phase, it is possible to identify the setting up of an operative method which tends to simplify drastically the organisation of each painter's work, of Bril's studio, painters specialised in vegetal or animal subjects.

The form of the giornate fits better with the structure of the arbour; in each cluster the giornate representing animals have been executed after the arbour giornate. This way of working minimised the disturbances between vegetation painters and animal painters. It made faster execution possible.

In the southern sector there is a boustrophedon progression of the clusters along the bays, from the centre to the short wall of the south side. In the northern side of the ceiling, the rationalisation of the work of Bril's studio is greater, because this rationalisation was adopted not only in the internal organisation of the clusters, but also in their planning. So there is a symmetrical organisation where an earlier execution of all the groins having the same giornate structure was preferred. The bays were executed consecutively - also in this case - from the centre to the peripheral short wall, the northern one.

After the completion of the decoration by Bril's studio, the third and last phase of the decoration involved only the execution of the eight remaining pendentives by Guido Reni. The previous execution of all the vegetation and the animals allows the painter to complete the decoration of the pendentives without the impediments due to the presence of the painters and workers of Bril's team.

The collaboration of two different studios is not so frequent. The example concerning the decoration of the vault in the Church of San Silvestro in Capite, in Rome, reflects a more frequent situation where the structure and the form of the giornate, and their mutual position, allow a large clustering. This clustering concerns groups of giornate having a border forming a unitary front. Obviously along this front, the directions of the overlaps for the plaster must be the same as for the giornate belonging to the same cluster.

In the resulting graph, there are two main roots for the whole decoration: the giornata containing the head of the Virgin - at the centre of the vault - and the one containing the Holy Spirit, on the upper border of the scene. Around the Virgin, the giornate with angels are isolated from the rest of the composition by an area without figures. So a crown of narrow and long giornate in which heaven is painted in a monochrome way surrounds the nucleus with the Virgin and the angels. For this nucleus, the clustering is evident.

The grouping of giornate is also clearly evident, which from the Holy Spirit on forms a continual front along the upper border of the composition. This front shows evidently that the group was executed with continuity, without interruptions or deviations towards secondary directions.

Conclusions

We have shown an informatic application able to perform the clustering of a graph representing the structure of giornate. The system can verify the validity of the hypothesis on the basis of which the cluster was done. In addition the system shows possible giornate concerning a loop in the execution of the algorithm.

After the indication of these giornate the user can verify again on the map of the giornate the hypothesis to select a possible new cluster, which will be tested by the system. The easier solution consists generally in inserting in the cluster the giornate not belonging to it, which have generated the loop. So the user can go forward in a progressive way in order to check a possible cluster. The clustering for both small and large groups can be made a second time only after having verified how the algorithm works on the whole of the information obtained from the overlaps of the intonaco on the joins between the giornate. The criteria underlying clustering must be sifted through withspecial attention.

Notes

1 The numbering of the giornate concerns only their identification. It has no relation with the ordering of the sequence.

2 The term pontata indicates a group of giornate situated at the same level of the scaffold used for the production of the fresco.

3 The sectors V0 and V5 refer to small portions in proximity to the two shorter walls.

References

1. Bertorello, C., Bordoni, L., Colagrossi, A., Martellotti, G. & Seccaroni, C. (1997) "Un sistema software per l'analisi della sequenza delle giornate in un affresco", Kermes, 29, 41-59.

2. Bertorello, C., Bordoni, L., Colagrossi, A., Martellotti, G. & Seccaroni, C. (1997), A software system for the analysis of the 'giornate' sequences in frescoes, Rapporto Tecnico ENEA, RT/STUDI/97/3, Roma.

3. Bottoni, M., Cordaro, M., Gaetani, M.C. & Provinciali, B. (1988), "Sviluppo di un sistema sperimentale per l'analisi dinamica delle fasi di esecuzione di affreschi. Finalità e fasi del progetto", Proceedings of 2nd International Conference on Non-Destructive Testing and Microanalylisis for the Diagnostics and Conservation of the Cultural and Environmental Heritage, Perugia, I/13.1-15.

4. Aho, A.V., Hopcroft, J.E. & Ullman, J.D. (1974), The Design and Analysis of Computer Algorithms, Addison Wesley, Reading, Mass.

5. Martellotti, G., (1996), "Note sulla tecnica esecutiva", (1996), Negro, A. (Ed.), Il giardino dipinto del Cardinal Borghese. Paolo Bril e Guido Reni nel Palazzo Rospigliosi Pallavicini a Roma. Àrgos, Roma, 135-138.

6. Negro, A. (1996) Il giardino dipinto del Cardinal Borghese. Paolo Bril e Guido Reni nel Palazzo Rospigliosi Pallavicini a Roma, Àrgos, Roma.