Department of Architecture and Civil Engineering
Parametric shape model for conservation oriented surveying
The present work is concerned with the survey of the scissors arches of Wells Cathedral. These arches brace the central crossing of the cathedral and were built following the uneven settlement of the central piers, after an initial attempt to heighten the central tower. Despite their striking architectonic, structural and historic value, they have not been properly studied or surveyed since Nicholson's work in 1912. The phases of intervention and the reasons and benefits of the reinforcement are still under discussion. The substantial archaeological work carried out by Rodwell et al. (2001) has only briefly touched on this.
The project has three main objectives:
- To identify the present geometry of the scissors arches, the central crossing and adjacent bays, with particular reference to their construction details, so as to provide reliable data for structural analysis.
- To record the exact state of conservation of this part of the church in terms of stone decay and mortar conditions, with particular reference to substitutions, alterations and manumissions occurred during its life.
- To develop a documentation methodology based on digital surveying techniques for the recording of the present state and of any future work carried out on the crossing and tower.
The main output of the project is a 3D digital model providing metric and qualitative information on the scissor arches via a searchable, query-oriented, database. The 3D model will consist of surface elements (mesh of triangles) and it is designed to fulfil two major requirements, consistent with structural conservation:
- accurate survey of the fabric and existing material
- interpretation of the existing deformations and structural pathology
For this purpose the target accuracy has been set to about 10 mm. While this level of accuracy is not sufficient to provide a reference for the monitoring of the evolution of active deformation phenomena, it will allow the identification and localisation of existing active problems and on the basis of analysis carried out with the structural models will allow better planning of future monitoring installations.
Different surveying techniques were considered: traditional techniques, digital photogrammetry (DP), reflectorless total stations (RTS), laser scanners (LS)… As accessibility problems favour non-contact techniques direct measurements were initially discarded. One further constraint is represented by the time to be spent on site and the possible disturbance of the daily routine of the cathedral.
LS was discarded on the ground of its cost. Moreover if LS were to be used, the density of point must be high to record accurately edges and mouldings and specific procedures need to be implemented to simplify the model, so as to make it manageable. If the number of points is not sufficient to reproduce the shape with the standards expected, post-processing will be needed. In any case, parts of the profiles remain hidden from any possible station. We will discuss later the implications of that fact. In our specific case, the post processing necessary in order to circumvent the above-mentioned difficulties was foreseen to be complex and overly laborious.
DP was identified as the most appropriate technique to collect the material and constructional information imbedded in the object, but the extraction of data useful for the building of 3d structural model requires substantial amount of post processing work. Direct measurements with RTS would be the answer to this, but the number of point to be directly measured quickly escalates to tens of thousands if the accuracy with respect to the fabric is not to be compromised. Also, once the points are measured, automatic routines need to be developed to connect them to obtain meaningful objects.
A possible solution to the problem was therefore identified in developing a hybrid approach, combining elements of RTS and DP.
The aim is to minimise the time spent on direct measurement and interpretation of the photogrammetric takes. The experimental nature of the approach and the software development necessary (a set of programs written in C++) let nevertheless uncertainty in that respect. Sufficient elements of generality are introduced in the procedure so that, once the methodology is fully developed, it can be used for the recording of similar artefacts.
The main phases are: (1) construction of a model of the shape from a reduced set of measurements (using RTS), (2) projection of high resolution pictures on the model (using DP), (3) construction of a database using the textured model (stones, pathology, phases of construction…) and (4) enrichment of the database with supplementary data and refinement of the model with data acquired by direct inspection.
Preliminary work
A control network (CN) of 28 points is established. It defines the main coordinate system, serves as the skeleton from which all further measurements are to be taken and as a datum for possible further surveys. In order to minimise interference with the building fabrics, a minority of control network points are materialised by topographical nails, while the others by holes of 3mm of diameter. These points are mostly set on the building's floor.
Planimetric measurements were taken with a RTS (Leica TCR307 or Leica TCR705) and high-precision fibre tape measure (for control). Levelling is made with a parallel plate level (Wild NAK2). Measurements are redundant to give control and increase accuracy. Points' coordinates are calculated in Excel, using the least-square method. The accuracy is estimated to be 3mm, for a network of about 60m by 40m.
Parametric model
Figure 1: Element types: (a) punctual, (b) linear, (c) surface
The first step is to measure the shape of the object.
All gothic buildings and Wells Cathedral particularly, have many columns, arches, clustered pillars or ribs. These elements have got a predominant dimension. They are formed by a profile, extruded along a path. Starting from this observation, we decided to classify architectural elements in: punctual (0D), linear (1D), surface (2D) (figure 1) and to devise ad-hoc measuring techniques. Elements are named following a uniform convention.
In our object, surfaces are present in the vaults' webs, spandrels, clerestory windows' trumeaux. Points are measured with RTS, on a regular pattern. The point cloud is then meshed using Delaunay triangulation. The distance between the measured points is chosen in order to give a smooth surface representation. The total station is connected to a laptop computer running a custom-made program drawing the points in real-time.
Figure 2: Linear element: (a) path profiles, (b) generated shape [click on the image to access a vrml version. require a vrml plugin]
Linear elements are the most common. Ideally, they can be represented by a path and a profile (figure 2.a). In fact, the profile varies along the path. Hence a number of profiles are measured along the path, and interpolation is used in between. This is not straightforward. The first operation is to measure the path. A well-defined edge is chosen. Points are measured regularly with a RTS along that edge (the number of points depends on the shape and regularity of the edge; typically 30 points have been measured). More points are then computer generated using B-spline interpolation (50-100).
Figure 3: Stages of profile construction: (a) rough measurements, (b) flatten profiles, (c) architectural sketches taken in-situ, (d) minimal set of points, (e) extruded element
The second operation is to measure the profiles (usually 3). Points are measured at close interval with a RTS (roughly perpendicularly to the path) (about 100, Figure 3.a). Follow a series of operations in office to 'normalise' the profile: (1) points are rotated and put in a mean plane perpendicular to the path (Figure 3.b), (2) profiles are edited in AutoCad to keep the number of point to a minimum maintaining a good shape fit and to insure that every profile has got the same amount of point (Figure 3.d). From the path and normalised profile, a shape is then generated (see Figure 2.b and Figure 3.e). If the surface is not smooth enough, the number of points along the path or the profiles can be increased.
Once the measurements are taken, most of the operations are automated. However, in order to develop the 3D surface, some editing is still required and this is labour intensive and time consuming. Even with a dense scanning and real-time control on the computer screen, the rough measurements are not sufficient to define precisely a profile. Many parts remain invisible. They can be measured from different points but that increases significantly the time necessary for the scanning. This was done in certain occasions but not systematically. Furthermore, it doesn't always solve the problems. From the measurements taken, it is therefore necessary to go on the site and from careful observation and knowledge about gothic profile design, to complete the profile and produce drawings like the one presented in Figure 3.c. This operation is time consuming but is also very interesting because it allows the surveyor to trace the original design of the templates. From the original measurements, with the help of the reconstructed template and using similar copies of similar profiles to possibly provide likely data in invisible zones, it is therefore possible to define the points to be used for the profile extrusion (Figure 3.d).
Capitals, baskets, are punctual elements. The sculptured elements are much more difficult to measure. Modelling their surface require the measurement of huge amount of points. They cannot be represented using shape primitives. As they represent not such an important surface of the object, we don't intend to measure them with the same standards. No decision is yet taken but we will probably only measure their bounding shape.
The elements constructed (0-2D) are then assembled to form the complete model. Intersections are not calculated, some triangles of one element are just hidden by triangles of another element (figure 4.a).
Figure 4: (a) composite model, (b) textured model [click on the image to access a vrml version. require a vrml plugin]
Image projection
The second step is to project images on the shape model.
Tests have been made with different cameras and negatives. Our final choice is to use a terrestrial photogrammetric camera (Wild P32) with Ilford PanF films. The negatives are scanned, put on PhotoCD (resolution is 6144 x 4096) and organised in a database.
No reference points are materialised on the building (difficulty of access and visual nuisance).
The first operation is to take pictures (with an average scale of 1/150) and have them scanned. Feature points are then marked on the picture and measured with RTS (fig5). Their image coordinates are measured (sub-pixel accuracy). Using images' and world's coordinates, the internal (focal length, radial distortion) and external (camera position and orientation: pose) parameters are then computed. The image is then un-warped and projected on the shape model (figure 4.b).
All these operations are done using custom-made programs.
Figure 5: Feature points are marked on the picture and measured with RTS
Database construction
The third step is to extract information using the textured model.
Between 1999 and 2001, a digital photogrammetric program was developed at the University of Louvain in Belgium (K.U.Leuven). This program (virterf) has a module to visualise and enrich textured models. It is used in this project and extended to deal with its specificity.
Virterf allow to define and organise information in themes (materials, pathology), comprising layers (materials' types for instance) and to visualise them by colour maps (figure 6.b). The extensions concern accessibility and ease of use. The data is now stored in a MySQL database, accessible through the internet. To faciltate the management, basic elements are defined. In our case they are the stones, defined by picking their borders on the textured model. PHP interfaces allow the user to add information (stones' attributes) from a web browser. Controls are provided to restrict the access to authorised individuals. Before editing a particular zone of the model, a suitable image has to be chosen. It is then loaded from a server and projected on the model.
The original Production of ortho-photographs, dxf files (for CAD exchange) is implemented. Points, lines and sections can also be drawn easily on the model surface (figure 6.a).
Figure 6: Database construction: (a) lines, (b) colour map
Validation
No point of the model is coming from direct measurements; they have been subjected to rotations, interpolations, extrapolations, projections… It is therefore necessary to have procedures to validate the model. Fortunately this is not complicated: (1) qualitative conformity can be controlled at the interface between basic elements (if there is a step in between them, its height is a measure of the quality), (2) conformity can also be controlled looking whether the images are projected correctly (the image of an edge should be projected on the model edge). (3) The inverse operation is also possible; parts of the model can be projected on the images (figure 7). Finally (4), quantitative conformity can be controlled by RTS measurements (distances between points measured at random on the physical object and on the model are measures of the precision) and by comparing model and photogrammetric coordinates.
Figure 7: Validation: projection of paths on an image
Rodwell W., Wells Cathedral excavations and
structural studies, 1978-93 Warwick Rodwell with contributions by Marion M.
Archibald ... [et al.]