Geometric reconstruction is the essential processing step for the creation of a 3D representation of an artefact or monument following the capture of 3D digitisation. This can be achieved using several relevant techniques which must be chosen based upon:

• The morphological complexity of the object

• The scale of the object

• What the final model will be used for (ranging from metric analysis to public dissemination)

Point Cloud Data

Once an artefact and monuments has been digitised the initial results (raw data) can be represented by a series of three dimensional data points in a coordinate system commonly called a point cloud. The processing of point clouds involves cleaning and the alignment phases. The cleaning phase involves the removal of all the non-desired data. Non-desired data would include the poorly captured surface areas (e.g. high deviation between laser beam and surface’s normal), the areas that belong to other objects (e.g. survey apparatus, people), the outlying points and any other badly captured areas.

Another common characteristic of the raw data is noise. Noise can be described as the random spatial displacement of vertices around the actual surface that is being digitised. Compared to active scanning techniques such as laser scanning, image based techniques suffer more from noise artefacts. Noise filtering is in an essential step that requires cautious application as it effects the fine morphological details been described by the data.

Processing Mesh Data

The next stage in the processing pipeline is the production of a surfaced or “wrapped” 3D model. The transformation of point cloud data into a surface of triangular meshes is the procedure of grouping triplets of point cloud vertices to compose a triangle. The representation of a point cloud as a triangular mesh does not eliminate the noise being carried by the data.

Nevertheless, the noise filtering of a triangular mesh is more efficient in terms of algorithm development due to the known surface topology and the surface normal vectors of the neighbouring triangles. Several processes must be completed to produce a topologically correct 3D mesh model.

*Image of point cloud data set and subsequent derived mesh model (Discovery Programme).*

Mesh Cleaning

Incomplete or problematic data from digitising an object in three dimensions is another common situation. Discontinuities (e.g. holes) in the data are introduced in each partial scan due to occlusions, accessibility limitation or even challenging surface properties. The procedure of filling holes is handled in two steps. The first step is to identify the areas that contain missing data. For small regions, this can be achieved automatically using currently available 3D data processing software solutions. However, for larger areas significant user interaction is necessary for their accurate identification.

Once the identification is completed, the reconstruction of the missing data areas can be performed by using algorithms that take into consideration the curvature trends of the holes boundaries. Filling holes of complex surfaces in not a trivial task and can only be based on assumptions about the topology of the missing data. Additional problems identi_ed in a mesh may include spikes, unreferenced vertices, and non-manifold edges, and these should also be removed during the cleaning stage. Meshing software (such as Meshlab or Geomagic Studio) has several routines to assist in the cleaning of problem areas of meshes.

*Illustration of the identification and closing of holes within the 3D mesh model (Discovery Programme).*

Mesh Simplification

The mesh simplification, also known as decimation, is one of the most common approaches in reducing the amount of data needed to describe the complete surface of an object. In most cases the data produced by the 3D acquisition system includes vast amounts of superfluous points. As a result, the size of the raw data is often prohibitive for interactive visualisation applications, and hardware requirements are beyond the standard computer system of the average user.

Mesh simplification methods reduce the amount of data required to describe the surface of an object while retaining the geometrical quality of the 3D model within the specifications of a given application. A popular method for significantly reducing the number of vertices of a triangulated mesh, while maintaining the overall appearance of the object, is the quadric edge collapse decimation. This method merges the common vertices from adjacent triangles that lie on flat surfaces, aiming to reduce the polygons number without sacrificing significant details from the object. Most simplification methods can significantly improve the 3D mesh efficiency in terms of data size.

*Illustration of high resolution polygon mesh model and simplified low polygon mesh model (Discovery Programme).*

Mesh Retopology

Extreme simplification of complex meshes, such as for use in computer games and simulations, usually cannot be done automatically. Important features are dissolved and in extreme conditions even topology is compromised. Decimating a mesh at an extreme level can be achieved by an empirical technique called retopology. This is a 3D modelling technique, where special tools are used by the operator to generate a simpler version of the original dense model, by utilising the original topology as a supportive underlying layer.

This technique keeps the number of polygons at an extreme minimum, while at the same time allow the user to select which topological features should be preserved from the original geometry. Retopology modelling can also take advantage of parametric surfaces, like NURBS, in order to create models of infinite fidelity while requiring minimum resources in terms of memory and processing power. Some of the commonly available software that can be used to perform the retopology technique include: 3D Coat, Mudbox, Blender, ZBrush, GSculpt, Meshlab Retopology Tool ver 1.2. Mesh retopologisation can be a time consuming process, however, it produces better quality light weight topology than automatic decimation. It also facilitates the creation of humanly recognizable texture maps.

*Image illustrating a low polygon mesh before (left) and after retopologisation (right).*

Texture Mapping

Modern rendering technologies, both interactive and non-interactive, allow the topological enhancement of low complexity geometry with special 2D relief maps, that can carry high frequency information about detailed topological features such as bumps, cracks and glyphs. Keeping this type of morphological features in the actual 3D mesh data requires a huge amount of additional polygons. However, expressing this kind of information as a 2D map and applying it while rendering the geometry can be by far more efficient.

This can be achieved by taking advantage of modern graphics cards hardware and at the same time keeping resource requirements at a minimum. Displacement maps are generated using specialised 3D data processing software, e.g. the open source software xNormal. The software compares the distance from each texel on the surface of the simplified mesh against the surface of the original mesh and creates a 2D bitmap-based displacement map.

*Diagram illustrating the different texture maps which can be employed to enhance the display of a lightweight 3D model. CLOCKWISE: UV map, normal map, image map and ambient occlusion map (Discovery Programme).*