# Geometric Reconstruction

Geometric reconstruction is the essential processing step for the creation of a 3D representation of an artefact or monument following data capture or 3D digitisation. There are several techniques which can be used, the relevant techniques are chosen based upon:

The morphological complexity of the object

The scale of the object

The intended use of the final model (which can 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 non-desired data, such as poorly captured surface areas (e.g. high deviation between laser beam and surface’s normal), areas that belong to other objects (e.g. survey apparatus, people), outlying points and any other badly captured areas.

Noise is a common characteristic of the raw data (noise can be described as the random spatial displacement of vertices around the actual surface that is being digitised). Image based techniques suffer from more noise artefacts compared to active scanning techniques. Noise filtering is in an essential step but requires cautious application as it affects the fine morphological details 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 form a triangle. The representation of a point cloud as a triangular mesh does not eliminate noise being carried by the data.

Nevertheless, 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.

### Mesh Cleaning

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

Once the discontinuities are identified, the missing data areas can be reconstructed by using algorithms that take into consideration the curvature trends of the holes boundaries. Filling holes in complex surfaces in not a trivial task and can only be achieved based on assumptions about the topology of the missing data.

Additional problems identifed 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.

### Mesh Simplification

Mesh simplification, also known as decimation, is one of the most common approaches used in reducing the amount of data needed to describe the complete surface of an object. In most cases the data produced by 3D acquisition includes vast amounts of superfluous points. As a result, the size of the raw data is 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 quadric edge collapse decimation. This method merges the common vertices from adjacent triangles that lie on flat surfaces, aiming to reduce the number of polygons without sacrificing significant details from the object. Most simplification methods can significantly improve the 3D mesh efficiency in terms of data size.

### 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 topology can be 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 using the original topology as a supportive underlying layer.

This technique keeps the number of polygons to the 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, 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.

### 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 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.

The diagram above illustrates the different texture maps which can be employed to enhance the display of a lightweight 3D model.

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