2. State of the Art: 2D/3D Segmentation and Classification Techniques
2.1. Segmentation Methods
2.2. Machine Learning for Data Segmentation and Classification
- A supervised approach is where semantic categories are learned from a dataset of annotated data and the trained model is used to provide a semantic classification of the entire dataset. If for the aforementioned methods the classification is a step after the segmentation, when using supervised machine learning methods, the class labeling procedure is planned before to segment the model. Random forest , described in detail at Section 4.2, is one of the most used supervised learning algorithms for classification problem [63,64].
- An unsupervised approach is where the data are automatically partitioned into segments based on a user-provided parameterization of the algorithm. No annotations are requested but the outcome might not be aligned with the user’s intention. Clustering is a type of unsupervised machine learning that aims to find homogeneous subgroups such that objects in the same group (clusters) are more similar to each other than those in other groups. K-Means is a clustering algorithm that divides observations into k clusters using features. Since we can dictate the number of clusters, it can be easily used in classification where we divide data into clusters that can be equal to or more than the number of classes. The original K-means algorithm presented by MacQueen et al.  has been then largely exploited for image and point clouds by various researchers [66,67,68,69,70].
- An interactive approach is where the user is actively involved in the segmentation/classification loop by guiding the extraction of segments via feedback signals. This requires a large effort from the user side but it could adapt and improve the segmentation result based on the user’s feedback.
3. Segmentation and Classification in Cultural Heritage
4. Project’s Methodology
- Create and optimize models, orthoimages (for 2.5D geometries) and UV maps (for 3D geometries) (Figure 6a–c).
- Segment the orthoimage or the UV map following different approaches tailored to the case study (clustering, random forest) (Figure 6d-e).
- Project the 2D classification results onto the 3D object space by back-projection and collinearity model (Figure 6f).
4.1. Image Preparation
- Planar objects (e.g. walls, Section 5.1): The object orthophoto is created and the procedure classifies and finally re-maps the information onto the 3D geometry.
- Regular objects (e.g. building or other 3D structures with certain level of complexity fit into this category, Section 5.2): Instead of creating various orthoimages from different points of view, unwrapped texture (UV maps) are generated and classified. To generate a good texture image to be classified, we followed these steps:
- Remeshing: Beneficial to improve the quality of the mesh and to simplify the next steps.
- Unwrapping: UV maps are generated using Blender, adjusting and optimizing seam lines and overlap (Figure 6c) to facilitate the subsequent analysis with machine learning strategies. This correction is made commanding the UV unwrapper to cut the mesh along edges chosen in accordance with the shape of the case study .
- Texture mapping: The created UV map is then textured (Figure 6d) using the original textured polygonal model (as vertex color or with external texture). This way the radiometric quality is not compromised despite the remeshing phase.
- Complex objects (e.g.; monuments or statue, Section 5.3): When objects are too complex for a good unwrap, the classification is done directly on the texture generates as output during the 3D modeling procedure.
4.2. Supervised Learning Classification
4.3. Unsupervised Learning Classification
4.4. Evaluation Method
5. Test Objects and Classification Results
- The Pecile’s wall of Villa Adriana in Tivoli: it is a 60 m L × 9 m H wall (Figure 7a) with holes on its top meant for the beams of a roof. The digital model of the wall was classified to identify the different categories of opus (roman building techniques), distinguishing original and restored parts.
- Part of a renaissance portico located in the city center of Bologna: It spans ca. 8 m L × 13 m H × 5 m D (Figure 7b). The classification aimed to identify principal parts and architectural elements;
- The Sarcophagus of the Spouses (Figure 7c): It is a late 6th century BC Etruscan anthropoid sarcophagus, 1.14 m high by 1.9 m wide, made of terracotta, which was once brightly painted . The classification aimed at identifying surface anomalies (such as fractures and decays) and quantifying the percentage of mimetic cement used to assemble the sarcophagus.
- The Bartoccini’s Tomb in Tarquinia (Figure 7d): the tomb, excavated in the hard sand in the 4th century, has four rooms—a central one (ca. 5 m × 4 m) and three later rooms (ca. 3 m × 3 m)—all connected through small corridors. The height of the tomb rooms does not exceed 3 m and it is all painted with a reddish color and various figures. The aim was to automatically identify the still painted areas on the wall and the deteriorated parts.
5.1. The Pecile’s Wall
5.2. Bologna’s Porticoes
- different architectural elements;
- diverse materials (bricks vs. stones vs. marble); and
- categories of decay (cracks vs. humidity vs. swelling).
5.2.1. Classification of 2D Data
5.2.2 Classification of 3D Data
5.3 The Etruscan Sarcophagus of the Spouses
5.4. The Etruscan Bartoccini’s Tomb in Tarquinia, Italy
5.4.1. Classification of 2D Data
5.4.2. Classification of 3D data
5.4.3. Quantification Analyses
6. Conclusions and Future Works
- shorter time to classify objects with respect to manual methods (Table 1);
- over-segmentation results useful for restoration purposes to detect small cracks or deteriorated parts;
- replicability of the training set for buildings of the same historical period or with similar construction material (e.g. roman walls);
- visualization of classification results onto 3D models from different points of view, using unwrapped textures;
- possibility to compute absolute and relative areas of each class (Table 3), useful for analysis and restoration purposes; and
- applicability of the pipeline to different kinds of heritage buildings, monuments or any other kind of 3D models.
- Difficult identification of the classes of analysis case by case (e.g. problems with the drainpipes classified as columns): the choice of the right classes during the training phase becomes fundamental.
- Misinterpretation of the shadows can introduce errors in the classification: the use of different color spaces from the classic RGB one, e.g. HSV and Lab, makes the lighting differences less problematic during the segmentation phase.
- Over-segmentation results in many classes, commonly useless in semantic analysis: this implies the need to make the regions more uniform in a post processing phase.
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|Random Tree||0.46||15 s|
|Random Forest||0.57||23 s|
|Fast Random Forest||0.70||120 s|
|Restored Opus latericium||0.2||0.73||0.02||0.02||0.18||0.01||0||0.85||0.63||0.72|
|Old Opus latericium||0.08||0.02||0.01||0.43||0.2||0.05||0.21||0.56||0.43||0.49|
|Opus reticulatum grey||0.06||0.05||0.01||0.08||0.66||0.05||0.08||0.47||0.67||0.55|
|Restored Opus reticulatum||0.02||0.01||0.01||0.01||0.07||0.83||0.06||0.77||0.82||0.8|
|Old Opus reticulatum||0.15||0.01||0.02||0.12||0.08||0.09||0.52||0.5||0.52||0.51|
|Classifier||% Eroded Surfaces||Area/Volume||Time for Elaborations|
|58%||2,8 m2||30 min|
|2D Unsupervised clustering||49%||2,4 m2||5 min|
|3D Supervised segmentation||56%||2,7 m2||10 min|
|Depth map||40%||1,96 m2 / 0,1m3||10 min|
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