Reconstructing a burial mound along the Via Appia

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Bachelor Informatica

Reconstructing a burial mound

along the Via Appia

Tom van de Looij

June 17, 2019

Supervisor(s): Hanan ElNaghy, Leo Dorst, Rens de Hond

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Abstract

3D reconstruction of archaeological findings have become a very active area in the field of cultural heritage. As part of the ’Mapping the Via Appia’ project we present a pipeline that allows archaeologists to partially reconstruct 3D scanned meshes and perform an in-depth error analysis. For this thesis in particular we investigate 3D meshes from fragments of a burial mound to try to find at least one fit. Finding such a fit would be a real archaeological breakthrough. The in-depth error analysis can provide solid evidence in finding a potential fit.

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Introduction

In the field of archaeology accurately registring observations has become an important activity in fieldwork. Many projects make use of 2D geographic information systems (GIS) and relational databases. This method of documentation is sufficient for most projects. For more complex sites this method of documentation requires much imaginative power of the archaeologist to analyse relations between objects and structures. Over the past few years Kleijn et al. have started developing a 3D GIS system for the ’Mapping the Via Appia’ project along the fifth and sixth mile. This project aims to gain further insight into the Roman interventions in the suburban landscape with the use of partial reconstruction of fragments found along the fifth and sixth mile of the Via Appia. Because of the size and complexity of this research area, a 3D GIS plays a significant part in the analysis and preservation of the excavation data.

The Via Appia was constructed in 312 BC and served as one of the most important roads in ancient Rome. In antiquity the Via Appia was an area with a lot of various cultural, economic, and religious activities. Traces are now found in the form of burial mounds, villas, and sanctu-aries. After the Roman empire fell in to decay, many of these remains were reused or raided by treasure hunters. Around 1800 it was decided to organise it as an archaeological area to protect the cultural fields of the Via Appia. Somewhere along the Via Appia a monumental burial mound was found. This burial mound consists of a concrete outer wall and multiple supporting walls. It is known that the outer wall was originally faced with a monumental wall of large decorative stone blocks. These stone blocks have been found as fragments in the excavation site. In part of the excavated concrete wall, one row of blocks that belonged to the concrete outer wall has been preserved in situ, in their original place. As part of the ’Mapping the Via Appia1’ project this research aims to fit at least one of the fragments found in the excavation trench to one of the in situ blocks. Finding such a fit will be a real archaeological breakthrough for the ’Via Appia Project’ [1].

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Figure 1.1a shows the excavation site from the Via Appia Project. The concrete in situ blocks are shown in front of the concrete outer wall. The fragments are displayed in the excavation site in front of the in situ blocks. Figure 1.1b shows a reconstruction of two burial mounds along the Via Appia drawn by Luigi Canina. The illustration shows clearly in what manner a burial mound was constructed and decorated.

(a) Excavation trench from the Via Appia

(b) Reconstruction of a burial mound by Luigi Canina from the 19th century

Figure 1.1: Two examples of a burial mound

The decoration of a burial mound was done in a structured manner. Finding one successful fit would be sufficient to proof that all other fragments found in proximity of excavation site would belong to this burial mound as well and did not end up there by chance. The other fragments can be placed on the correct position based on the position of the successfully fitted fragment. Reconstructing such a burial mound would tell us a lot about how a burial mound was constructed by that time.

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The fragments were scanned on site using photogammetry using the Agisoft Photoscan soft-ware and stored as 3D meshes. All meshes used in this thesis have a vertices count of 50.000. Figure 1.2 illustrates a top-view of twenty fragments and five in situ blocks. Of those twenty fragments thirteen are available for testing.

Figure 1.2: Digital representation of the fragments and the in situ blocks.

Two pairs of those fragments are known earlier to be matching via visual inspection There are also five fragments that have either a smooth right or a smooth left side. This indicates that they can only be positions on either the left end or the right end of an in situ block. We will call those fragments side fragments. The eight other fragments contain no smooth left or right side and can be positioned anywhere in the middle of the in situ blocks. Those fragments will be called middle fragments during this thesis.

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CHAPTER 2

Background

2.1 Related work

There have been several approaches developed for reconstructing broken objects. Reconstructing 3D solids was first developed by Papaioannou et. al[2]. The underlying assumption of this method is that the fracture faces match each other perfectly. The fragments found along the Via Appia have been eroded over time and therefore will not match perfectly. Others have also tried to reconstruct broken objects via feature description and matching. This section will talk about those methods and their inadequacy for this specific project.

Huang et. al[3] presented a method to reassemble fractured objects that consists of a graph-cuts segmentation algorithm to identify potential fracture facets and feature-based robust global registration for pairwise matching of fragments. First features are selected using multiple de-scriptors that are based on the integral invariants. Two features potentially correspond if they were computed using the same descriptor and have the same descriptor signatures. This initial set of correspondences is quite large and is therefore pruned to create a set of high quality feature correspondences. A forward search method is then used to mark all correspondence pairs that are valid. The underlying assumption of this implementation is that all fracture surfaces will have a complete match. As opposed to other reconstruction papers we are dealing with a partial reconstruction problem. In this project we try to fit a small fracture surface (fragment) to a much larger fracture surface (in situ block).

The assembly of 3D fragments is not only by done by matching fracture regions but also using the intact ’skin’ regions of a fragment. [4] have presented a method to reconstruct 3D fragments by not only using the fracture surface but also using the intact surfaces of a fragment. Their approach is done via a 3-step pipeline: initial reassembly guided by a template, pairwise fracture matching between fragments, multi-piece matching integrating both intact and fracture information. Their implementation performs very well in reconstructing small fragments that lack geometric saliency. It performs best in constructing fractured skulls and broken ceramic object using a template for a base alignment. As for this research, there is no template available. Our project also differs in the way we are reconstructing fragments.

There has already been a lot of work done in the field of reconstructing fragments. Our project differs than previously introduced methods in three different ways. First, previous work focuses mainly on the complete reconstruction of a broken object where fracture surfaces with the same surface size are matched. In this research we try to fit a small fracture surface to a much larger fracture surface. We are looking for a way to partially reconstruct fragments. Second, aside from drawn illustrations there is no clear template of a burial mound. We rely solely on the fracture surfaces in order to find a fit. The final difference is the data. The broken objects that were used in the methods mentioned above are objects that have either been artificially broken

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apart. The fragments and in situ blocks found at the excavation side are highly abraded by external factors such as weather and mechanical erosion. This research aims to create an easy to use pipeline for archaeologists of the Via Appia project that focuses on the error analysis of potential matches. By providing quantitative measurements of potential matches researchers of the Via Appia project can provide evidence that fragments found in an excavation trench originally belonged to an object of interest.

2.2 Theoretical Background

A common way of finding a fit between two point clouds is by using the Iterative Closest Point (ICP) algorithm. The main principle of ICP is to calculate a corresponding set registration that solves the coordinate transformation matrix and to find the relationship between two point sets. ICP works very well when an initial guess of the position can be made. Because it is currently unknown where one of the fragments might be positioned on the in situ row of blocks an initial guess has to be made. This initial guess will be based on the best fitting plane of both fracture surfaces and their orientations. ICP can then be used to fit the fragments as best as possible to the in situ block. In this section we will first describe ICP in detail, to then describe our implementation using an adapted version of the Open3D [5] library.

2.2.1 Iterative Closest Point

Let M and S be two point clouds where S is the source point cloud and M is the model point cloud. In ICP we are looking for the rigid transformation which finds the best correspondence between the two given point clouds. We first compute the nearest point in point cloud S for every point in point cloud M by calculating the Euclidean distance:

di= min(

q m2

i − s2j) j = 1, ..., NS (2.1)

If the distance di is smaller than a threshold we remove the point from the correspondence set.

This threshold is the maximum Euclidean distance we allow for each iteration of ICP. We then compute the rotation matrix R and translation vector t using the least square method to minimize the distance between two points. This minimization is defined by the following equation:

E(R, T ) = NM X i=1 NS X i=1 wij||mi− (Rsj+ t)||2 (2.2)

where wija are the weights for the corresponding points. ICP will continue iterating until either

the error is lower than the threshold or the maximum number of iterations that has been set by the user is reached. [6]

The minimization function as shown above is the standard ICP error function. The Open3D library provides us with two different implementations of ICP, called to-point and point-to-plane. These two versions differ in the error function. Point-to-point uses the objective function developed by [7] where T is the transformation and (p, q) are two points from the set of corresponding point K

E(T ) = X

(p,q)∈K

||p − T q||2 _(2.3)

Point-to-plane uses a slightly different error function where np is the normal of point p.

E(T ) = X

(p,q)∈K

((p − T q) ∗ np)2 (2.4)

Figure 2.1 shows the tangent plane that is used to minimize the distance between the source point and the destination point in point-to-plane ICP.

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Figure 2.1: Point-to-plane error between two surfaces [8]

2.2.2 Error Analysis

During each iteration of ICP three different types of error metric are returned. These error metric can be used to analyse the convergence of a fit and to assert the final quality of a fit.

The first error metric is the Root Mean Square Error (RMSE) of the inliers and it is defined as:

RM SE = r

d

N (2.5)

Where d is the sum of the Euclidean distances between each corresponding point and N is the total number of corresponding points. The lower the RMSE is the better the quality of the fit is. The second metric is the fitness of a fit. The fitness measures the overlapping area of a fit. It is defined as the number of inlier correspondences divided by the total number of points in the target. The final metric to analyse the distribution of the error is the MSE density. This is a new type of error that we introduce. It is defined as:

M SE density = PN i=0d 2 i ∗ A 2 i A (2.6)

where di is the Euclidean distance between a source point and a target point from the

corre-spondence set. Aiis the surface area of this point from the correspondence set and A is the total

surface area of the correspondence set.

2.2.3 Initial Alignment

Because fragments that have no smooth left or right side can be placed anywhere on the in situ blocks we have to make an automatic initial alignment that is based on the best fitting plane of the fracture surfaces. Therefore we have to find a plane that minimizes distances in the y-axis the equation of our plane is:

ax + bz + c = y (2.7)

We set up our data in matrices:

    x0 z0 1 x1 z1 1 . . . xn zn 1       a b c  =     y0 y1 . . . yn     (2.8)

This can be rewritten as:

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We have more that three data points and therefore the system is over-determined. We calculate the pseudo-inverse which will then result in the coefficients of the plane.

A+= (ATA)−1AT (2.10)   a b c  = (ATA)−1ATB (2.11)

We will then use the equation of a fragment and the equation of the in situ block to align the two meshes at the same height. Using the principal normal of the best fitting plane for each fragment we can calculate the rotation matrix that is needed to tilt a fragment to the same orientation of an in situ block. The rotation matrix R is defined as:

R = I + [v]x+ [v]2x

1 − c

s2 (2.12)

Where s is the sine of the angle and c is the cosine of the angle. [v]x is the skew-symmetric

cross-product of the cross-product of the two principal normal vectors.

[v]x=   0 −v3 v2 v3 0 −v1 −v2 v1 0   (2.13)

Applying this rotation allows the user to slide a fragment horizontally parallel to an in situ block using the arrow keys. This automatic alignment ensures that the probability of finding a match does not rely heavily on a manual visual alignment. Figure 2.2 illustrates the best fitting plane for a fragment before and after applying the rotation and translation. The smaller rectangle in the top-left is the best fitting plane of a fracture surface of a fragment. The larger rectangle on the right is the best fitting plane of the fracture surface of an in situ block. The darker rectangle in the middle of the in situ plane is the best fitting plane of a fragment after applying the rotation and translation. The movement of the fragment by the user is now limited to a horizontal slide along the fracture surface of the in situ block.

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CHAPTER 3

Implementation

In this section the first implementation of a visualizer is described. First we will outline the requirements set to make this implementation easy to use. Then the theory needed to implement a visualizer is explained. And finally the method to implement ICP, using the transformation matrix set by the visualizer, is outlined.

3.1 Requirements

A shortcoming of ICP is that in order to run the algorithm an initial alignment guess is needed. Because it is unknown where a fragment might fit on the in situ wall of concrete blocks, an easy to understand visualizer is needed to display one fragment and a part of the in situ block. Using this visualizer an archaeologist can move a fragment inside a 3D modeller to position the fracture surface of the fragment as close as possible to the fracture surface of the in situ block. It has to be easy to understand for a person that is not familiar with ICP or computer vision to use this implementation to find a match between two fragments. After an initial guess is made, a user can either choose to accept to run ICP or to try to modify the initial guess themselves. After a successful run of ICP, the quality of the fit is displayed inside the visualizer. The quality of the fit is determined by the error function of ICP.

3.2 Preprocessing the Data

The fragments and in situ blocks are stored as .ply files. These files are first imported into the 3D modelling software Blender. Blender is used to manually extract the fracture surfaces of the in situ blocks and the fragments found in the excavation trench. This reduces the number of points that need to be evaluated in the ICP phase of the pipeline, only the fracture surfaces are of importance in the reconstruction of the burial mound. Per block we know exactly which surface to extract because the decoration on the outer surface shows us in which orientation the fragment was originally positioned. This step is needed because the faceting software implemented by [9] only works with watertight meshes. We also use blender to rotate the fragments in the right orientation (top-side up). After all the fracture surfaces are extracted and the fragments are correctly oriented, they are ready to be used in our implementation.

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3.3 3D Modeller

The first phase of the program is the 3D-modeller. This version is an adapted version of Erick Dransch1_{. It is implemented in Python using the PyOpenGL bindings. The data set is first read}

using the PyMesh library. This library allows for easy processing of .PLY files. The extracted vertices are then used in a Vertex Array Buffer (VBO) in the PyOpgenGL framework. Figure 3.1 shows a 3D scene with two fragments found in the excavation trench of the North Moulding Base (NMB) displayed as point clouds. By using a mouse a user can rotate the camera around the two objects in the scene and move them in any direction to determine an initial transformation that ICP will use in the next phase of the pipeline. The 3D modeller will only be used to make an initial alignment. Rendering the fragments after a fit and the visualization of the error metrics is done in a different phase of the pipeline. A separate render stage to analyse the error metrics and final transformation allows for quick read in and adjustments to the initial position of the 3D point clouds.

Figure 3.1: Fragments NMB 28 and NMB 29 displayed as point clouds before an initial trans-formation has been made in the 3D modeller.

By pressing the key ’v’ a user can proceed to the next phase of the pipeline as described in the next section. This will create a interactive render of the two fragments. By pressing the key ’i’ the pipeline will execute the point-to-point version of ICP with the initial transformation set by the user. By pressing the key ’p’ the pipeline will use the point-to-plane version of ICP.

3.4 Visualizing a potential match

To visualize two fragments the visualization library of Open3D is used. Open3D is an open-source library written in C++ with wrappers for Python. Its core features are basic 3D processing and visualization with also more advanced features for scene reconstruction and surface alignment [5]. Figure 3.2a shows fragment NMB 28 and NMB 29 after a user has made an initial transformation with the 3D modeller as demonstrated in section 3.3. Figure 3.2b shows the same two fragments after a successful run of ICP. In this phase of the program the user can move around the fragments to interpret the quality of the match. If the quality of the match is not satisfactory the user can quit this phase of the program and go back to the 3D modeller of section 3.3 to adjust the initial alignment.

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(a) after an initial alignment. (b) after a successful run of ICP.

Figure 3.2: A render of fragment NMB 28 and NMB 29.

After a visual inspection, the user can assert the quality of the fit user is able to also look at the final error metric computed by ICP. This final error metric is determined by computing the distance of the nearest neighbor for each point in the two point clouds. Figure 3.3 displays a heatmap of the fracture surface of fragment NMB 29. Points colored in blue show a smaller Euclidean distance than surfaces colored in green or red.

Figure 3.3: Heatmap of fragment NMB 29

When the heatmap shows an unusual distribution of the error, the initial alignment can be enhanced to improve the result of ICP.

This concludes the user experience of the first implementation of the pipeline. In the next section we will try to use this implementation to fit fragments to the in situ concrete wall.

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CHAPTER 4

Experiments

In this section we will discuss how we have tested the reliability of our pipeline. To benchmark this reliability we will first test both versions of ICP on two pairs of fragments that are known to be a match via visual fitting. These fragments are a guaranteed match and they will illustrate clearly how our pipeline performs. The fragments that we will test are NMB 28 and NMB 29.

4.1 Point-to-Point versus Point-to-Plane

For this experiment the point-to-point and point-to-plane versions of ICP will use the same initial guess made by a user and ICP runs for maximum number of iterations set by the user or until the RMSE is lower than 1e−6. Figure 4.1 shows the two fragment before running ICP. For visualization purposes the full models of the fragments are displayed. While running ICP we will only use the fracture surfaces that significantly contributes to the fitting process. These fracture surfaces have been previously manually extracted in Blender. This will reduce the number of outliers in the first stage of ICP.

Figure 4.1: Fragment NMB 28 and NMB 29 after an initial alignment

Figure 4.2 shows the two fragments after running both versions of ICP. ICP is run with the default settings of 10 iterations, a maximum distance of 0.01 of a corresponding point distance per iteration (threshold), and a RMSE stopping condition of 1e−6. The number of iterations and the threshold are parameters that can be set by the user.

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(a) Point-to-Point (b) Point-to-Plane

Figure 4.2: Fragment NMB 28 and NMB 29 after running ICP.

A discussed in the previous chapter we then render a heatmap to investigate the distribution of the error. This heatmap is based on the Euclidean distance between corresponding points. Figure 4.3 displays the heatmap for fragment NMB 29 after running both point-to-point and point-to-plane ICP.

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Figure 4.4: RMSE of ICP during the 10 iterations (lower is better)

Figure 4.4 shows the convergence of ICP during each iteration. It is clear that point-to-plane converges in a steady pace after each iteration. The last metric to quantify our ICP implementation is the returned fitness. That is, the number of correspondence points divided by the number of total points in the target. Figure 4.5 illustrates the returned fitness of point-to-point and point-to-point-to-plane ICP during the 10 iterations. Although both versions reach almost the same level of fitness, point-to-plane ICP converges much quicker than point-to-point ICP.

Figure 4.5: Fitness of ICP during the 10 iterations (higher is better)

Table 4.1 illustrates the final error values for point-to-point ICP and point-to-plane ICP. Point-to-plane ICP performs better in all three types of error metrics.

point-to-point point-to-plane RMSE 0.004475 0.002852 Fitness 0.09579 0.12448 MSEdensity 0.00241 0.001355

Table 4.1: Final errors for point-to-point and point-to-plane

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Point-to-plane displays vastly better results in both the final transformation and the converge speed but also in the robustness to the initial alignment. Point-to-plane ICP performs better because it accounts for the normal vector of the corresponding destination point. Instead of minimizing the distance between the source point and the destination point point-to-plane minimizes the distance between the source point and the tangent plane at the destination point. As illustrated in 2.1 the direction of the normal vector allows to planes to slide on to each other, therefore point-to-plane will also perform better in flat surfaces. As most fracture surfaces of the middle and side fragments are relatively flat we expect that point-to-plane will also perform better in those experiments.

The robustness is of importance to fitting fragments to the in situ wall where small differences in the alignment could result in very different final transformations. The combined fragments in this section can also be used in matching to the in situ blocks. The combined fragments have a larger fracture surface which could increase the chance of finding a successful fit. For our next experiments that include fitting different fragments to different parts of the in situ wall we will use the point-to-plane implementation.

4.2 Fitting side fragments to the in situ wall

For this section we will to try to fit the fragments from figure 1.1 to the in situ wall. To increase our chances of finding a successful fit we first inspect the fragments for smooth surfaces. As shown in figure 1.1 the in situ wall consists of five blocks where the left side of the most left block is buried in the dirt. This is also true for the right side of the most right block.

Some fragments have either a smooth left side or a smooth right side. This means that they were originally positioned at the and the end of an in situ block. Therefore we will start our experiment with the fragments displayed in table 4.2.

Fragment ID Side NMB 31 Right NMB 42 Right NMB 50 Left NMB 71 Right NMB 72 Right

Table 4.2: Fragments with a smooth side

For each fragment we will try to make an initial alignment on the four right or left sides of the in situ block that are not buried in the dirt. From sections 4.2.1 until 4.2.1 the results of this first experiment are displayed. Each column contains the initial alignment, final transformation, heatmap, and the RMSE on each iteration. For some in situ blocks it will appear that a fragment is not placed at the very end of an in situ block. The fragments are aligned based on the smooth sides and not the very end of a the mesh.

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4.2.1 Visual results

Fragment NMB 31

(a) Initial alignment block 1 (b) Initial alignment block 2 (c) Initial alignment block 3 (d) Initial alignment block 4

(e) Transformation block 1 (f) Transformation block 2 (g) Transformation block 3 (h) Transformation block 4

(i) Heatmap block 1 (j) Heatmap block 2 (k) Heatmap block 3 (l) Heatmap block 4

(m) RMSE block 1 (n) RMSE block 2 (o) RMSE block 3 (p) RMSE block 4

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Fragment NMB 42

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Fragment NMB 50

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Fragment NMB 71

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Fragment NMB 72

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4.2.2 Quantitative results

Table 4.11 illustrates the final RMSE and the size of the set of corresponding point for each fragment for all in situ blocks. The best fit for each fragment on an in situ block based on the RMSE or the density are marked in gray.

NMB 31 NMB 42

In situ block RMSE Density RMSE Density 1 0.003 944 0.003086 0.004 312 0.004329 2 0.004 468 0.003 773 0.004167 0.004 726 3 0.004 071 0.003 205 0.004 408 0.004 607 4 0.00375727 0.003 092 0.004 252 0.004 601

5 n/a n/a n/a n/a

NMB 50 NMB 71

In situ block RMSE Density RMSE Density

1 n/a n/a 0.004 265 0.004 101 2 0.004056 0.004 554 0.004 599 0.003742 3 0.004 256 0.004 516 0.004211 0.005 115 4 0.004 457 0.004391 0.004 432 0.004 825 5 0.004 255 0.004 540 n/a n/a NMB 72

In situ block RMSE Density 1 0.004 686 0.004 659 2 0.004 540 0.004 847 3 0.004 254 0.004 591 4 0.004107 0.004377

5 n/a n/a

Figure 4.11: RMSE and the RMSE density from the experiments in the previous section.

Using the results from these experiments a user can quantify the matches and choose to further inspect specific combinations of fragments and in situ blocks. For example, the match between fragment NMB 72 and in situ block 4 shows to be a good fit in both the final RMSE and the density of the RMSE on the fracture surface. This could be a reason for a user to further analyse this specific combination of fragment and in situ block.

4.3 Fitting middle fragments to the in situ wall

As discussed in in the introduction there are eight fragments that contain no smooth left or right side. They can be placed on any position on the in situ wall and there are no reference points on the in situ wall that could indicate an already initial alignment. As discussed in chapter two we will first calculate the best fitting plane of both the fracture surface of the in situ wall and the fracture surface of a fragment. Aligning those two planes will assure that both the in situ wall and a fragment are positioned at the same orientation. In this section we will look at three of those fragments: NMB 28, NMB 29, NMB 39, and NMB 70. The first two fragments are a known match as shown earlier. We will use this match as a new fragment to increase the total fracture surface of the fragment and therefore increase our chances of finding a successful fit. We will combine those two fragments and call them fragment NMB 28 29.

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4.3.1 Visual results

Fragment NMB 28 29

(a) Initial alignment (b) Fit after point-to-plane ICP

Figure 4.12: Fragment NMB 28 29 and in situ block 4

Figure 4.12a shows the initial alignment based on the best fitting planes. Figure 4.12b illustrates the final transformation after running point-to-plane ICP.

(a) Heatmap of NMB 28 (b) RMSE

Figure 4.13: Fragment NMB 28 29 and in situ block 4

Figure 4.13 shows the error metric of the best fit for fragments NMB 28 29. The final RMSE is 0.00431 with a RMSE density of 0.004298.

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Fragment NMB 39

Figure 4.14: Fragment NMB 39 and in situ block 1

Figure 4.15 shows the error metric of the best fit for fragment NMB 39. The final RMSE is 0.004218 with a RMSE density of 0.003704.

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Fragment NMB 70

Figure 4.17: Fragment NMB 70 andin situ block 2

Figure 4.17 show the error metric of the best fit for fragment NMB 39. The final RMSE is 0.004552 with a RMSE density of 0.004573.

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4.3.2 Quantitative results

Table 4.3 illustrates the final error metrics computed after running ICP for 10 iterations and a threshold of 0.01. Fragments NMB 28 29 and NMB 39 show a relative high fitness and relative low density. Combined with the heatmap and convergence of the RMSE these combinations of fragment and in situ block could be of interest for closer examination.

NMB 28 29 + 4 NMB 39 + 1 NMB 70 + 2 RMSE 0.004317 0.004218 0.004552 Fitness 0.1347 0.0518 0.1212 Density 0.004298 0.003704 0.004573

Table 4.3: Final errors for the middle fragments and the corresponding in situ block number.

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CHAPTER 5

Conclusions

5.1 Discussion

We have presented a user-friendly pipeline that can be used for the partial reconstruction of fragments. It is designed to work very well with 3D meshes that have been scanned along the fifth and sixth mile of the Via Appia. This pipeline can now be used by archaeologists of the Via Appia Project to thoroughly analyse the fragments found in the excavation trench of the northern burial mound.

During this research we have willingly focused on error analysis of a potential match. From an archaeologist’s perspective having enough different types of error metrics that can provide evidence for a potential fit is more valuable than finding a match based on feature description. We have used four different type of easy to understand error metrics (RMSE, fitness, density, heatmap) that will help asserting the quality of a fit. The produced graphs containing the RMSE and fitness tell us how ICP has converged in finding a fit. A fit with a lot of fluctuation in the RMSE and fitness is likely to not be a fit. We have also introduced a new type of error metric, the MSE density. Such density can tell us what the average Euclidean distance is in a point based on the Euclidean distance of a corresponding point weighted by the surface area this point occupies in the fracture surface. The heatmap can be used to quickly determine the distribution of the error between corresponding points which can then be used to make small manual adjustments in the initial alignment.

Results show that our implementation of ICP works very well with the available data. We have also shown that for highly eroded fragments point-to-plane ICP results in a better performance than point-to-point. ICP finds good fits for fragments that are known to be a match.

5.2 Archaeologist’s Feedback

Rens de Hond is an archaeologist at the Radboud University in Nijmegen. He as been working on the Via Appia project as PhD researcher. He presented the problem of partially reconstructing fragments of the northern burial mound. He will be using the pipeline to further analyse the fragments of the burial mound. In this paragraph he will provide his perspective on the presented pipeline.

”This work has resulted in a tool that promises to be a great asset to archaeological research projects like Mapping the Via Appia that gather and analyse large amounts of 3-D data, but do not have the knowledge and skills to build custom digital tools. Available tools tend to focus on user friendly interfaces and automatic matching of fragments, but they often fail somewhere along the process, leaving the archaeologist empty handed. The pipeline presented in this thesis may require more input and guidance by the archaeologist, but it works as a solid tool that produces transparent results in a white-box process. We are very keen on implementing this pipeline into our project

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and hope it will yield many breakthroughs in the reconstruction of the ancient monuments along the Via Appia.” - Rens de Hond.

5.3 Limitations and future work

There is some pre-processing needed on the fragments before they can be properly used in the pipeline. Fragments are originally not oriented top-side up and fracture surfaces are manually extracted using Blender. In future work the faceting algorithm of [9] could be used to extract the fracture surface of the fragments. A current limitation of ICP in this research is the penetration of fragments. For highly eroded fragments ICP will always try to find a fit which will inevitable lead to penetration of fragments.

As mentioned above to improve the chances of finding a match the pipeline could easily be extended to find a match based on feature description. Together with the introduced error analysis it would provide a solid basis for finding a match between fragments. Currently the heatmap is only used for a visual inspection of the distribution of the Euclidean distances. In a future project this distribution could be used to provide a new initial guess for ICP. In figure 4.3b there is a clear direction from a low to a higher distance. This gradient could be used for a better initial guess before running ICP again.

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Bibliography

[1] M.-R. S. de Kleijn, de Hond, “A 3d geographic information system for ’mapping the via appia’,” Research Memorandum VU, 2015.

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Reconstructing a burial mound along the Via Appia

Bachelor Informatica