Feature Line Extraction of Stone Tools Based on ...Feature extraction methods have been introduced over the past two decades. Gumhold et al. [7] rst formulated curvature using PCA

The Journal of the Society for Art and Science, Vol. 18, No. 1, pp. 51 – 62 (2019)

Feature Line Extraction of Stone Tools Based on MahalanobisDistance Metric

Shurentsetseg Erdenebayar1) Kouichi Konno2)

Graduate School of Engineering, Iwate University

{shurentsetseg} (at)lk.cis.iwate-u.ac.jp

AbstractPoint-cloud-based technique plays a very significant role in 3D model restoration. In the archaeologicalapplication of stone tools, the scale drawing, which is hand-drawn from measured stone tools, istraditionally used. In the scale drawing creation, a base drawing which consists outline and ridgelines is initially drawn from geometric features of shape. After that other lines are extracted fromknowledge of making stone tools and are added to the base drawing. It requires special knowledge toextract feature lines from stone tools so that scale drawing is time-consuming. Therefore, if the basedrawing is automatically extracted, the working hours are reduced. To overcome this issue, this paperproposes a feature line extraction method using the Mahalanobis distance metric. First, the pointson outline are extracted from a point cloud. Then, the surface variation is calculated with a variousnumber of neighbors and thus the potential feature points are detected by the analysis of its surfacevariation. After that, the potential feature points are thinned towards the highest variation pointsby using Laplacian smoothing. Then, the thinned feature points are shrunk to the potential featurepoints. Finally, a feature line is extracted by connecting the nearest thinned feature points locatingin the Mahalanobis distance field. To verify our method, the extracted feature lines are comparedto the ground truth of base drawing drawn by archaeological illustrators. Our method is applied tostone tools, and we confirm the effectiveness of our method.

1 Introduction

In recent years, point clouds are a very popu-lar representation of 3D objects among scientistsin the world since higher precision cameras andlaser scanners are developed. According to thesedevices, real objects of any size can be convertedinto 3D digital data. One of the areas that bene-fit from point clouds is cultural heritage research.The study of point clouds is contributing to cul-tural heritage saving for the next generation. Oneexample is the study of stone tool illustrationswhich is called ”Scale Drawing” [1].

A scale drawing is a representation of the shapefeature of stone tools. It is generally used in theexcavation report in the archaeology area. Topublish an excavation report, archaeologists mea-

Ver

tica

l ax

is

Outline Ridge lines Rings and fissure

lines

(a) (b)

Figure 1: (a) An example of manual scale drawing[2], (b) an example of the steps of the scaledrawing

sure stone tools and then make scale drawingsby manual operations. However, it is a time-consuming process, and the automatic generationof Scale Drawing is required. In general, scaledrawing is represented by four elements, such as

– 51 –


Point

cloud

Extracted

ridge lines

using

Euclidean

distance

Figure 2: Point cloud of stone tools [2] and result of ridge line extraction [3].

outlines, ridge lines, rings, and fissures [1]. Out-lines and ridge lines can be extracted from geo-metric features of the shapes. Rings and fissureshave to be investigated from precise observationof specialists and extracted on the knowledge ofmaking stone tools.

Figure 1(a) shows an example of scale drawingfrom the front, side and back, done by a lithicspecialists [2]. Figure 1 (b) shows the steps ofmaking a scale drawing of the stone tool viewedfrom the front. First, the specialist allocates adrawing area. The longitudinal of a stone tool isdrawn along the vertical axis. After that out-lines are measured and marked in the sketch.Then outlines are drawn by tracing the measuredpoints. After finishing the outlines, the pointson the ridge lines are measured and plotted inthe sketch. These points are traced in the samemanner. In this paper, the illustration of out-line and ridge line calls base drawing. Finally,rings and fissures are added to the base draw-ing. Making scale drawings from hundreds ofstone tools is quite time-consuming. Therefore,efficiency methods are required to reduce timeconsumption by using point clouds. Outlines andridge lines are clearer to be extracted and com-pared to the rings and fissures because these linesare geometric features. On the other hand, to ex-

tract rings and fissures require special knowledgeof archaeology. Therefore, if outlines and ridgelines are extracted and base drawing is automati-cally generated, the creation time of scale drawingbecomes compressed.

A flake surface is defined by the closed areawhich is bounded by ridge line. Therefore, allof the flake surfaces are represented by the closedline sequence into the base drawing even if the ge-ometric shape of ridge line may be an ambiguousshape.

There are several techniques to extract featurelines from point clouds [4, 5, 6, 7, 8], while theycannot sufficiently extract feature lines like basedrawing. Since a stone tool contains ambiguousshape, closing of flake surface boundary and find-ing the connection point may be difficult. There-fore, the feature lines to make a base drawing arenot sufficiently extracted.

In this paper, a novel feature line extractionmethod which is expanded by [3] is proposed.The proposed method introduces more flexibledistance metric to extract feature lines for a basedrawing creation automatically. Our algorithmselects candidate points on feature lines using itsdependence on neighbor propagation. Featurelines extracted from a point cloud are evaluatedby comparing with for technical hand drawing

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and we verify our method has effectiveness.

2 Related works

2.1 Previous study for extracting features

Feature extraction methods have been introducedover the past two decades. Gumhold et al. [7]first formulated curvature using PCA (PrincipalComponent Analysis) for point clouds. Enkhba-yar et al. [3] expanded spectral analysis, and theysuccessfully approached the Fast Fourier Trans-form to estimate the curvature of a point cloud.Then, feature points can be detected by the prin-cipal curvature.

Pauly et al. [9, 10] accomplished multi-scalePCA on a point cloud by using an adaptive num-ber of neighborhood points. Due to varying shapeof stone tools, a variation of each dimension issuitable to detect potential feature points by us-ing multi-scale PCA. [9, 7, 6] used a minimumspanning tree to construct feature lines. Enkhba-yar et al. [3] introduced a line growing techniqueto construct feature lines. These techniques arecalculated in Euclidean space.

In the base drawing, the ridge lines are drawnalong the longest sharp edges of stone tools.The detected feature points of such edges havehigh variation. Therefore, longitudinal connect-ing along the edges is the best optimization tocreate the base drawing. Feature points cannotbe easily connected depending on variation, be-cause Euclidean distance considers all dimensionshave the same variation. Another disadvantage isif there is no feature point to grow in a certaindistance, [9, 7, 6] cannot sufficiently constructfeature lines. Increasing the connecting radius isnot optimal for modifying the feature lines. Fig-ure 2 shows the result of ridge line extraction [3]with principal curvature [11]. When using Eu-clidean distance, lines cannot be sufficiently ex-tracted and there are gaps between lines.

Today semi-automated illustration systemPEAKIT [12] which is used in the archaeologicalapplication has introduced in markets. It createsan image illustrating both geometric and archae-ological features of stone tools. First features areextracted by openness [12]. Then, extracted fea-

psd1

d2

p1

p2Major axis

Min

or a

xis

Figure 3: Euclidean distance and Mahalanobis

distance

tures are traced by manual operation. Therefore,PEAKIT system still has time complexity. If out-lines and ridge lines are extracted and base draw-ing is automatically generated, the creation timeof scale drawing becomes compressed.

2.2 Mahalanobis Distance Metric forPoint Clouds

The connection of feature points is hardly re-quired to make a closed area for base drawing cre-ation. For this purpose, our research introducesa Mahalanobis distance metric for constructingfeature lines. The Mahalanobis distance metricestimates a distance between two feature pointsin space for their relevant features. Units in eachdirection are different because variances in eachdirection are different. The distribution of pointswhich located the same distance from the cen-ter point has a circular or spherical shape in theEuclidean distance metric. Whereas the distri-bution of points which located the same distancefrom the center point has ellipse or ellipsoid inthe Mahalanobis distance metric, depending onthe distribution of the nearby points. Therefore,connecting feature points along the major axis ofan ellipse is efficient to extract closed ridge lines.

Figure 3 shows a comparison between the Eu-clidean distance and the Mahalanobis distance.The ellipse shown in Figure 3 presents the dis-tribution shape of points which are located thesame distance from the center point in the Ma-halanobis distance metric. In Figure 3, selectedpoint ps and its nearest neighbor points p1 andp2 are described. According to the Euclidean dis-tance metric, the p2 is located far from the ps

compared to the p1. However, according to theMahalanobis distance metric, the p1 and p2 is

– 53 –


located same distance from the ps.Given two data points pi and pj , the Maha-

lanobis distance can be calculated as follows:

dMi,j =√

(pi − pj)TC−1(pi − pj). (1)

where C−1 is the inverse covariance matrix of theselected point set. In this work, a covariance ma-trix is derived from the projected feature points.

3 Feature extraction

To achieve our goal, three-dimensional featuresare extracted from the point cloud and the featurelines are constructed using the features.

3.1 Outline Extraction

The outline is extracted first in the same manneras actual scale drawing process. After a viewpointis set, outline extraction is performed using alpha-shape of Point Cloud Library.

3.2 Potential Feature Point Detection

A shape of a flake surface is sometimes created bychance with hitting operation. Thus, the shapearound ridge lines becomes sometimes ambigu-ous. Since local surface properties are suitable fordetection of potential feature points, surface vari-ation at a point is introduced. In our method, ex-traction of the potential feature point is based onPauly et al. [10]. Measured points xi(i = 0, ..., n),where i is the index of point xi and n + 1 is thenumber of input points, is evaluated by surfacevariation σji for point xi as

σji =λ0

λ0 + λ1 + λ2(2)

where λ0,λ1, and λ2 are the eigenvalues of covari-ance matrix C with λ0 6 λ1 6 λ2 and j is thenumber of the neighborhood of point xi. In theexperiment, the number of the neighborhood ofeach point was selected (j = 10, 20, 30, ..., 200).Using the surface variation with the differentnumber of the neighborhood has the advantageto reduce the noise.

To detect potential feature points, the surfacevariation on every point is calculated with the

various number of neighbors. After the calcula-tion, every point xi obtains a set of surface vari-ations (σ10i , σ

20i , σ

30i , ..., σ

200i ). If all surface vari-

ations σji are greater than given threshold ε, thepoint xi is determined the potential feature pointpcy (y = 0, ...,m), where m + 1 is the number of

potential feature points, as shown in the follow-ing Eq.(3). In other words, if above-mentionedcondition is satisfied, point xi can be noted pc

y

because of pcy = xi. Moreover, surface variation

σji of pcy can be noted σjy. Otherwise, that point

is not assumed to the potential feature point.{pcy if all σjy is satisfied ε < σjy

O other(3)

The sphere radius is used to detect neighboringpoints in Section 3.2, 3.3 and 3.4. The numberof neighbors varies with each point depending onthe sphere radius. The sphere radius R is definedby Eq.(4).

R = a · d (4)

where a is a scale value of iteration and d is theaverage distance [3] between the points shown inEq.(5).

d =1

n+ 1

n∑i=0

|xi − q| (5)

where q is one nearest point of xi, and |xi−q| isthe distance between points xi and q.

In this work, each potential feature point pcy

is attributed to corresponding surface variationand covariance matrix in order to extracting fea-ture lines. To extract the point which is usedfor constructing the feature lines, the correspond-ing surface variation is defined for each potentialfeature point. To calculate the Mahalanobis dis-tance, the inverse covariance matrix is calculatedon each potential feature point.

Since every pcy needs to one corresponding sur-

face variation, the corresponding surface varia-tion of potential feature points pc

y is evaluated bythe maximum surface variation of a set of surfacevariations. After the evaluation, every point pc

y

obtains one corresponding surface variation σmaxy .

The second attribute which belongs to pcy is co-

variance matrix Cy. Firstly the tangent plane atpcy is defined by the normal vector that is derived

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(b)(a) (c) (d) (e)Figure 4: The main structure of feature line extraction for a stone tool:(a) A PEAKIT image of a

stone tool [12] (b) extracted outline of the stone tool (c) frontal view of the potential featurepoints (d) frontal view of thinning feature points after Laplacian smoothing operation (e)frontal view of extracted feature lines based on Mahalanobis distance metric.

by the eigenvector corresponding to the minimumeigenvalue. Then the neighbor potential featurepoints of pc

y are projected onto the tangent plane.Then the covariance matrix is constructed fromthe projected potential feature points. The co-variance matrix Cy at selected potential featurepoint is defined as:

Cy =1

k

k∑l=1

(pcl − p)T (pc

l − p) (6)

where k is number of neighbor projected potentialfeature points at pc

y when a is equal to 10 andp is the average point of the projected potentialfeature point set Vl(l = 1, ..., k) shown in Eq.(7):

p =1

k

k∑l=1

(Vl) (7)

Then the inversion of covariance matrix C−1i isderived.

Figure 4(a) shows a PEAKIT image of a stonetool which is extracted feature line from three-dimensional data of an object by using openness[12], (b) shows the extracted outline of the stonetool. (c) is the potential feature points and (d)shows the result of thinning. Finally, (e) is ob-tained, which shows the constructed feature linesusing the Mahalanobis distance. Detail of thin-ning process and constructing feature lines aredescribed section 3.3 and 3.4.

Width

Width

Figure 5: The width example of potential feature

points

3.3 Thinning Feature Point

Potential feature points described in Section 3.2have the width and the density as shown in Figure5. Since our method to apply potential featurepoints, the amount of feature points are detectedaround the sharp edges in Figure 5. To build pre-cise feature lines, some potential feature pointsare selected to the constructing feature lines. Se-lecting a number of potential feature points iscalled the thinning process in this research. Thethinning process is evaluated on the only poten-tial feature points. This section describes how tothin potential feature points.

To construct feature lines, the potential fea-

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Rp1

Feature line

Far point

Close point

p2

Far pointp3

Potential feature points

Neighbor

points

Figure 6: The example of the potential feature

points.

ture points have to be thinned. For this purpose,all potential feature points are thinned using asurface variation weighted Laplacian smoothingfilter.

The ridge points are detected as the poten-tial feature points. However, some potential fea-ture points are extracted far from the real featurelines. Figure 6 shows an example of the far andclose potential feature points. If the potential fea-ture point is far from the feature line, the numberof neighbors, which is inside of the sphere, is few.On the other hand, if the potential feature pointsare close to the feature line, the number of neigh-bors is many.

In the thinning process, some unnecessary fea-ture points can be removed as previous situation.The remaining points that are close to the fea-ture line will be moved closer to the feature lines.The potential feature points are thinned by thefollowing two parts.

Part1: Remove unnecessary potential featurepoints

Step 1. Initialize a = 5

Step 2. Calculate number of the neighbor poten-tial feature points v inside the sphere radiusR.

Step 3. The potential feature points with lessthan three neighboring points are removedinside the sphere radius R.

Step 4. If no remove points this process is fin-ished. If it is exist, goto Step 2.

In the second part, some remained potentialfeature points are selected to the constructing fea-ture lines by the following iteration.

Part2: Thinning process

Step 1. Moving to a new position

- Initialize a = 5

- Calculate number of the neighbor potential fea-ture points v inside the sphere radiusR of pc

y.Let Qf (f = 1, ..., v) be the neighbor poten-tial feature points.

- For the potential feature points pcy, a new posi-

tion pcy is calculated by the averaging of the

neighbor potential feature points by Eq.(8)

pcy =

1

v

v∑f=1

Qf (8)

- All potential feature points pcy are moved to the

calculated new position pcy.

Step 2. Obtaining a point with high surface vari-ation

- Initialize a = 0.5

- Calculate number of the neighbor potential fea-ture points u inside the sphere radius R ofpcy. Let Uz(z = 1, ..., u) be the neighbor po-

tential feature points.

- Create a set (σmax1 , σmax

2 , σmax3 , ..., σmax

u ) of sur-face variations at each neighbor potentialfeature point Uz. The corresponding surfacevariation which is already calculated in theprevious section, is used.

- For the potential feature point pcy, find the po-

tential feature point which has the highestsurface variation from a set of surface varia-tion, as a temporary potential feature pointec. Figure 7 (a) shows the temporary poten-tial feature point ec.

- For all potential feature points pcy, temporary

potential feature points are obtained.

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R

Feature line


Neighbor potential feature

points Uz

py

Temporary potential feature point

(a) Before

(b) After

Feature line

ec

Potential feature points with high surface variation

c

Figure 7: The example of selected potential featurepoints with highest surface variation inneighbor potential feature points

Step 3. Temporary potential feature points areselected as the potential feature points forthe Step 4. Other unselected potential fea-ture points are removed. In this step, num-ber of potential feature points will be re-duced. Green points in Figure 7 (b) showsobtained potential feature points with highsurface variation after this step is finished.

Step 4. If the new potential feature points nolonger selected, the process is finished. If itis selected, goto Step 1. Figure 8 shows theexample of final potential feature points.

The number of the thinning feature point can becontrolled by the parameter of a scale value ofiteration.

After the thinning process, the potential fea-ture points are moved. Therefore, the potentialfeature points are shrunk to the initial position ofpcy. After the potential feature points are moved,

we call these points are thinning feature pointsprz(z = 0, ..., t), where t+1 is the number of thin-

ning feature points.

R

Feature line


pyc

Figure 8: The example of final potential feature

points

These extracted thinning feature points are se-lected to construct the feature lines.

Filtration steps do not significantly affect theposition of the real point. Because feature pointwith the highest surface variation is usually de-tected on the edges of a stone tool.

3.4 Extraction of Feature Lines

In our method, feature line extraction approachcombines a Mahalanobis distance metric algo-rithm. Feature line construction is not an easytask for stone tools and many approaches havebeen proposed [13, 14, 15]. However, base draw-ings cannot be completely connected by usingprevious works.

To construct feature lines, [13, 14, 15] connectthe nearest feature points one by one. As sug-gested in [3], the feature lines are initialized atthe seed points, and arbitrary points obtainedby thinning feature points can be chosen as thenew seed points. To select a point on the featureline, the nearest thinning feature point should befound sequentially.

This study connects thinning feature points de-pendent on the variation of neighboring points.Thinning feature points are selected along theprincipal direction. To find the nearest thinningfeature point, the Mahalanobis distance metricevaluates the distances between the current seedpoint and its nearest thinning feature points. Thedistances between the current seed point ps andthe thinning feature points pr

z are calculated byEq. (9).

dMz,s =

√(pr

z − ps)TC−1s (pr

z − ps). (9)

– 57 –


where the inverse covariance matrix C−1s is al-ready calculated in the section 3.2. Let De(e =1, ..., h), where h is the number of neighbor thin-ning feature point, be the Mahalanobis distancesof the neighboring thinning feature points at ps.The nearest distance is found by a sorting algo-rithm.

The proposed feature line constructing algo-rithm consists of two steps. At first, featurepoints are connected to each other by the Ma-halanobis distance metric regardless of branch.The initial seed point is selected from the begin-ning of thinning feature points. The degree of anangle α defined by three points such as the pre-viously selected thinning feature point ps−1, cur-rent seed point ps and a detected nearest thinningfeature point ps+1, is calculated. Figure 9 showsthe angle α between the aforementioned thinningfeature points. If the α is greater than a giventhreshold value θ, the detected nearest thinningfeature point ps+1 is added to the feature line L.In contrast, the detected angle α is lower than agiven threshold value θ, the next nearest thinningfeature point ps+2 is checked.

L =

{ps+1 if α is satisfied α ≥ θps+2 otherwise

(10)

To construct feature lines, the satisfied thinningfeature point ps+1 should be selected as a newseed point ps based on the Mahalanobis distance.

Second, the distinct feature lines are connectedto each other. End points of the distinct featurelines are connected to the nearest feature pointlocated on the nearest feature line by the Ma-halanobis distance metric. In the Figure 10, theresult of the extracted edges of sample stone toolsare shown.

4 Results and limitation

4.1 Experiment Results

This section describes the result from our exper-iments. The experiments were performed in anIntel Core i7-6700 CPU 3.40 GHz machine with8GB of RAM and Intel(R) HD Graphics 530. Weused the Point Cloud Library (PCL). The input

psps-1

ps+1

Figure 9: An example of constructing feature line.

data is point data of stone tools obtained by four-directional 3D laser scanners [16].

This paper automatically extracts a base draw-ing of stone tools. The stone tools are evalu-ated on the front pose. We tested our proposedmethod on the six actual stone tools. The ex-tracted base drawings of the stone tools are shownin Figure 10. In this figure, first left column showsthe scale drawing and the second column showsthe base drawing which is referred to as groundtruth. The third column shows the result of theproposed method. To reduce the working hoursof creating scale drawing, this paper aims to au-tomatically extract base drawing.

To evaluate the similarity between the groundtruth of base drawing and the extracted basedrawing, the approximation of pixels are mea-sured [17]. Using the real sizes of the stonetools, the images of the ground truth and the ex-tracted base drawing are quantified by the one-pixel width of 0.1mm. Table 1 shows the numberof points, physical properties of the actual stonetools and some evaluation. The similarity of theextracted base drawing and ground truth is de-fined on the distance 0.5mm.

To define whether the manually created basedrawing can be replaced with the automaticallyextracted scale drawing is possible, extractedbase drawing and hand-drawn base drawing arecompared quantitatively. To measure the extrac-tion accuracy, F1 score, the harmonic average ofthe precision and recall (PR), is evaluated in eachstone tool data where the F1 score reaches its bestvalue at 1 and worst score at 0. Figure 11 showsthe F1 scores of the extracted base drawing for allsix stone tools. The best value at 1 of the F1 scoreindicates that the extracted base drawing is thesame as the ground truth, and the extracted basedrawing can be reduce working hours of manu-ally creating a base drawing. F1 score takes both

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Stone tool 1

Stone tool 2

Stone tool 5

Stone tool 6

Stone tool 4

Stone tool 3

Figure 10: The result of the proposed method. The first left column shows the scale drawings of stonetools, second column shows the ground truth of base drawings, the third column shows theresults of the proposed method and fourth column shows the results of the previous work.

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Table 1: Physical size of stone tools and evaluations

Measured Points Stone tool sizes Average

stone tools Height Length Width Similarity distance F1 score

(mm) (mm) (mm) (mm)

1 174393 80.4 31.8 8.1 83.126 0.403 0.876

2 201679 72.5 44.1 10.8 82.373 0.410 0.899

3 144306 68.0 25.2 7.7 94.885 0.402 0.930

4 46469 29.2 25.6 5.1 87.872 0.397 0.925

5 52913 48.8 15.3 4.2 78.028 0.416 0.813

6 45230 37.2 14.1 4.0 87.343 0.412 0.904

Figure 11: Graph of F1 score of extracted lines.

false negative and false positive pixels into ac-count. False negative pixels express undetectededges from the ground truth. False positive pixelsexpress unnecessary edges of the extracted basedrawing in Figure 12(a).

Moreover, average distance d′ is measured byEq.(11).

d′ =

n∑i=0

widi

n∑i=0

wi

(11)

where wi is the overlapped pixel within the dis-tance di. The average distance is measured be-tween the distance 0.1mm to 0.6mm within a step0.1. The result of average distance is shown inTable 1.

We introduced the comparison of automati-

Stone tool 1 Stone tool 2Stone tool 2 Stone tool 3

(a) (b)

Figure 12: The unnecessary edges and undetected

edges of the results.

cally extracted base drawing and ground truthimages. The base drawing of ground truth isdrawn by hand and the proposed base drawingis extracted from the point cloud. When usingthe Euclidean distance metric, feature lines con-structed by the previous method shown in thefourth column of Figure 10 cannot be fully con-structed and a lot of gaps between feature lines.Some unconnected edges with hard to see are en-larged in Figure 10. Moreover, some feature linesare unextracted. Our proposed method can ex-tract closed base drawing and the edges are com-pletely connected. Figure 10 shows the result ofcompletely connected edges which is enlarged andcannot be connected by the previous method. Inthe experiment, the similarities of the stone toolsare between 78.028 to 94.885. Our method canproperly extract long ridge lines. The averagedistances of extracted base drawings are between

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0.397 to 0.416 in all six stone tools.

4.2 Limitation

Figure 13 shows the types of ridge lines in scaledrawing. The limitation of our method is that itis difficult to extract corner small ridge lines of astone tool. The corner small ridge lines need morespecialist knowledge because the shapes aroundsmall ridges are ambiguous. The small ridge linesare magnified in Figure 13.

The unnecessary ridge lines are extracted in thestone tools 2 and 3 shown in Figure 12(a) andsome referenced ridge lines are not extracted inthe stone tool 1 and 2 shown in Figure 12(b). Inthese cases, extracting ambiguous ridge lines arehardly extracted by the geometric approach. Insuch a case, an archaeologist may help to extractsmall ridge lines.

Figure 13: Types of the ridge lines

5 Conclusion

In this paper, a novel method of the extractingbase drawing is proposed. The main idea of themethod is to select a candidate point of featurelines by its Mahalanobis distance. The advantageof our method is that Mahalanobis distance canreference the covariance of the local neighbor set.For stone tools, the feature lines are usually linedup. In such manner, Mahalanobis distance met-ric can extract feature lines more properly thanEuclidean distance metric for stone tools. In thefurther research, more precise extraction for smallridge lines are introduced.

The basic concept of our method has alreadybeen presented in NICOGRAPH 2017 [11] and

this paper extended the concept. We are ex-tremely grateful for lots of efficient advice fromthe paper reviewers.

Acknowledgments

Part of this work was supported by JSPS KAK-ENHI Grant Number JP18H00734.

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Shurentsetseg Erdenebayar

Shurentsetseg Erdenebayar is a doctor coursestudent at the Graduate School of Engineering,Iwate University from 2016. She received the BEdegree in School of Information and Technology,National University of Mongolia in 2007. Shereceived her ME degree in School of Engineer-ing and Applied Sciences, National University ofMongolia in 2014. Her research interest includesgeometric modeling and computer graphics. Sheis a member of The Society for Art and Science.

Kouichi Konno

Kouichi Konno is a professor of Faculty of Engi-neering at Iwate University. He received a BS inInformation Science in 1985 from the Universityof Tsukuba. He earned his Dr.Eng. in preci-sion machinery engineering from the Universityof Tokyo in 1996. He joined the solid model-ing project at RICOH from 1985 to 1999, andthe XVL project at Lattice Technology in 2000.He worked on an associate professor of Facultyof Engineering at Iwate University from 2001 to2009. His research interests include virtual re-ality, geometric modeling, 3D measurement sys-tems, and computer graphics. He is a member ofEurographics.

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Feature Line Extraction of Stone Tools Based on ...Feature extraction methods have been introduced over the past two decades. Gumhold et al. [7] rst formulated curvature using PCA

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