**4.3 Shape matching**

The shape descriptions of two coins are compared by a linear combination of global and local shape matching. The local matching is derived from the difference of Fourier shape descriptors, whereas the correlation coefficient between the curves serves as global measure of shape similarity.

where *i* + *u* might exceed *l* and modulo addition is applied. The maximum *DG* = (1 − max*i*=1...,*<sup>l</sup>* ncc(*i*))/2 is used as a measure of global shape match. Similarly, the MSE is given

Automatic Coin Classification and Identification 141

In the case of MSE, the maximum *DG* = max*i*=1...,*<sup>l</sup>* mse(*i*) is used as a measure of global dissimilarity. The position of the minimum of *DG* is related to the rotation angle between the compared coins. While the MSE requires *l* shifts of the signal and *l* evaluations of eqn. 14, the

where the weighting factor *α* ∈ [0, 1] controls the influence of local and global dissimilarity

In order to be invariant with respect to mirroring, the *DG* is replaced by the minimum of global dissimilarity obtained from matching the signal and the reversed signal. Mirror invariance

A framework for classification and identification based on preselection, classification and Bayesian fusion is presented. For modern coins preselection based on correlation, classification based on Eigenspace representation and prior information, and fusion of obverse and reverse class probabilites is discussed. For identification of ancient coins preselection on shape features and classification based on fusion of shape and a local features based

In the Eigenspace approach, we consider a collection of reference coefficient vectors Ω*<sup>r</sup>* =

corresponding to the coin side to be classified. Classification starts from two observation vectors together with a set of hypotheses, ranked by their corresponding correlation measure. We introduce the following notation with typical values of parameters given in brackets:

(*ωr*1,..., *ωrD*)*T*, *r* = 1, . . . , *R* and an observed coefficient vector Ω*<sup>s</sup>* = (*ω<sup>s</sup>*

enables the matching of coins irrespective of which side is shown on the image.

*dA*(*i*) − *dB*(*i* + *u*)

D*AB* = *αDL* + (1 − *α*)*DG* (15)

<sup>2</sup> (14)

<sup>1</sup>,..., *<sup>ω</sup><sup>s</sup>*

*<sup>D</sup>*)*T*,

*<sup>l</sup>* ∑ *i*=1,...,*l*

mse(*u*) = <sup>1</sup>

NCC is efficiently computed in a more efficient way (Lewis, 1995).

The overall measure of shape dissimilarity becomes

**5. Classification and information fusion**

**5.1 Classification and information fusion of modern coins**

*R* number of reference coefficient vectors (typically *R* = *K* · 20) ,

representations is demonstrated.

*S* number of coin sides (usually *S* = 2),

*<sup>h</sup>* hypothesis number *h* on side *S*,

*K* number of classes (typically *K* = 2 . . . 113), *H* number of hypotheses (usually *H* = 5),

*<sup>r</sup>* distance to *r*-th coefficient vector on side *S*,

*<sup>r</sup>* label of r-th coefficient vector on side *S*.

*D* dimension of coefficient vector (typically *D* = 32),

by

terms.

*Gs*

*ds*

*l s*

Fig. 9. Cumulative sum of Eigenvalues depending on the number of Eigenvectors for different variants of Eigenspace representation.

The mean absolute or squared distance between the magnitude values of the Fourier coefficients is used as local measure of dissimilarity, i.e.

$$D\_L = \sum\_{i=\upsilon,\ldots,l-u} \frac{||\text{sd}\_{\text{A}}(i) - \text{sd}\_{\text{B}}(i)||\_p}{l - u - v + 1} \tag{12}$$

where �·�*p*, *p* ∈ {1, 2} is the *Lp* norm. The lower *v* ≥ 1 and upper offsets *u* ≥ 0 for the Fourier descriptors are small constants and used to limit errors stemming from imprecise circle fitting and quantization noise.

The global shape matching is obtained from a measure of dissimilarity or similarity, e.g. from the mean squared error (MSE) or the normalized cross correlation (NCC) coefficient *ncc*(*u*) for a shift of *u* samples

$$\text{ncc}(u) = \frac{\sum\_{i=1,\ldots,l} d\_A(i) \cdot d\_B(i+u)}{\sqrt{\sum\_{i=1,\ldots,l} d\_A(i)^2 \cdot \sum\_{i=1,\ldots,l} d\_B(i)^2}}\tag{13}$$

14 Will-be-set-by-IN-TECH

(a) Intensity Eigenspace (b) Equalized intensity Eigenspace

(c) Edge Eigenspace (d) Eigenhills

The mean absolute or squared distance between the magnitude values of the Fourier

where �·�*p*, *p* ∈ {1, 2} is the *Lp* norm. The lower *v* ≥ 1 and upper offsets *u* ≥ 0 for the Fourier descriptors are small constants and used to limit errors stemming from imprecise circle fitting

The global shape matching is obtained from a measure of dissimilarity or similarity, e.g. from the mean squared error (MSE) or the normalized cross correlation (NCC) coefficient *ncc*(*u*) for

ncc(*u*) = <sup>∑</sup>*i*=1,...,*<sup>l</sup> dA*(*i*) · *dB*(*<sup>i</sup>* <sup>+</sup> *<sup>u</sup>*)

�sdA(*i*) − sdB(*i*)�*<sup>p</sup>*

<sup>∑</sup>*i*=1,...,*<sup>l</sup> dA*(*i*)<sup>2</sup> · <sup>∑</sup>*i*=1,...,*<sup>l</sup> dB*(*i*)<sup>2</sup>

*<sup>l</sup>* <sup>−</sup> *<sup>u</sup>* <sup>−</sup> *<sup>v</sup>* <sup>+</sup> <sup>1</sup> (12)

(13)

Fig. 9. Cumulative sum of Eigenvalues depending on the number of Eigenvectors for

different variants of Eigenspace representation.

and quantization noise.

a shift of *u* samples

coefficients is used as local measure of dissimilarity, i.e.

*DL* = ∑

*i*=*v*,...,*l*−*u*

where *i* + *u* might exceed *l* and modulo addition is applied. The maximum *DG* = (1 − max*i*=1...,*<sup>l</sup>* ncc(*i*))/2 is used as a measure of global shape match. Similarly, the MSE is given by

$$\text{mse}(\boldsymbol{\mu}) = \frac{1}{l} \sum\_{i=1,\ldots,l} \left( d\_A(i) - d\_B(i+\boldsymbol{\mu}) \right)^2 \tag{14}$$

In the case of MSE, the maximum *DG* = max*i*=1...,*<sup>l</sup>* mse(*i*) is used as a measure of global dissimilarity. The position of the minimum of *DG* is related to the rotation angle between the compared coins. While the MSE requires *l* shifts of the signal and *l* evaluations of eqn. 14, the NCC is efficiently computed in a more efficient way (Lewis, 1995).

The overall measure of shape dissimilarity becomes

$$D\_{AB} = \mathfrak{a}D\_L + (1 - \mathfrak{a})D\_G \tag{15}$$

where the weighting factor *α* ∈ [0, 1] controls the influence of local and global dissimilarity terms.

In order to be invariant with respect to mirroring, the *DG* is replaced by the minimum of global dissimilarity obtained from matching the signal and the reversed signal. Mirror invariance enables the matching of coins irrespective of which side is shown on the image.

#### **5. Classification and information fusion**

A framework for classification and identification based on preselection, classification and Bayesian fusion is presented. For modern coins preselection based on correlation, classification based on Eigenspace representation and prior information, and fusion of obverse and reverse class probabilites is discussed. For identification of ancient coins preselection on shape features and classification based on fusion of shape and a local features based representations is demonstrated.

#### **5.1 Classification and information fusion of modern coins**

In the Eigenspace approach, we consider a collection of reference coefficient vectors Ω*<sup>r</sup>* = (*ωr*1,..., *ωrD*)*T*, *r* = 1, . . . , *R* and an observed coefficient vector Ω*<sup>s</sup>* = (*ω<sup>s</sup>* <sup>1</sup>,..., *<sup>ω</sup><sup>s</sup> <sup>D</sup>*)*T*, corresponding to the coin side to be classified. Classification starts from two observation vectors together with a set of hypotheses, ranked by their corresponding correlation measure. We introduce the following notation with typical values of parameters given in brackets:


*α<sup>j</sup>* for side 2 (e.g. reverse) using

The prior probability *P*2(*G*<sup>1</sup>

to be a good choice.

formula

*P*2(*G*<sup>2</sup>

*<sup>j</sup>* ) = *<sup>P</sup>*2(*G*<sup>1</sup>

*<sup>h</sup>*, *<sup>G</sup>*<sup>2</sup>

difference for coins turned upside down between sides.

*Ps* (*G<sup>s</sup> h*|Ω*<sup>s</sup>*

both sides is done by the product rule (Kittler et al., 1998)

*<sup>P</sup>*(*Gk*|Ω) = *<sup>P</sup>*(*G*<sup>1</sup>

are conditionally independent (Shi & Manduchi, 2003).

fusion of coin side results is also possible.

**5.2.1 Classification of ancient coins**

can be assumed.

**5.2 Classification and information fusion of ancient coins**

*<sup>h</sup>*, *<sup>G</sup>*<sup>2</sup>

*<sup>j</sup>* ) = *<sup>a</sup>* <sup>+</sup> *bP*(*α*<sup>1</sup>

Automatic Coin Classification and Identification 143

The weights *a* and *b* account for the fact that a number of coins exist which appear similar under rotation. The constant term is chosen relatively small, in our study *a* = 0.08 turned out

difference for coins with same orientation on front and back side and around 180 degree angle

The fusion of probabilities estimated of both coin sides and prior information uses the Bayes

We concentrate on the nominator since the denominator is a constant term. Combination of

where probabilities are only derived for hypotheses present for both sides. The product rule of combination is equivalent to naive Bayes fusion of classifiers. Naive Bayes fusion of classifiers in turn coincides with Bayes classification over composite descriptors if the individual features

Apart from shape features, descriptors based on local features were used for classification and identification of ancient coins in related papers (Huber-Mörk et al., 2008; Kampel et al., 2009; Zaharieva et al., 2007). Local features based on SIFT (Lowe, 2004) were used in preselection for shape feature matching. Probabilities are derived from ranked results from shape matching and fused with results from local features based matching. Fusion of ancient coins is performed similar to modern coins. In cases were images of both coin sides are available,

Local features based approaches and shape descriptors deliver distance measures between the coin in question and all other images in the database. In this case, a two-stage rank based strategy is possible, i.e. a small subset is preselected based on shape comparison and further processed using local features based matching (Huber-Mörk et al., 2008). Here, we follow a strategy combining probabilities which are derived from distance measures through a rule of combination (Huber-Mörk et al., 2010), e.g. the product rule Kittler et al. (1998). Conditional independence between shape and local features, as well as between coin sides,


*<sup>i</sup>*=<sup>1</sup> *<sup>P</sup>S*(Ω*s*|*G<sup>s</sup>*

*<sup>j</sup>* <sup>|</sup>Ω1, <sup>Ω</sup>2) = *<sup>P</sup>*1(*G*<sup>1</sup>

) = *<sup>P</sup>s*(Ω*<sup>s</sup>*

∑*<sup>H</sup>*

*<sup>h</sup>* <sup>=</sup> *<sup>G</sup>*<sup>2</sup>

*<sup>h</sup>*, *<sup>α</sup>*<sup>2</sup>

*<sup>j</sup>* ) is assumed normally distributed around zero angle

*i*)*Ps*(*G<sup>s</sup>*

*<sup>h</sup>*|Ω1) · *<sup>P</sup>*2(*G*<sup>2</sup>

*<sup>j</sup>*), *a* + *b* = 1 (19)

*<sup>i</sup>*) (20)

*<sup>h</sup>*|Ω2) (21)

The selection of the parameter *R* is motivated by the balance between representing occurring variation within a coin and efficient construction of the Eigenspace. The Eigenproblem for general *<sup>R</sup>* <sup>×</sup> *<sup>R</sup>* matrices require on the order of *<sup>R</sup>*<sup>3</sup> arithmetic operations (Pan & Chen, 1999), accordingly a small *R* is preferred. The number of coin sides *S* is obviously equal to 2. The maximum number of classes per Eigenspace is determined by preselection of classes, usually based on measurements of diameter and thickness, if available. This means multiple Eigenspaces, each of which holding a limited number of classes to discriminate, are build and selected from geometric measurements (Huber et al., 2005). The number of hypotheses *H* generated from ranking of correlation values was limited to 5. This decision is motivated by observing the necessary number of hypotheses to ensure that the valid decision is included in the considered set of hypotheses. From a validated set of coins, it was observed, that the correct coin class is contained in 92.62, 95.15, 96.91, 98.04 or 98.88% of all cases when retaining the first 1,2,3,4 or 5 hypotheses, respectively. This means, a classification scheme considering the highest ranking result only would not do better than 92.62%. On the other hand, considering 5 hypotheses limits a classification and fusion system to 98.88%, which is a reasonable limit for practical application.

#### **5.1.1 Classification of modern coins**

The distance to the *r*-th coefficient vector on side s is calculated by the Euclidean distance

$$d\_r^s = \sum\_{i=1}^D (\omega\_i^s - \omega\_{ri})^2 \tag{16}$$

The class labels *l s <sup>r</sup>* ∈ {1, . . . , *<sup>K</sup>*} correspond to the distances *<sup>d</sup><sup>s</sup> <sup>r</sup>*. The distance for hypothesis *h* on side *s* is derived as the average distance to coefficient vectors with class label *G<sup>s</sup> <sup>h</sup>* ∈ {1, . . . , *K*}

$$D\_h^s = \frac{1}{N\_h} \sum\_{r=1}^{R} d\_r^s \delta\_{rh'}^s \qquad \delta\_{rh}^s = \begin{cases} 1 \text{ if} \quad l\_r^s = G\_h^s\\ 0 \text{ else} \end{cases} \tag{17}$$

where *Nh* is the number of training samples for class *G<sup>s</sup> <sup>h</sup>*. The conditional probability for observation Ω*<sup>s</sup>* depending on hypothesis *G<sup>s</sup> <sup>h</sup>* on side *s* is estimated to be inversely proportional to the distance *D<sup>s</sup> h*

$$P^s(\Omega^s | \mathbb{G}\_h^s) = 1/\left(D\_h^s \sum\_{i=1}^H 1/D\_i^s\right) \tag{18}$$

where the summation term in the denominator accounts for normalization.

#### **5.1.2 Information fusion of modern coins**

A-priori probabilities *Ps*(*G<sup>s</sup> <sup>h</sup>*) are either set to equal probability, e.g. *<sup>P</sup>*1(*G*<sup>1</sup> *<sup>h</sup>*) = 1/*H* for side 1 and *P*1(*G*<sup>1</sup> *<sup>h</sup>*) = 1/*H* for side 2, respectively. If the coins are imaged in way that there is no rotation between obverse and reverse images, one can make use of this knowledge as modern coins are characterized by either 0 or 180 degrees of rotation between sides. In this case, the *Ps*(*G<sup>s</sup> <sup>h</sup>*) are derived from the difference in rotation angle *α<sup>h</sup>* for side 1 (e.g. obverse) and angle *α<sup>j</sup>* for side 2 (e.g. reverse) using

16 Will-be-set-by-IN-TECH

The selection of the parameter *R* is motivated by the balance between representing occurring variation within a coin and efficient construction of the Eigenspace. The Eigenproblem for general *<sup>R</sup>* <sup>×</sup> *<sup>R</sup>* matrices require on the order of *<sup>R</sup>*<sup>3</sup> arithmetic operations (Pan & Chen, 1999), accordingly a small *R* is preferred. The number of coin sides *S* is obviously equal to 2. The maximum number of classes per Eigenspace is determined by preselection of classes, usually based on measurements of diameter and thickness, if available. This means multiple Eigenspaces, each of which holding a limited number of classes to discriminate, are build and selected from geometric measurements (Huber et al., 2005). The number of hypotheses *H* generated from ranking of correlation values was limited to 5. This decision is motivated by observing the necessary number of hypotheses to ensure that the valid decision is included in the considered set of hypotheses. From a validated set of coins, it was observed, that the correct coin class is contained in 92.62, 95.15, 96.91, 98.04 or 98.88% of all cases when retaining the first 1,2,3,4 or 5 hypotheses, respectively. This means, a classification scheme considering the highest ranking result only would not do better than 92.62%. On the other hand, considering 5 hypotheses limits a classification and fusion system to 98.88%, which is a

The distance to the *r*-th coefficient vector on side s is calculated by the Euclidean distance

*rh*, *<sup>δ</sup><sup>s</sup>*

*<sup>h</sup>*) = 1/(*D<sup>s</sup>*

rotation between obverse and reverse images, one can make use of this knowledge as modern coins are characterized by either 0 or 180 degrees of rotation between sides. In this case, the

*<sup>h</sup>*) are derived from the difference in rotation angle *α<sup>h</sup>* for side 1 (e.g. obverse) and angle

*<sup>i</sup>* − *ωri*)

*rh* =

*h H* ∑ *i*=1

*<sup>h</sup>*) are either set to equal probability, e.g. *<sup>P</sup>*1(*G*<sup>1</sup>

*<sup>h</sup>*) = 1/*H* for side 2, respectively. If the coins are imaged in way that there is no

 1 if *l s <sup>r</sup>* = *G<sup>s</sup> h*

1/*D<sup>s</sup>*

<sup>2</sup> (16)

0 else (17)

*<sup>h</sup>*. The conditional probability for

*<sup>i</sup>*) (18)

*<sup>h</sup>* on side *s* is estimated to be inversely proportional

*<sup>r</sup>*. The distance for hypothesis *h* on

*<sup>h</sup>* ∈ {1, . . . , *K*}

*<sup>h</sup>*) = 1/*H* for side

*ds <sup>r</sup>* = *D* ∑ *i*=1 (*ω<sup>s</sup>*

*<sup>r</sup>* ∈ {1, . . . , *<sup>K</sup>*} correspond to the distances *<sup>d</sup><sup>s</sup>*

*R* ∑ *r*=1 *ds rδs*

side *s* is derived as the average distance to coefficient vectors with class label *G<sup>s</sup>*

reasonable limit for practical application.

**5.1.1 Classification of modern coins**

*s*

*Ds <sup>h</sup>* <sup>=</sup> <sup>1</sup> *Nh*

observation Ω*<sup>s</sup>* depending on hypothesis *G<sup>s</sup>*

**5.1.2 Information fusion of modern coins**

*h*

A-priori probabilities *Ps*(*G<sup>s</sup>*

where *Nh* is the number of training samples for class *G<sup>s</sup>*

*Ps* (Ω*<sup>s</sup>* |*Gs*

where the summation term in the denominator accounts for normalization.

The class labels *l*

to the distance *D<sup>s</sup>*

1 and *P*1(*G*<sup>1</sup>

*Ps*(*G<sup>s</sup>*

$$P^2(G\_j^2) = P^2(G\_{h'}^1 G\_j^2) = a + bP(a\_{h'}^1 a\_j^2), \quad a + b = 1 \tag{19}$$

The weights *a* and *b* account for the fact that a number of coins exist which appear similar under rotation. The constant term is chosen relatively small, in our study *a* = 0.08 turned out to be a good choice.

The prior probability *P*2(*G*<sup>1</sup> *<sup>h</sup>*, *<sup>G</sup>*<sup>2</sup> *<sup>j</sup>* ) is assumed normally distributed around zero angle difference for coins with same orientation on front and back side and around 180 degree angle difference for coins turned upside down between sides.

The fusion of probabilities estimated of both coin sides and prior information uses the Bayes formula

$$P^{s}(G\_{h}^{s}|\Omega^{s}) = \frac{P^{s}(\Omega^{s}|G\_{h}^{s})P^{s}(G\_{h}^{s})}{\sum\_{i=1}^{H}P^{s}(\Omega^{s}|G\_{i}^{s})P^{s}(G\_{i}^{s})} \tag{20}$$

We concentrate on the nominator since the denominator is a constant term. Combination of both sides is done by the product rule (Kittler et al., 1998)

$$P(G\_k|\Omega) = P(G\_h^1 = G\_j^2|\Omega^1, \Omega^2) = P^1(G\_h^1|\Omega^1) \cdot P^2(G\_h^2|\Omega^2) \tag{21}$$

where probabilities are only derived for hypotheses present for both sides. The product rule of combination is equivalent to naive Bayes fusion of classifiers. Naive Bayes fusion of classifiers in turn coincides with Bayes classification over composite descriptors if the individual features are conditionally independent (Shi & Manduchi, 2003).

#### **5.2 Classification and information fusion of ancient coins**

Apart from shape features, descriptors based on local features were used for classification and identification of ancient coins in related papers (Huber-Mörk et al., 2008; Kampel et al., 2009; Zaharieva et al., 2007). Local features based on SIFT (Lowe, 2004) were used in preselection for shape feature matching. Probabilities are derived from ranked results from shape matching and fused with results from local features based matching. Fusion of ancient coins is performed similar to modern coins. In cases were images of both coin sides are available, fusion of coin side results is also possible.

#### **5.2.1 Classification of ancient coins**

Local features based approaches and shape descriptors deliver distance measures between the coin in question and all other images in the database. In this case, a two-stage rank based strategy is possible, i.e. a small subset is preselected based on shape comparison and further processed using local features based matching (Huber-Mörk et al., 2008). Here, we follow a strategy combining probabilities which are derived from distance measures through a rule of combination (Huber-Mörk et al., 2010), e.g. the product rule Kittler et al. (1998). Conditional independence between shape and local features, as well as between coin sides, can be assumed.

**6.1 Results for modern coins**

**6.1.1 Direct edge matching based approach**

**6.1.2 Edge Eigenspace based matching**

Image data of modern coins was acquired trough a coin collection which took place in the course of the implementation of the Euro currency in twelve European countries at the turn of the year 2001 to 2002. During this campaign 300 tons of coins coming from virtually all countries of the world but predominately from the twelve Euro member states have been collected by the Dagobert coin sorting system. Results are presented for two samples of 11 949 coins and 12 949 coins, respectively, taken randomly from the collected money. Those coins have been manually labeled into valid and invalid coins. Valid coins are coins from 30 countries including most European countries, the USA, Canada and Japan. The portion of valid coins in the sample was 91.6% or 94.15%, depending on the considered set. The remaining 8.4% or 5.85%, respectively, are dominated by coins from Asia, South-America, Africa and former socialist countries. Figure 1 (b) shows examples for these coin images.

Automatic Coin Classification and Identification 145

Apart from image sensors for obverse and reverse coin sides sensors for thickness and area measurements are present in the Dagobert system. Based on their measurements a first rough pre-selection of potential master coins is determined, in our case a set of 6 coins are preselected. This provides us with a set of master coins that have almost the same diameter and that have to be distinguished. A total number of 12949 coin images were validated manually as well as tested against 913 master coin patterns of all diameters in the recognition

> Valid coins Correct classification False classification False Rejection 94.15% 79.83% 0.10% 14.22% Invalid coins False acceptance Correct rejection 5.85% 0.10% 5.75%

The Dagobert system was used to sort several tons of coins and is able to meet the real-time conditions, i.e. to process 5 to 6 coins per second. Using the obverse and reverse face for the recognition task, approximately 85% of the material is either sorted into classes defined in the recognition pattern set, i.e. the set of valid coins, which contained around 1500 patterns of coin faces, or is correctly rejected. Random tests performed on classified sets of coins indicate

We discuss results including rejection based on the a-posteriori probability *P*(*Gk*|Ω). A coin pattern Ω is accepted to be of class *Gk* if *P*(*Gk*|Ω) ≥ *t*, and rejected if *P*(*Gk*|Ω) *< t* , where *t* ∈ [0, 1] is the rejection threshold. The parameter *t* is used to tune the system towards the desired trade-off between false rejection and false acceptance. The trade-off between false acceptance rate (FAR) and false rejection rate (FRR) is an important performance measure in verification and recognition systems. False acceptance of invalid coins is measured by the

Acceptance Rejection

pattern set. Table1 shows the results. The set of incorrectly sorted coins is quite small.

All coins Correct descisions 100% 85.58% Table 1. Classification results for modern coins using edge based matching

that we seem to meet the goal of having less than 0.1% false classifications.

From ranking the shape dissimilarity *DAB* for shapes given in eqn. 15 for shape *B* matched to shape *A* results in a preselection set P. From an observed shape description *A* we derive a conditional probability for a coin side label L assigned to *B*. The conditional probability for a *Pshape*(L|*A*) is estimated to be inversely proportional to the dissimilarity given in eqn. 15 between coin *A* and coin *B* labelled L:

$$P\_{shape}(\mathcal{L}|A) = \frac{1}{\mathbf{D}\_{AB}\sum\_{\mathbb{C}} \mathbf{1}/\mathbf{D}\_{A\mathbb{C}}} \tag{22}$$

where the summation term in the denominator accounts for normalization.

A similar argument is applied to derive a conditional probability for observed local descriptors *X* matched to local descriptors *Y* labeled L and corresponding to an image contained in the preselection set P:

$$P\_{local}(\mathcal{L}|\mathbf{X}) = \frac{M\_{XY}}{\sum\_{\mathbf{Z} \in \mathcal{P}} M\_{X\mathbf{Z}}} \tag{23}$$

where *MXY* denotes the number of matches between the query image with local descriptors *X* and the coin side image with local descriptors *Y* and the denominator accounts for normalization.

#### **5.2.2 Information fusion of ancient coins**

As local and shape features describe different properties of a coin, it is reasonable to assume statistical independence between shape and local feature measurements. Thus, the combination is performed by the product rule Kittler et al. (1998):

$$P(\mathcal{L}|A,X) = P(\mathcal{L}\_{shape} = \mathcal{L}\_{local}|A,X) \tag{24}$$

$$= P\_{shape}(\mathcal{L}|A) \cdot P\_{local}(\mathcal{L}|X)$$

where L*shape* and L*local* are labels derived from shape and local descriptions.

The idea of fusion of different descriptor outputs is extended to a fusion of more than one image of a coin. Typically, a coin is presented by images of the obverse and reverse side. Fusion of coin sides is obtained in a straightforward fashion. Eqn. 24 is extended to the following four terms

$$P(\mathcal{L}|A\_{i\prime}X\_{i}) = P\_{\text{shape}}(\mathcal{L}|A\_{1}) \cdot P\_{\text{local}}(\mathcal{L}|X\_{1}) \cdot P\_{\text{shape}}(\mathcal{L}|A\_{2}) \cdot P\_{\text{local}}(\mathcal{L}|X\_{2}) \tag{25}$$

where *Ai* and *Xi* corresponds to shape and local feature descriptions of the *i*−th coin side.

#### **6. Results**

In this section we summarize results for classification of modern coins and identification of ancient coins.

### **6.1 Results for modern coins**

18 Will-be-set-by-IN-TECH

From ranking the shape dissimilarity *DAB* for shapes given in eqn. 15 for shape *B* matched to shape *A* results in a preselection set P. From an observed shape description *A* we derive a conditional probability for a coin side label L assigned to *B*. The conditional probability for a *Pshape*(L|*A*) is estimated to be inversely proportional to the dissimilarity given in eqn. 15

A similar argument is applied to derive a conditional probability for observed local descriptors *X* matched to local descriptors *Y* labeled L and corresponding to an image

*Plocal*(L|*X*) = *MXY*

where *MXY* denotes the number of matches between the query image with local descriptors *X* and the coin side image with local descriptors *Y* and the denominator accounts for

As local and shape features describe different properties of a coin, it is reasonable to assume statistical independence between shape and local feature measurements. Thus, the

The idea of fusion of different descriptor outputs is extended to a fusion of more than one image of a coin. Typically, a coin is presented by images of the obverse and reverse side. Fusion of coin sides is obtained in a straightforward fashion. Eqn. 24 is extended to the

where *Ai* and *Xi* corresponds to shape and local feature descriptions of the *i*−th coin side.

In this section we summarize results for classification of modern coins and identification of

= *Pshape*(L|*A*)· *Plocal*(L|*X*)

*P*(L|*Ai*, *Xi*) = *Pshape*(L|*A*1) · *Plocal*(L|*X*1) · *Pshape*(L|*A*2) · *Plocal*(L|*X*2) (25)

<sup>D</sup>*AB* <sup>∑</sup>*C*∈P 1/D*AC*

<sup>∑</sup>*Z*∈P *MXZ*

*P*(L|*A*, *X*) = *P*(L*shape* = L*local*|*A*, *X*) (24)

(22)

(23)

*Pshape*(L|*A*) = <sup>1</sup>

where the summation term in the denominator accounts for normalization.

combination is performed by the product rule Kittler et al. (1998):

where L*shape* and L*local* are labels derived from shape and local descriptions.

between coin *A* and coin *B* labelled L:

contained in the preselection set P:

**5.2.2 Information fusion of ancient coins**

normalization.

following four terms

**6. Results**

ancient coins.

Image data of modern coins was acquired trough a coin collection which took place in the course of the implementation of the Euro currency in twelve European countries at the turn of the year 2001 to 2002. During this campaign 300 tons of coins coming from virtually all countries of the world but predominately from the twelve Euro member states have been collected by the Dagobert coin sorting system. Results are presented for two samples of 11 949 coins and 12 949 coins, respectively, taken randomly from the collected money. Those coins have been manually labeled into valid and invalid coins. Valid coins are coins from 30 countries including most European countries, the USA, Canada and Japan. The portion of valid coins in the sample was 91.6% or 94.15%, depending on the considered set. The remaining 8.4% or 5.85%, respectively, are dominated by coins from Asia, South-America, Africa and former socialist countries. Figure 1 (b) shows examples for these coin images.

## **6.1.1 Direct edge matching based approach**

Apart from image sensors for obverse and reverse coin sides sensors for thickness and area measurements are present in the Dagobert system. Based on their measurements a first rough pre-selection of potential master coins is determined, in our case a set of 6 coins are preselected. This provides us with a set of master coins that have almost the same diameter and that have to be distinguished. A total number of 12949 coin images were validated manually as well as tested against 913 master coin patterns of all diameters in the recognition pattern set. Table1 shows the results. The set of incorrectly sorted coins is quite small.


Table 1. Classification results for modern coins using edge based matching

The Dagobert system was used to sort several tons of coins and is able to meet the real-time conditions, i.e. to process 5 to 6 coins per second. Using the obverse and reverse face for the recognition task, approximately 85% of the material is either sorted into classes defined in the recognition pattern set, i.e. the set of valid coins, which contained around 1500 patterns of coin faces, or is correctly rejected. Random tests performed on classified sets of coins indicate that we seem to meet the goal of having less than 0.1% false classifications.

## **6.1.2 Edge Eigenspace based matching**

We discuss results including rejection based on the a-posteriori probability *P*(*Gk*|Ω). A coin pattern Ω is accepted to be of class *Gk* if *P*(*Gk*|Ω) ≥ *t*, and rejected if *P*(*Gk*|Ω) *< t* , where *t* ∈ [0, 1] is the rejection threshold. The parameter *t* is used to tune the system towards the desired trade-off between false rejection and false acceptance. The trade-off between false acceptance rate (FAR) and false rejection rate (FRR) is an important performance measure in verification and recognition systems. False acceptance of invalid coins is measured by the

incorrect decisions FCR, FRR and FAR are equally weighted and we aim at minimization of the sum of false decisions FD=FCR+FAR+FAR. We find the optimum value for the rejection threshold t as the minimum of FD. This can be seen from Fig. 10 (c), in which the minimum of FD is found for t = 0.006. At the same time correct decisions, i.e. correct classification and

Automatic Coin Classification and Identification 147

Considering only valid coins, i.e. the 91.6% coins included in the 30 countries mentioned above, and using no rejection mechanism, correct classification was made for 98.27% of valid coins, which is close to the practical optimum of 98.88% mentioned in Section 5.1 With rejection at the chosen level of t=0.006, a percentage of correct classification of 94.54%, 0.53% false classification and 4.93% false rejection is achieved for valid coins. Considering only invalid coins, i.e. the 8.4% coins not included in the 30 countries mentioned above, and rejection at the chosen level of t=0.006 classification into any of the known coin classes happens for 20.47% of the unknown coins. Correct rejection of unknown coins is performed for 79.53% of invalid coins. Examining at the mixed sample, a correct decision, i.e. correct classification or rejection, was made for 93.23% of all coins. False decisions, i.e. either false classification, false rejection or false acceptance, took place for 6.77% of all coins. Table 2 summarizes the

> Valid coins Correct classification False classification False Rejection 91.6% 86.64% 0.49% 4.52% Invalid coins False acceptance Correct rejection 8.4% 1.76% 6.59%

Table 2. Classification results for modern coins using edge Eigenspace based matching.

To evaluate our approach on coin data, we use an image database provided by the Fitzwilliam Museum, Cambridge, UK, which consists of 2400 images of 240 different ancient coins of the same class. Figure 1 (b) shows four of the coins contained in the data set. Each row shows the same coin acquired by different devices at varying conditions and different orientations. In particular, each coin side was acquired at three different angles of rotation using a scanner device and two acquisitions were made using a digital camera and varying illumination. At first sight, all coins bear the same characteristics. However, the coins shown in the different rows are produced by different dies. What makes this data set special and ideal to thoroughly test identification methods, is that all the coins are very similar. All the images are issued in the time of, or at least in the name of, Alexander the Great who came to power in Macedonia in 336 BCE and died as emperor in 323 BCE. Some of the coins are from much later and were minted in places around the Black Sea, in Egypt, in modern-day Turkey, Iran, etc. All coins follow the same basic standard: on the obverse side there is the head of Heracles in a lion-skin. The reverse side shows the god Zeus, seated left on a throne. Nevertheless, there is a huge range of detail in the minor variations that experts use to deduce the mint and date of the coin.

All coins Correct descisions 100% 92.23%

Acceptance Rejection

correct rejection rates, are maximized.

final results.

**6.2 Results for ancient coins**

FAR, and false rejection for valid coins is measured by FRR. A classification method should maximize correct classification for valid coins and correct rejection for invalid coins. Apart from FAR and FRR the case of wrong classification of a valid coin is also an undesired event termed false classification rate (FCR).

Fig. 10. Results for modern coin classification.

0.1 0.2 0.3 0.4

Figure 10 (a) shows the distribution of fused probabilities for correctly classified valid coins as the solid line. Incorrectly classified valid coins are shown by the dashed line. The fused probability distribution for invalid coins is represented by the dotted line. Selection of threshold *t* on governs FAR, FCR and FRR, e.g. increasing t reduces FAR and FCR and increases FRR. From a receiver operator characteristics (ROC) curve, as shown in Fig. 10 (b), the tradeoff between FCR plus FAR and FRR can be identified. An operating point, corresponding to a specific *t*, is found on the ROC curve, e.g. for perfect classification with FAR + FCR ≈ 0, a very high FRR has to be taken into account (i.e. FRR > 0.5). If the

<sup>0</sup> 0.01 0.1 <sup>1</sup> <sup>0</sup>

Correct Classification + Correct Rejection

rates on rejection threshold

Rejection Probability Threshold

(c) Dependency of correct and false descision

20 Will-be-set-by-IN-TECH

FAR, and false rejection for valid coins is measured by FRR. A classification method should maximize correct classification for valid coins and correct rejection for invalid coins. Apart from FAR and FRR the case of wrong classification of a valid coin is also an undesired event

> 0.94 0.95 0.96 0.97 0.98 0.99 1

<sup>0</sup> 0.01 0.1 <sup>1</sup> <sup>0</sup>

False Classification + False Rejection + False Acceptance

Correct Classification + Correct Rejection

rates on rejection threshold

Rejection Probability Threshold

(c) Dependency of correct and false descision

Figure 10 (a) shows the distribution of fused probabilities for correctly classified valid coins as the solid line. Incorrectly classified valid coins are shown by the dashed line. The fused probability distribution for invalid coins is represented by the dotted line. Selection of threshold *t* on governs FAR, FCR and FRR, e.g. increasing t reduces FAR and FCR and increases FRR. From a receiver operator characteristics (ROC) curve, as shown in Fig. 10 (b), the tradeoff between FCR plus FAR and FRR can be identified. An operating point, corresponding to a specific *t*, is found on the ROC curve, e.g. for perfect classification with FAR + FCR ≈ 0, a very high FRR has to be taken into account (i.e. FRR > 0.5). If the

1−(False Classification Rate + False Acceptance Rate)

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 0.93

(b) Receiver operator curve

False Rejection Rate

termed false classification rate (FCR).

50

classification result

100

150

Frequency

200

250

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 <sup>0</sup>

Correct Classification Wrong Classification Unknown Coin

Fused Probability

(a) Distribution with respect to fused

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 10. Results for modern coin classification.

Rate

incorrect decisions FCR, FRR and FAR are equally weighted and we aim at minimization of the sum of false decisions FD=FCR+FAR+FAR. We find the optimum value for the rejection threshold t as the minimum of FD. This can be seen from Fig. 10 (c), in which the minimum of FD is found for t = 0.006. At the same time correct decisions, i.e. correct classification and correct rejection rates, are maximized.

Considering only valid coins, i.e. the 91.6% coins included in the 30 countries mentioned above, and using no rejection mechanism, correct classification was made for 98.27% of valid coins, which is close to the practical optimum of 98.88% mentioned in Section 5.1 With rejection at the chosen level of t=0.006, a percentage of correct classification of 94.54%, 0.53% false classification and 4.93% false rejection is achieved for valid coins. Considering only invalid coins, i.e. the 8.4% coins not included in the 30 countries mentioned above, and rejection at the chosen level of t=0.006 classification into any of the known coin classes happens for 20.47% of the unknown coins. Correct rejection of unknown coins is performed for 79.53% of invalid coins. Examining at the mixed sample, a correct decision, i.e. correct classification or rejection, was made for 93.23% of all coins. False decisions, i.e. either false classification, false rejection or false acceptance, took place for 6.77% of all coins. Table 2 summarizes the final results.


Table 2. Classification results for modern coins using edge Eigenspace based matching.

## **6.2 Results for ancient coins**

To evaluate our approach on coin data, we use an image database provided by the Fitzwilliam Museum, Cambridge, UK, which consists of 2400 images of 240 different ancient coins of the same class. Figure 1 (b) shows four of the coins contained in the data set. Each row shows the same coin acquired by different devices at varying conditions and different orientations. In particular, each coin side was acquired at three different angles of rotation using a scanner device and two acquisitions were made using a digital camera and varying illumination. At first sight, all coins bear the same characteristics. However, the coins shown in the different rows are produced by different dies. What makes this data set special and ideal to thoroughly test identification methods, is that all the coins are very similar. All the images are issued in the time of, or at least in the name of, Alexander the Great who came to power in Macedonia in 336 BCE and died as emperor in 323 BCE. Some of the coins are from much later and were minted in places around the Black Sea, in Egypt, in modern-day Turkey, Iran, etc. All coins follow the same basic standard: on the obverse side there is the head of Heracles in a lion-skin. The reverse side shows the god Zeus, seated left on a throne. Nevertheless, there is a huge range of detail in the minor variations that experts use to deduce the mint and date of the coin.

Table 3 shows the identification rates for the single descriptors and their combination with a leave-one-out evaluation scheme. The shape-based preselection of size 10 was performed accordingly to the given side of the test coin image. The DCSM alone gives an identification rate of 97.04% on the whole data set of 2400 images. For a preselection size of 10, there are only 13 cases (0.54%) where the correct coin is not contained in the preselected set. Consequently, local feature matching on the preselected set and fusion with the label probabilities from

Automatic Coin Classification and Identification 149

Descriptor DCSM SIFT DCSM + SIFT Accuracy 97.04% 71.77% 98.54%

Usually, a reference object, e.g. a cone, a square prism or a cylinder, is scanned and measured manually when the accuracy of the scanner needs to be calculated. After gathering all the dimensions, the values can be compared to the values determined from the 3D reconstruction. Additionally, scanner resolution evaluations can be made. Due to the fact that in our case the scanned object is small and both the surface and the shape of historical coins are not regular or flat, many dimensions cannot be measured precisely (e.g. coin profile details). Since we cannot provide the same accurate values for coins as we can provide for known objects, like cones or cylinders, our results will be based on a comparison between manually measured values from ancient coins and the values determined from the 3D model counterparts. As

evaluation parameters, the maximal diameter and the volume of each coin are used.

The models are analyzed using Geomagic Studio, a commercial software for 3D data processing. The volumes of the original coins are calculated manually after computing the density by using the uplift of the coin in water and by measuring the weight of the coin. The compared diameter value represents the maximal existing value on the coin's surface. The maximal diameter from a real world coin is also determined manually. From a 3D model, the volume can be calculated using Geomagic Studio. The maximum diameter can be computed by segmenting one side of the coin and taking the largest distance between two border points. Because of the irregular shape of some coins, both the obverse and the reverse side of a coin

In total, we scanned 22 coins: 14 ancient coins from the Roman era and 8 tornese silver coins from medieval age. Figure 12 (a) shows the volume of both the original ancient coins using the water volume calculation and their 3D model counterparts using Geomagic Studio. The maximum difference between manual and automatic measurements is 36.24 *mm*3. The smallest difference between real-world data and the data gathered from 3D models is 0.57 *mm*3. Figure 12 (b) shows the maximum diameter of both the real world manually measured one and the value calculated by using 3D models in Geomagic Studio. A maximum difference of 1.12 mm is measured, two coins have exactly the same diameter measured from 3D models and from real-world data. Table 4 shows maximum difference, minimum difference, and the

mean variation coefficient of all volume and diameter measurements.

Table 3. Identification rates derived from leave-one-out accuracy estimation.

DCSM lead to an identification rate of 98.54%.

**6.2.2 3D extensions**

must be taken into account.

#### **6.2.1 2D matching**

It takes 0.006 seconds to compare two coins based on their shape description on a Intel Core 2 CPU with 2.5 GHz. Therefore, shape matching is suited as a preselection step to the less efficient matching based on local features which typically takes two orders of magnitude longer (Bay et al., 2006). The size of the preselection set is determined experimentally from Precision-Recall curves. Recall measures the ratio given by true positives divided by the sum of true positives and false negatives, i.e. *rec* = *TP*/(*TP* + *FN*) and precision is given by *prec* = *TP*/(*TP* + *FP*), where *FP* is the number of false positives. Figure 11 (a) shows plots of precision versus recall for the test set of 240 different images containing 10 images of each coin. Different settings of the shape matching weight parameter *α* show that a relatively large value of *α*, which directs the matching dissimilarity towards more local influence, performs best. In order to obtain a preselection set of moderate size and high quality, i.e. the coin in question should likely be contained, a high recall is aspired. This is obtained by selecting the set size corresponding to the sudden decrease in Fig. 11 (a). Figure 11 (b) shows that this sudden decrease in precision versus recall corresponds to a preselection set size of 9 to 10 images.

Fig. 11. Results for ancient coin classification based on shape.

We combine shape and local descriptors to increase the identification rate. Preselection based on shape matching allows for the restriction of required comparisons for local features matching. As a result we achieve speed up of the identification process and higher accuracy rate. Since our shape descriptor is mirroring invariant, preselection can be performed either on the whole available coin data, i.e. the preselected set can contain images of the second coin side, or preselection can be performed on the relevant coin side directly.

As a conclusion the preselection size was set to 10. Therefore, for the experiments presented here, *Pshape*(L|*A*) is computed for the 10 images with lowest dissimilarity and *Plocal*(L|*X*) for the same 10 images. The final decision is made according to the product rule given in Equ 24. Table 3 shows the identification rates for the single descriptors and their combination with a leave-one-out evaluation scheme. The shape-based preselection of size 10 was performed accordingly to the given side of the test coin image. The DCSM alone gives an identification rate of 97.04% on the whole data set of 2400 images. For a preselection size of 10, there are only 13 cases (0.54%) where the correct coin is not contained in the preselected set. Consequently, local feature matching on the preselected set and fusion with the label probabilities from DCSM lead to an identification rate of 98.54%.


Table 3. Identification rates derived from leave-one-out accuracy estimation.

### **6.2.2 3D extensions**

22 Will-be-set-by-IN-TECH

It takes 0.006 seconds to compare two coins based on their shape description on a Intel Core 2 CPU with 2.5 GHz. Therefore, shape matching is suited as a preselection step to the less efficient matching based on local features which typically takes two orders of magnitude longer (Bay et al., 2006). The size of the preselection set is determined experimentally from Precision-Recall curves. Recall measures the ratio given by true positives divided by the sum of true positives and false negatives, i.e. *rec* = *TP*/(*TP* + *FN*) and precision is given by *prec* = *TP*/(*TP* + *FP*), where *FP* is the number of false positives. Figure 11 (a) shows plots of precision versus recall for the test set of 240 different images containing 10 images of each coin. Different settings of the shape matching weight parameter *α* show that a relatively large value of *α*, which directs the matching dissimilarity towards more local influence, performs best. In order to obtain a preselection set of moderate size and high quality, i.e. the coin in question should likely be contained, a high recall is aspired. This is obtained by selecting the set size corresponding to the sudden decrease in Fig. 11 (a). Figure 11 (b) shows that this sudden decrease in precision versus recall corresponds to a preselection set size of 9 to 10

<sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> <sup>12</sup> <sup>14</sup> <sup>16</sup> <sup>18</sup> <sup>20</sup> 0.1

(b) Precision and recall versus preselection set size

Preselection set size

Precision

Recall

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

We combine shape and local descriptors to increase the identification rate. Preselection based on shape matching allows for the restriction of required comparisons for local features matching. As a result we achieve speed up of the identification process and higher accuracy rate. Since our shape descriptor is mirroring invariant, preselection can be performed either on the whole available coin data, i.e. the preselected set can contain images of the second coin

As a conclusion the preselection size was set to 10. Therefore, for the experiments presented here, *Pshape*(L|*A*) is computed for the 10 images with lowest dissimilarity and *Plocal*(L|*X*) for the same 10 images. The final decision is made according to the product rule given in Equ 24.

Precsion, Recall

**6.2.1 2D matching**

images.

0.4 0.5 0.6 0.7 0.8 0.9 1

Precision

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

α=0

α=0.25

Fig. 11. Results for ancient coin classification based on shape.

side, or preselection can be performed on the relevant coin side directly.

α=1

α=0.75

Recall

(a) Precision versus recall

Usually, a reference object, e.g. a cone, a square prism or a cylinder, is scanned and measured manually when the accuracy of the scanner needs to be calculated. After gathering all the dimensions, the values can be compared to the values determined from the 3D reconstruction. Additionally, scanner resolution evaluations can be made. Due to the fact that in our case the scanned object is small and both the surface and the shape of historical coins are not regular or flat, many dimensions cannot be measured precisely (e.g. coin profile details). Since we cannot provide the same accurate values for coins as we can provide for known objects, like cones or cylinders, our results will be based on a comparison between manually measured values from ancient coins and the values determined from the 3D model counterparts. As evaluation parameters, the maximal diameter and the volume of each coin are used.

The models are analyzed using Geomagic Studio, a commercial software for 3D data processing. The volumes of the original coins are calculated manually after computing the density by using the uplift of the coin in water and by measuring the weight of the coin. The compared diameter value represents the maximal existing value on the coin's surface. The maximal diameter from a real world coin is also determined manually. From a 3D model, the volume can be calculated using Geomagic Studio. The maximum diameter can be computed by segmenting one side of the coin and taking the largest distance between two border points. Because of the irregular shape of some coins, both the obverse and the reverse side of a coin must be taken into account.

In total, we scanned 22 coins: 14 ancient coins from the Roman era and 8 tornese silver coins from medieval age. Figure 12 (a) shows the volume of both the original ancient coins using the water volume calculation and their 3D model counterparts using Geomagic Studio. The maximum difference between manual and automatic measurements is 36.24 *mm*3. The smallest difference between real-world data and the data gathered from 3D models is 0.57 *mm*3. Figure 12 (b) shows the maximum diameter of both the real world manually measured one and the value calculated by using 3D models in Geomagic Studio. A maximum difference of 1.12 mm is measured, two coins have exactly the same diameter measured from 3D models and from real-world data. Table 4 shows maximum difference, minimum difference, and the mean variation coefficient of all volume and diameter measurements.

containing 11 949 coins. False decisions, i.e. either false classification, false rejection or false

Automatic Coin Classification and Identification 151

In order to facilitate prevention and repression of illicit trade of stolen ancient coins technologies aimed at allowing permanent identification and traceability of coins become of interest. Since every individual coin has signs, caused by minting techniques for pre-industrial ones or by use-wear for more recent ones, that make it unique and recognizable to an expert's eye, traceability of pre-industrial coins can make use of visual inspection. We presented an approach for object identification based on the combination of shape and local descriptors and applied it to the task of ancient coins identification. Shape matching was used to match coin edges whereas the die of the coin was matched by means of local features. From the output of each of these two methods individual coin label probabilities were estimated and finally fused. On a data set of 2400 coin images the combination of shape and local features outperform the

The results for classification of modern coins and identification of ancient coins are regarded to be almost perfect. Due to large intra-class variance, the classification of ancient coins is still a challenging task, especially if attempted from single 2D images. Additional information, e.g. from 3D measurements, or complementary information, e.g. textual descriptions, is supposed

The research was funded by the Austrian Science Fund (FWF): TRP140-N23-2010. The authors would also like to thank Dr. Mark Blackburn†(Fitzwilliam Museum, UK) for providing images for 2D image analysis and Mario Schlapke (Thüringisches Landesamt für Denkmalpflege und

Akca, D., Gruen, B., Breuckmann, B. & Lahanier, C. (2007). High definition 3D-scanning of

Arandjelovi´c, O. (2010). Automatic attribution of ancient roman imperial coins, *Proc. of*

Bay, H., Tuytelaars, T. & Gool, L. V. (2006). SURF: Speeded up robust features, *Proc. of Europ. Conf. on Comput. Vision*, Vol. 3951/2006 of *LNCS*, Springer, pp. 404–417. Besl, P. & McKay, N. (1992). A method for registration of 3D shapes, *IEEE Trans. Patt. Anal.*

Bischof, H., Wildenauer, H. & Leonardis, A. (2001). Illumination insensitive eigenspaces, *Proc.*

Canny, J. (1986). A computational approach to edge detection, *IEEE Trans. Patt. Anal. Mach.*

Chen, Y. & Medioni, G. (1992). Object modeling by registration of multiple range images,

Cooley, J. W. & Tukey, J. W. (1965). An algorithm for the machine calculation of complex

*Conference on Computer Vision Pattern Recognition*, pp. 1728–1734.

*of International Conference on Computer Vision*, pp. 233–238.

*Image and Vision Computing* 10(3): 145–155.

fourier series, *Math. Comput.* 19: 297–301.

arts objects and paintings, *Optical 3-D Measurement Techniques VIII*, Vol. 2, pp. 50–58.

accuracy rate of the single features and achieved an identification rate of 98.83%.

to improve the classification task for ancient coins significantly.

Archäologie, Weimar, Germany) for providing the coins for 3D scanning.

**8. Acknowledgements**

*Mach. Intell.* 14(2): 239–256.

*Intell.* 8(6): 679–698.

**9. References**

acceptance, were obtained for 6.77% of the test coins.

Fig. 12. Results for automatic 3D measurements and manual 2D measurements of ancient coin properties.


Table 4. Maximum difference, minimum difference and coefficient of variation between automatic 3D measurements and manual 2D measurements of ancient coin properties.

## **7. Conclusion**

We have presented methods for coin classification and identification applicable to coin collections comprising either a large number of coin classes, e.g. modern coins, or high intra-class variation, e.g. ancient coins.

Modern coins represent financial value only if the coins are sorted and returned to the respective national banks. A tunable system is required as national banks accept coins only if they are delivered with a high degree of purity. The rejection mechanism based on the probabilistic fusion result allows to adjust a tradeoff between rigorous classification (yielding high reliability against false acceptance but a higher rate of false rejections) versus tolerant classification (yielding more false acceptances but fewer false rejections). Coin class probabilities for both coin sides are combined through Bayesian fusion including a rejection mechanism. Correct decision into one of the 932 different coin classes and the rejection class, i.e. correct classification or rejection, was achieved for 93.23% of coins in a test sample 24 Will-be-set-by-IN-TECH

(a) Coin volume

(b) Coin diameter

We have presented methods for coin classification and identification applicable to coin collections comprising either a large number of coin classes, e.g. modern coins, or high

Modern coins represent financial value only if the coins are sorted and returned to the respective national banks. A tunable system is required as national banks accept coins only if they are delivered with a high degree of purity. The rejection mechanism based on the probabilistic fusion result allows to adjust a tradeoff between rigorous classification (yielding high reliability against false acceptance but a higher rate of false rejections) versus tolerant classification (yielding more false acceptances but fewer false rejections). Coin class probabilities for both coin sides are combined through Bayesian fusion including a rejection mechanism. Correct decision into one of the 932 different coin classes and the rejection class, i.e. correct classification or rejection, was achieved for 93.23% of coins in a test sample

Maximum difference Minimum difference Coefficient of variation

Fig. 12. Results for automatic 3D measurements and manual 2D measurements of ancient

Volume 36.24 *mm*<sup>3</sup> 0.57 *mm*<sup>3</sup> 1.23% Diameter 1.12 *mm* 0.00 *mm* 0.26% Table 4. Maximum difference, minimum difference and coefficient of variation between automatic 3D measurements and manual 2D measurements of ancient coin properties.

coin properties.

**7. Conclusion**

intra-class variation, e.g. ancient coins.

containing 11 949 coins. False decisions, i.e. either false classification, false rejection or false acceptance, were obtained for 6.77% of the test coins.

In order to facilitate prevention and repression of illicit trade of stolen ancient coins technologies aimed at allowing permanent identification and traceability of coins become of interest. Since every individual coin has signs, caused by minting techniques for pre-industrial ones or by use-wear for more recent ones, that make it unique and recognizable to an expert's eye, traceability of pre-industrial coins can make use of visual inspection. We presented an approach for object identification based on the combination of shape and local descriptors and applied it to the task of ancient coins identification. Shape matching was used to match coin edges whereas the die of the coin was matched by means of local features. From the output of each of these two methods individual coin label probabilities were estimated and finally fused. On a data set of 2400 coin images the combination of shape and local features outperform the accuracy rate of the single features and achieved an identification rate of 98.83%.

The results for classification of modern coins and identification of ancient coins are regarded to be almost perfect. Due to large intra-class variance, the classification of ancient coins is still a challenging task, especially if attempted from single 2D images. Additional information, e.g. from 3D measurements, or complementary information, e.g. textual descriptions, is supposed to improve the classification task for ancient coins significantly.
