**2. State of the art in coin image analysis**

For modern coins, i.e. machine struck coins, judging systems using electromechanical devices are wide-spread. Those systems are commonly based on measuring weight, diameter, thickness, permeability and conductivity (Davidsson, 1996), oscillating electromagnetic field characteristics (Neubarth et al., 1998), and photo- and piezoelectric properties (Shah et al., 1986). Typically, such systems are only capable to discriminate a small number of different coin denominations and are mostly limited to a specific currency.

Approaches towards classification of modern coins using image processing are described in various papers and patents. A neural network approach capable of discriminating between 500 Won and 500 Yen coins was published by Fukumi et al. (1992). A number of coin authentification methods employing optical means are described in patents, e.g. a system by which both sides of a coin are first imaged by cameras, followed by feature extraction from binarized images, and finally combined with a magnetic sensor measurement is described by Hibari & Arikawa (2001). The so called Dagobert coin recognition system was developed for high volumes of coins and a large number of currencies (Fürst et al., 2003; Nölle et al., 2003). Image binarization followed by area measurement and comparison of coin center and center of gravity was also suggested in a patent (Onodera & M., 2002). Another system based on the analysis of one side of a coin by transformation of its image into polar coordinates and matching of profiles taken along angle direction was described by Tsuji & Takahashi (1997). A special acquisition device for coins employing colored illumination from various angles was suggested by Hoßfeld et al. (2006). Methods based on matching gradient directions (Reisert et al., 2006; 2007) and color, shape and wavelet features (Vassilas & Skourlas, 2006) were suggested. An approach based on multiple Eigenspaces aims at classification for a large number of classes (Huber et al., 2005). This approach initially obtains a translationally and rotationally invariant description and secondly an illumination-invariant Eigenspace is selected from multiple Eigenspaces (Leonardis et al., 2002). Finally probabilities for coin classes are derived for the obverse and reverse sides of each coin and Bayesian fusion is performed.

For ancient coins, i.e. hand struck coins, some publications discussing approaches for classification appeared. Early approaches, which achieved a moderate classification performance, were based on matching of contour and texture features (Van Der Maaten & Postma, 2006) or make use of interest point extraction and matching of local features (Zaharieva et al., 2007). More recently, an approach based on interest points and improved feature description and matching was reported (Arandjelovi´c, 2010). The inherent properties of hand struck coins result in individual features of each coin and a large intra-class variance. Therefore, object classification becomes challenging. However, in contrast to object classification, object identification relies on those unique features which distinguish a given object from all other members of the same class. Results on identification of ancient coins were

(a) Coin image (b) Smoothed image (c) Edge image (d) Label image

Automatic Coin Classification and Identification 131

(e) Convex hull (f) Overlay image

whereas ancient coins deviate from this shape, but still stay close to a circular outline. Therefore, approaches based on edge detection and application of the Hough transform (Duda & Hart, 1972) were applied to modern coins (Reisert et al., 2006) as well as to ancient coins (Arandjelovi´c, 2010), where a modified version of the Hough transform was

For a modern coin, such as shown in Fig.2 (a), we suggest an edge based technique to segment the coin from the background. The detection of the coin employs a common segmentation approach and works reliably for controlled lighting conditions and relatively clean background, e.g. a moderately dirty conveyor belt. Problems might be caused by very dark coins, i.e. coins which reflect only a small amount of light towards the camera. A multi-stage segmentation procedure is suggested. The outline of the suggested segmentation

2. Edge filtering using a Laplacian of Gaussian approach followed by zero-crossing detection

3. Labeling of the detected regions, see Fig.2(d), and selection of the region with largest

An example of an overlay of the extracted blob onto the input image is shown in Fig.2(f). Coin position and diameter are estimated from the detected blob, which directly delivers access to

For ancient coins we employ a measure of compactness *ct* related to a threshold *t* defined as

*ct* = 4*πAt*/*P*<sup>2</sup>

where *At* is the area of the region covered by the coin and *Pt* is the perimeter of the coin. The measures *At* and *Pt* are obtained by connected components analysis (Sonka et al., 1998)

*<sup>t</sup>* (1)

4. Form a blob by computing the convex hull of the coin region candidate, see Fig.2(e)

1. Smoothing of the image to suppress noise and background texture, see Fig.2(b).

Fig. 2. Image of a modern coin, intermediate detection results and segmentation.

used.

method is:

(Marr & Hildreth, 1980), see Fig.2(c).

a translation invariant description.

bounding box as coin region candidate.

reported by Huber-Mörk et al. (2008), where the combination of shape and local descriptors to capture the unique characteristics of the coin shape and die information was suggested. For ancient coin recognition features from the Scale-invariant feature transform (SIFT) (Lowe, 2004) was used and compared to algorithms based on shape matching i.e. a shape context description and a robust correlation algorithm (Zaharieva et al., 2007). Ancient coins are in general not of a perfect circular shape. From a numismatic point of view, the shape of a coin is a very specific feature. Thus, the shape described by the edge of a coin serves as a first clue in the process of coin identification and discrimination. A shape based method tuned to the properties of ancient coins was combined with matching of local features through Bayesian fusion (Huber-Mörk et al., 2010).
