Fast 3D-Vision System to Classify Metallic Coins by their Embossed Topography

Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 Fast 3D-Vision System to Classify Metallic Coins by their Embossed Topography Michael Hossfeld∗, Weiyi Chu∗, Markus Adameck+Manfred, and Eich∗ ∗Hamburg University of Technology, Eissendorfer Strasse 38, D-21073 Hamburg, Germany +Hella KGaA Hueck & Co., Beckumer Strasse 130, D-59552 Lippstadt, Germany Received 13 September 2005; accepted 02 October 2006 Abstract This paper presents a security-related machine-vision solution for real-time classification of moving objects with highly reflective metallic surfaces and complex 3D-structures. As an application example of our so called Three-Color Selective Stereo Gradient Method (Three-Color SSGM) a classification system for three main coin denominations of Euro coins is presented. Such coins are quickly moving in a coin validation system. The objective is to decide only from comparison of specially measured and processed 3D-surface information with characteristic topographical data stored in a database whether a coin belongs to one of the reference classes or has to be rejected as a foreign or counterfeit coin. Under illumination from a three-color light emitting diode equipped ring a single image of the moving coin is captured by a digital color camera. Exploiting the spectral properties of the illumination sources, which correspond to the special spectral characteristics of the camera, three independent subimages can be extracted. Comparison between these subimages leads to a discrimination between a coin with real 3D-surface and a counterfeit coin based on a photographic image of a coin of the same type. After the coin has been located and segmented, grey value based rotation and translation invariant features are extracted from a normalized image. In combination with template matching methods, a coin can be classified. Classification results will be reported for the three main coin denominations of Euro coins. Key Words: Object Recognition, Structural Pattern Analysis, Specular Metallic Surfaces, Three-Color Selective Stereo Gradient Method (Three-Color SSGM) 1 Introduction Modern coin validators measure precisely different coin features of which electromagnetic properties of the coin materials are the most important nowadays. On January 1st, 2002, Euro bank notes and coins began circulating within the European Monetary Union. At the same time the coin validator’s task to verify genuine Euro coins and to reject coins of foreign currencies or counterfeit coins became more difficult for various reasons. Each of the 12 members of the Monetary Union (before May 1st, 2004) embosses its own sets of eight different Euro coins with an individual minting pattern on the national sides. Several European manufacturers produce the metal alloys for the coin blanks which are embossed in 15 different European mints. Despite of Correspondence to: <[email protected]> Recommended for acceptance by <Walter F. Bischof> ELCVIA ISSN:1577-5097 Published by Computer Vision Center / Universitat Aut` onoma de Barcelona, Barcelona, Spain 48 M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 a quality control system implemented by the European Central Bank for all aspects of the Euro coin production, the large number of members and manufacturers increase the range of variation in the coin’s properties, especially of the electric conductivity of the coin material. To compensate this effect, the intervals for permitted measurements of coin properties in coin validators have to be widened compared to the previous single national coin detection scheme. A loss of identification quality and a slightly higher probability to falsely accept foreign or counterfeit coins would be the consequence. This scenario, therefore, has to be avoided especially because of the newly observed strong increase of counterfeit Euro coins in some countries [1]. Only coin properties not yet acquired in coin validators and thus used as additional information to the existing electromagnetic properties guarantees a more effective rejection of foreign and counterfeit coins. In addition, we expect the prospect of improved recognition quota of genuine Euros. To identify such coin properties a wide range of possible sensor technology not yet used in modern coin validators had been intensively tested for applicability. It soon turned out that the obvious visual 3D-appearance of the coined pattern as a whole bore high discriminative potential that had not yet been exploited for classification purposes in coin validators today. Verifying as well a coin’s visual structural information excludes effectively attempts of coin validator fraud with specially designed metallic tokens whose only purpose is to simulate the electromagnetic properties of a genuine coin in order to trigger an acceptance signal. Their optical appearance is insignificant. Against the background of the presented facts we have developed the so called Three-Color Selective Stereo Gradient Method (Three-Color SSGM)[2]-[4]. It is in general a non-destructive and contact-free optical inspection system for real-time classification of moving objects with highly reflective metallic surfaces and complex structures. A Three-Color SSGM-system which classifies minted patterns of moving Euro coins into classes corresponding to their country of origin serves as an application example. The rotation and translation invariant classification is based solely on 3D-topographical information of the embossed profile. 3D-information is not directly extracted. Instead image characteristics resulting from the fact that a coin has 3D-contour are analyzed to determine the coin class. Characteristic intervals for acceptable measurement values are derived from a training set. As a proof of the Three-Color SSGM classification principle, hardware and image processing algorithms of a PC-based laboratory demonstrator are described, for which the classification performance is presented and discussed. We concentrate our development primarily on three basic coin denominations 2 Euro, 1 Euro, and 50 Cent, but the method can easily be extended to other face values. It will be shown that the coin diameter can be determined with an accuracy of less than 0.1 mm (see chapter 4.2). As an important system property the average false rejection rate is determined to be less than 0.6% (see chapter 6). This ”first coin insertion” result is much better than in many existing electromagnetic based coin validation systems. With a Three-Color SSGM-system installed in existing coin validators in addition to the electromagnetic sensors the robustness of such machines toward coin recognition and coin rejection can be improved. An optically based visual pattern recognition system can, in principle, be deceived by photographic images of the objects to be classified. This aspect is normally neglected in industrial inspection tasks. But in the realm of security systems and anticounterfeiting tasks a classification system has to cope with this kind of trivial attempts of fraud. Therefore a 3D-verification algorithm has been developed which is as well described. 2 General Concept of the Three-Color Selective Stereo Gradient Method The surface of coins exhibits a fine structure resulting from both embossing and wear and tear. Under illumination this structure reflects light characteristically towards an observer. Intensity values in a digital image of a coin carry information about the three-dimensional local shape of the embossing’s structure. To exploit this information for classification purposes it is necessary to understand what governs the observed intensity. In this section we briefly address light reflection from diffuse and specular surfaces. M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 49 2.1 Determining Surface Orientation If the elevation h=h(x, y)of a surface above the x−y−plane in a Cartesian coordinate system is given, the first partial derivatives of hwith respect to xand ywill be defined as p(x, y) = ∂h(x, y) ∂x q(x, y) = ∂h(x, y) ∂y (1) The vectors (1,0, p)and (0,1, q)are tangent to the surface in point (x, y). The normal vector of the surface in this point is the cross-product of these two, resulting in [−p, −q, 1]. By convention the viewer looks into the (0,0,−1)-direction of the negative z-axis, so usually the opposite normal vector [p, q, −1] is considered. The quantity (p, q)is called gradient of h(x, y). The (p, q)-space is a nonlinear representation of the surface orientation. A reflectance map R(p, q)is a convenient model to describe the image intensities as a function of the surface orientation (p, q). It takes into account a fixed object illumination, the surface reflectance of an object’s material given a particular light source in form of an explicit mathematical description, and the imaging geometry. We assume, that the image projection is orthographic and that the incident illumination comes from a single distant point source. Even then the calculation of the surface orientation from the image intensity is difficult, because a non-linear first-order partial differential equation has to be solved for pand q. Since there is only one equation at hand, the system is underdetermined [5]-[6]. Until today, photometric stereo methods are well-known techniques for extracting surface normals [7]. The photometric stereo method according to Woodham [8] uses reflectance maps to solve the problem of finding the surface orientation. The idea is to vary the direction of incident illumination between successive views of the same object, while holding the viewing direction constant. If it is known how light is reflected at a surface, R(p, q)can be calculated. Woodham showed for Lambertian surfaces that three views with their corresponding R(p, q)are sufficient to uniquely determine both surface orientation and reflectance factor at each image point. 2.2 Reflectance Models Besides rendering the correct 3D-shape of the object to create realistic images in computer graphics, a reflectance model is needed for each illuminated reflective surface in the scene. For modeling object shapes there are a number of known techniques such as range image merging, photometric stereo or shape from shading [9][10]. Some techniques are capable of modeling both shape and reflectance properties [11]-[13]. The most accurate way to model the reflectance mechanism alone is given by Maxwell’s equations since they describe the physical nature of the interaction between electromagnetic waves and matter. Although there are reflectance models which are based on solving Maxwell’s equations [14] such a direct approach is usually computationally very extensive. The bi-directional reflectance distribution function (BRDF), defined by the National Bureau of Standards, formally describes the reflectance mechanism [15]. It is the angular dependent ratio of the reflected radiance dLr(within solid angle dωr) in direction towards the viewer to the incident irradiance dEi(within solid angle dωi) in direction of an infinitesimally small part of the surface’s area: fr(θr, φr;θi, φi) = dLr(θr, φr;θi, φi, Ei) dEi(θi, φi)(2) where the polar angles θand the azimuth angles φtogether indicate a direction. The subscripts i and r denote incident and reflected radiant flux (see Fig. 1). Equation 2 assumes monochromatic light. If a BRDF term can be explicitly given for a surface, its brightness or shading can be accurately calculated in synthesized images. BRDF data can be achieved in two ways: gonioreflectometers can measure the BRDF for each object of a scene. Exhaustive measurements of the entire hemisphere is required here because image rendering algorithms must evaluate the BRDF in arbitrary directions [16] such that this method is not suitable for practical purposes. 50 M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 Figure 1: Nomenclature for the definition of geometric quantities in the BRDF (adapted from [15]). A second way is to assume a certain reflectance behaviour for the surfaces. A very simple and widely used model is the Lambertian reflection under which an object surface appears equally bright from all viewing directions [17]. The Lambertian BRDF can lead to satisfactory approximations of surface appearances but usually the surfaces appear somewhat unreal because the model neglects specular reflection components. NonLambertian parametric models for real-world objects can be divided into physically-based and empiricallybased models [18]. Although they lead to highly accurate surface rendering, physically-based models like the Torrance and Sparrow reflection model [19] are still used only occasionally because of their complexity and because parameters are not readily available for real time computing [16]. The best known empirical model is the Phong reflectance model [20] because of its simplicity and its good surface rendering results. It describes the shading at a surface point as a superposition of Lambertian and specular behaviour. Lr,P hong =ρ[cos(θi)(1 −d) + d]+W(θi)[cos(γ)]n(3) where ρis the reflection coefficient of the object’s surface, d the environmental diffuse reflection coefficient, W(θi)the ratio of specular reflected light, γthe angle between direction of the reflected light and the direction of the viewer. The exponent nis a power which models the specularly reflected part of the incident light and depends on the material. 2.3 Reflection at specular metal surfaces Reflection at metal surfaces differs significantly from diffuse reflection. Most notably it is dominantly specular, strongly forward oriented into a narrow solid angle, and therefore does not produce smooth shading on the surface. For our Three-Color Selective Stereo Gradient Method we choose the Phong reflectance model to describe this characteristic reflectance because it approximates the angle dependent reflection of metallic surfaces very well as we will show experimentally (see Fig. 2). A 1-Euro-coin is illuminated under a fixed incidence angle θi= 45◦by a widened and collimated beam of a laser. The average surface’s normal and the vectors of incident and reflected direction are coplanar. An image sensor is moved around the reflected maximum in discrete angle steps. At every position a grey-value image of the coin is taken. The camera’s optical axis lies within the plane of the three vectors. In all images the mean grey value of the same plane surface patch of 5×5 mm2is measured. As expected, the maximum at γ= 0 of the measured reflection is found where the reflection angle θrequals θi. The angle M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 51 Figure 2: Reflection at specular metal surfaces. Left: Experimental setup for measuring the reflectivity property of a metallic coin. Center: The reflected specular intensity can be approximated with the Phong shading Model. Dark dots: Measurement; Line: Model fit. Right: Cut through a profile contour. θr, which fulfills the reflection condition at the point of incidence on the surface, is named here as θspec. The measured data, indicated as dots in Fig. 2, middle, can be approximated by the predominant cos(γ)n-term of the Phong shading model according to equ. 3, which yields n > 600. The extreme high value of nemphasizes the highly specular property of the metallic surface. 2.4 Modelling the embossed profile and selecting a gradient In our model the three-dimensional nature of the embossed metal structure is described by an infinite number of infinitesimally small surface elements all tangential to the 3D-structure relief across the coin surface. By determining gradients we are able to both identify the embossed structure for classification and investigate the nature of the relief to sort out photos. Determining surface orientations using Woodham’s photometric stereo method [8] would be possible here, but requires demanding lighting with a great number of point light sources, illuminating the scene from different directions. Many images taken from one scene view by activating the light sources one at a time have to be analyzed to calculate all gradients of the objects. Due to this drawback, this method appears often to be very time consuming and not suitable for real-time applications∗. Still, Woodhams approach can be used here to classify coin embossings, if reasonable simplifying assumptions can be found: since coins are flat, thin, mostly circular objects, it is convenient to observe them by an image sensor from top view and to assume that image projection is orthographic. To get hold of the coined structure it is not necessary to determine all gradients, not even numerically. Under the assumption of a uniform albedo of the coin’s surface, partial knowledge about one gradient value suffices for a safe classification. This is explained in the schematic sketch of Fig. 2, right. A metallic ridge of the profile of a coin, illuminated by a distant point light source, is cut perpendicularly to the coin surface and drawn as seen from the side. It is observed by an image sensor from the top view. The azimuth angle φiof the incident illumination is fixed, as well as the camera, whose image sensor lies parallel to the coin surface. For an arbitrary but then fixed polar angle θ0 iof incidence light measured now in a viewer-oriented coordinate system against the main surface normal of the coin, only one bright spot appears in the camera. The light which causes this spot, originates from that point P on the ridge, where the normal vector of its tangential small surface element bisects θ0 i. From all points on the profile this occurs for this and only for this surface element since only there the reflection condition is locally fulfilled for a given viewing and observation direction: θi=θr=θspec =θ0 i 2(4) This results as a consequence of the strongly forward oriented specular metallic reflection. ∗see for example [21], in which an inspection system for specular solder joints of surface mounted components is described. A hemisphere of 127 point light sources are used to extract all local surface orientations of each solder joint. 52 M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 Simultaneously, the camera detects one gradient (p0, q0)with absolute value |(p0, q0)|graphically. For every point on the ridge profile there is ideally only one θ0 iby which it appears as bright spot on the image sensor. Therefore, a minted edge appears as a single bright line as shown in Fig. 3, left. One predetermined absolute gradient value |(p0, q0)|of interest can unambiguously be selected by chosing a special θ0 iusing one single light source instead of three different light sources according to Woodham’s photometric stereo if the albedo varies less over the observed area. This is the principle of the SSGM. Figure 3: Left: A minted edge appears as a single bright line representing gradients with absolute value |(p0, q0)|. Center and right: Sometimes more than one point on the ridge can locally fulfill the reflection condition. Depending on the individual form of a coin’s profile and the angle θ0 ichosen two or even more points on the ridge can fulfil locally the reflection condition. This is shown schematically in Fig. 3, center. Since the gradient images are taken from a distant image sensor the separate two lines indicating the same absolute value |(p0, q0)|are very close together and nearly merge into one single line. This effect has negligible influence on the recognition accuracy. If all gradients with absolute value |(p0, q0)|can be captured over the coin’s surface the image sensor receives a representation of the embossed structure. 2.5 Development of a suitable illumination A problem-adapted taylored illumination is half the solution of nearly every vision system. The demands on our illumination here are extensive. To detect all points with gradient value |(p0, q0)|, an azimuthally 360◦- illumination ring with constant θ0 ifor all illumination directions is necessary. Each source has to illuminate the object plane homogeneously to ensure rotation invariance of the features. In chapter 4.5 we will show how the 3D-property of the embossing can be verified. The verification module is fundamentally based on multiple images showing the same coin profile from different illumination directions. To avoid stopping the coin in its motion for taking these images and to limit the number of sensors to one, we resorted to a scheme which encodes different illumination directions by colors. We achieve good results with three different illumination directions, encoded by red, green, and blue light sources and arranged circularly in three 120◦-ringshaped sectors. Now, only one color image is necessary, which can be taken while the coin is in motion. The software module separates the color image into three independent subimages (see chapter 4.1), bearing disjunct information about the coin profile from different ranges of azimuth angles. Calculating difference images from pairs of these subimages allows conclusions to be drawn about the 3D-nature of the coin. The difference image method requires that each detected gradient originates only from one single light source. This is important at the border of two adjacent colors. If a profile segment is simultaneously illuminated by two colors, the information about the profile contour in this segment will vanish in the difference image. To ensure this feature, the illumination ring has to be composed of individual light sources. From the graph shown in Fig. 2 can be inferred that the reflected intensity of a metallic surface even from a point light source M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 53 deviates substantially (intensity ≥5%) from zero only between an angle of ±8◦. This indicates a separation of at least 16◦azimuthally between each light source, making the 24◦between each of 15 equally spaced sources an adequate azimuthal distance. Then the border condition is fulfilled. Figure 4: Grey value and thresholded images of two top views on perfectly reflecting spheres with radius one. Its shadings are calculated according to the Phong reflection model. This requirement seems to be inconsistent with the above mentioned requirement for a rotation invariant continuous illumination. But it can be shown that a continuous detection of a gradient can be built up with individual light sources as well. Fig. 4 shows 8-bit-grey value images of two top views on perfectly reflecting metallic spheres with radius one. Its shadings are calculated†according to the reflection model of Phong (equ. 3). The first sphere is illuminated by 5, the second by 15 point light sources, all emitting at the same polar angle. The geometric distances of the model correspond to the situation in the illumination ring of Fig. 5. The right part of Fig. 4 shows the same grey value images now thresholded by grey value 229. It can be seen that 15 individual light sources are enough to detect continuously one single gradient value. 3 Experimental Setup In order to prove and to evaluate the working and recognition principle of the Three-Color SSGM, a laboratory demonstrator is set up, based on moving coins rolling down an inclined plane. The illumination ring with inner diameter of 30 mm consists of 15 color LEDs‡separated azimuthally 24◦ and arranged in three 120◦-sectors of 5 monochromatic LEDs circularly around the field of view (see Fig. 5, left). The polar angle of θ0 i= 63◦is the same for all LEDs. It is chosen as a compromise between achieving the brightest profile contours from the middle part of the edge curvature and the darkest background. Figure 5: Left: Schematic top view on the illumination ring. 15 color LEDs are arranged in 3 sectors around the coin centered in the middle. Right: Side view on the experimental setup of the 3-Color-SSGM. †with MATLABTM : The Mathworks, Inc., 3 Apple Hill Drive, Natick, MA, USA; Internet: www.mathworks.com ‡light-emitting diodes from Infineon Technologies AG; Red: LA E67B; Green: LT E67C; Blue: LB E67C 54 M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 LED irradiance is always inhomogeneous (see Fig. 6, A). To compensate this effect, we use planoconvex plastic lenses in a special setup. By properly positioning the LED within the focal length of the lens and tilting the optical axis of lens and LED against each other, a very good illumination homogeneity of the object plane of 30 mm in diameter can be achieved even with LEDs (see Fig. 6, B and C). For image acquisition we use Figure 6: Inhomogeneous illumination of a single LED: top view on a 90◦-sideways illuminated surface of 30 mm in diameter without any lens. Detected radiant light along the arrow line as grey values plotted in the graph (A). Compensation of inhomogeneous illumination using a sideways positioned lens (B and C). a digital, progressive, color CCD camera with 1024 ×768 pixels. The camera comes with an 1/3inch sensor ICX204AL from Sony with a Bayer-Pattern and is connected to a digital frame grabber from EuresysT M . The LEDs are chosen in such a way that their spectral emission characteristics meet the spectral selection function of the Bayer-Pattern mosaic filter in front of the image sensor (shown in Fig. 7). Figure 7: Spectral transmission properties of the Bayer-Pattern mosaic filter elements (solid lines, abbreviated B.-P.) and the spectral emission characteristics of the three sorts of LEDs (dashed lines). When a coin rolls down the guideway of the inclined plane into the recognition system, it passes a photoelectric IR-barrier in the middle of the ring. After 300 ms all 15 LEDs flash for 100 ms, the camera captures one single 8-bit grey value image, which is sent to the PC for further analysis. 4 Image Processing and Classification We refer to the three main coin denominations 2 Euro, 1 Euro and 50 Cent simply as ”coin sort” and to the countries of origin within each sort as ”classes”. The objective of the image processing algorithm is to decide from standardized information extracted from an image of the 3D-profile contour of the coin’s minting with absolute gradient value |(p0, q0)|to which coin sort and class a specimen belongs and whether the specimen is a photographic image or not. The image processing algorithm follows the schematic diagram shown in Fig. 8. Its individual moduls are described in the following sections. M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 55 Figure 8: Schematic flow diagram illustrating the most important steps of the image processing algorithm, implemented to classify coins according to the Three-Color SSGM. 4.1 Data Preprocessing After grabbing a coin image F(x, y), three grey value subimages R(x, y),G(x, y), and B(x, y)of the red, green, and blue illumination sector are extracted from F(x, y). Because there are twice as many green filter elements as compared to blue or red ones, every second green Pixel is skipped in order to yield three subimages of same image dimension. The original image size of 1024 ×768 pixels is reduced to 511 ×383 pixels. A maximum image M(x, y)is calculated according to M(x, y) = max[R(x, y); G(x, y); B(x, y)] ∀(x, y)∈M(5) in which for each point (x, y)in the maximum image Mthe highest intensity in the set of the three pixels R(x, y)or G(x, y)or B(x, y)is chosen. Since the background in each of the three images is mostly dark, this operation leads here to a contrast improvement. Original and maximum image are shown in Fig. 9. All coin images in this article are shown inverted because much more details can be visually perceived. Figure 9: Inverted original image F(x, y), three grey value subimages R(x, y),G(x, y), and B(x, y)and maximum image M(x, y)of the international side of a 2-Euro-coin. 62 M. Hossfeld et al. / Electronic Letters on Computer Vision and Image Analysis 5(4):47-63, 2006 presented Three-Color SSGM-system is an excellent result. No errors have been observed in determining the coin sort and the country of origin within the test set. No coins have been classified as photos and all photos of 2-Euro-coins have been sorted out. The Three-Color SSGM can easily be adopted to further Euro denominations, to other currencies and to related problems of 3D-surface analyses. 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