Detection of counterfeit coins based on 3D height-map image analysis

Highlights

• Creating six height-map image datasets for fake coin detection.

• Proposing 3D Precipice Border Detection Algorithm for detecting 3D borders.

• No need for image restoration for degraded images in this method.

• Extracting features with a high discriminating capability.

• Feeding an ensemble classifier by feature matrices instead of feature vectors.

Abstract

Detecting a counterfeit coin using 2D image processing is nearly impossible in some cases, especially when the coin is damaged, corroded or worn out. Edge detection is one of the most widely used techniques to extract features from 2D images. However, in 2D images, the height information is missing, losing the hidden characteristics. In this paper, we propose a 3D approach to detect and analyze the precipice borders from the coin surface and extract significant features to train an ensemble classification system. To extract the features, we also propose Binned Borders in Spherical Coordinates (BBSC) to analyze different parts of precipice borders at different polar and azimuthal angles. The proposed method is robust even against degradation which appears on shiny coins after 3D scanning. Therefore, there is no need to restore the degraded images before the feature extraction process. Here, the system has been trained and tested with four types of Danish and two types of Chinese coins. We take advantage of stack generalization to classify the coins and add the reject option to increase the reliability of the system. The results illustrate that the proposed method outperforms other counterfeit coin detectors. The accuracy obtained by testing Danish 1990, 1991, 1996, and 2008 datasets are 98.6%, 98.0%, 99.8%, and 99.9% respectively. In addition, results for half Yuan Chinese 1942 and one Yuan Chinese 1997 were 95.5% and 92.2% respectively.

Introduction

Over the past several decades, a lot of counterfeit money has caused significant damage to the society. They have been made by criminals or unknown coin collectors for thousands of years as an illegal industry (Travers, 2008). It is worth noting that as a significant topic of security, counterfeit coin detection has become the focus of research in the field of numismatics. The data drawn from the Counterfeit Monitoring System (CMS) indicate that only in Europe, the total number of counterfeit euro coins removed from circulation from 2013 to 2017 was equal to 837,910 pieces whose value amounted to 1,330,401 Euros (“The protection of Euro coins in 2017,” 2017). It is expected a very large number of counterfeit euro coins still remain in circulation. In addition, as an example of an old coin which is being traded in the market, we can mention a half Chinese Yuan 1942. The price of the best quality of this coin in the market is over $1200, which illustrates the importance of counterfeit detection for old coins.

With the continuous development of 3D technologies and the fast evolution of depth sensors attached to handheld devices, 3D approaches have become a hot topic of computer vision due to its applications in areas such as recognition, security, and biometrics. It also motivates the extension of novel image processing and computer vision techniques. Because of the progress of 3D applications for different purposes, the notion of 3D approaches has determined itself as one of the most significant alternatives for 2D approaches and has attracted considerable attention of the community in recent years. In addition, it is worth noting that 3D approaches are gradually emerging as an appealing area for the design and implementation of a classification scheme, especially by those employing image datasets. Up to now, several studies based on image processing techniques and classification algorithms have been proposed that exploit images for counterfeit coin detection. Fundamentally, fake coin detection is an effortful procedure because of widely varying input templates, cluttered images, and various rotations which are the big challenges. Most of the existing image-based methods for counterfeit coin detection relied only on 2D images, failing to equip some statistical information about the height and depth, and often lose the hidden characteristics or suffer from low accuracy. Although researchers have recently achieved fruitful results in 2D image-based systems, these studies have an important drawback: it is not conceivable to rely only on 2D images, when the coins are corrupted, colored, or worn out and 2D detected edges are the only source of information. As a remedy to this limitation, the development of techniques to establish a 3D structure from a coin image can discover the complex characteristics of the coin.

Based on the type of analysis carried out, the potential of a 3D image-based method has not yet been applied for counterfeit coin detection and is still an open field of research. Despite the significance of the 3D technologies, the research in this regard is relatively scant. In this paper, we propose a 3D approach to detect and analyze the coin surface and extract significant features to train an ensemble classification system. To do this, a novel method to detect specific parts of objects on the coins that we name it Precipice Border Detection Algorithm (PBDA) will be proposed which is incorporated into the proposed framework for counterfeit coin detection. Considering the nature of the data in height-map images, we extract effective 3D features related to height or depth of the coin surface and prove the robustness of the method with cases not considered in previous works (Khazaee et al., 2018, Khazaee et al., 2017). In this method, the height-map image of the coins will be triangulated, and a clustering scheme based on the Fuzzy C-Means algorithm (Bezdek, 1981, Bezdeket al., 1984) will cluster the triangles to detect precipice borders of the coin surface. Then, we propose a method to analyze the precipice borders and extract the valuable features for training a stacking classifier with a reject option.

The focus of this paper is to propose a method to detect counterfeit coins. However, the proposed algorithms have much broader applications in the context of 3D image classification. The major contributions of the proposed framework are summarized as the following:

• Creating six height-map image datasets and proving the competency of 3D approaches in counterfeit coin detection: we successfully detect the precipice border of the surface on the coin with our proposed 3D Precipice Border Detection Algorithm (PBDA) and use it for the feature extraction process.

• No need for image restoration or enhancement for degraded images: the precipice borders are not affected by the degradation problem.

• Extracting features with a high discriminating capability: we propose a system to consider the direction of the precipice borders as well as their approximate areas in the feature extraction module that we name it Binned Borders in Spherical Coordinates (BBSC).

• Feeding an ensemble classifier by feature matrices: a feature extraction methodology is proposed to extract a feature matrix instead of a feature vector in which each row of the matrix is used separately.

The rest of the paper is organized as follows. To illustrate the current state of research on the field of image-based coin detection, we provide a literature review in Section 2. The preprocessing steps like resizing, rotation, and normalization are described in Section 3. Section 4 presents the concept and proposes a method for precipice border detection and analysis. Section 5 discusses the design of an efficient ensemble classifier with a reject option for the classification process. In Section 6, the experimental results are given to show the performance of the proposed method regarding counterfeit coin detection. Finally, the paper concludes with a summary of the primary contributions of this research and suggests an outline for future work in Section 7.