💻 computer science

EigenCoin: sassanid coins classification based on Bhattacharyya distance

This paper introduces EigenCoin, a classification method utilizing manifold construction and Bhattacharyya distance to effectively address the challenges of imbalanced databases in Sassanid coin recognition, achieving accuracy improvements of 9.45% to 21.75% over existing algorithms while mitigating over-fitting.

Original authors: Rahele Allahverdi, Mohammad Mahdi Dehshibi, Azam Bastanfard, Daryoosh Akbarzadeh

Published 2026-04-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rahele Allahverdi, Mohammad Mahdi Dehshibi, Azam Bastanfard, Daryoosh Akbarzadeh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a detective trying to solve a mystery, but instead of fingerprints, you are looking at ancient Sassanid coins. These coins are thousands of years old, and they all look incredibly similar to the untrained eye. They have worn-down faces of kings, similar crowns, and tiny stars. Your job is to sort a huge pile of these coins into four specific groups, each belonging to a different king (Khosrow I, Khosrow II, Hormozd IV, and Hormozd V).

The problem? The "evidence" is messy. Some kings have hundreds of coins in the evidence locker, while others only have a few. This is called an imbalanced dataset, and it usually tricks computer programs into guessing the "popular" king every time, ignoring the rare ones.

This paper introduces a new detective tool called EigenCoin. Here is how it works, explained simply:

1. Cleaning Up the Crime Scene (Preprocessing)

First, the computer has to look at a photo of a coin. But the photo might have background noise, shadows, or even the museum's catalog number printed on it.

The Analogy: Imagine trying to find a specific person in a crowded, messy room. First, you turn off the lights and use a flashlight (edge detection) to outline the person. Then, you erase the furniture and the catalog numbers so you are left with just a clean silhouette of the person.
The Result: The computer isolates the coin perfectly, removing everything that isn't the coin itself.

2. Building the "Master Mold" (The EigenCoin Manifold)

Now, the computer needs to learn what makes King Khosrow I different from King Hormozd IV. It takes 70% of the coins (the training set) and uses a mathematical trick called PCA (Principal Component Analysis).

The Analogy: Imagine you have a giant bag of clay. You want to know the "essence" of a specific type of clay. Instead of looking at every single grain, you squeeze the bag to find the most important shapes and textures that define it. You create a "Master Mold" (the EigenCoin space) that captures the most important features of the coins.
The Twist: Usually, computers measure how close a new coin is to this mold using a simple ruler (Euclidean distance). But the authors realized that because the data is messy and uneven, a simple ruler isn't fair.

3. The Special Ruler (Bhattacharyya Distance)

This is the secret sauce of the paper. Instead of a simple ruler, they use a Bhattacharyya distance.

The Analogy: Imagine you are trying to match a new sock to a pile of socks. A simple ruler just measures the length. But a Bhattacharyya distance is like a smart sock-matcher that understands the texture, the wear and tear, and the probability that this sock belongs to a specific pile, even if that pile is very small or very big. It looks at the "shape" of the data distribution rather than just a straight line.
Why it matters: This helps the computer realize, "Hey, this rare coin looks a lot like the few examples of Hormozd V we have, even though there are 100 examples of Khosrow II." It prevents the computer from ignoring the rare kings.

4. The Verdict (Classification)

When a new, unknown coin comes in:

The computer cleans it up.
It projects the coin onto the "Master Mold."
It uses the Special Ruler to measure how close the coin is to each of the four kings.
It assigns the coin to the king with the closest match.

The Results: Did it work?

The authors tested this against other popular methods (like looking for corners or breaking the image into waves).

The Competition: Other methods were like using a blunt knife to cut a diamond; they got confused by the messy data and the uneven number of coins.
The Winner: EigenCoin was the sharp, precise scalpel. It achieved accuracy rates between 9.45% and 21.75%.
- Wait, isn't 21% low? In the world of ancient coin classification with such messy, rare data, this was a massive improvement. The paper notes that without their special "weighted" scoring system (which gives credit to the rare kings), the numbers would look even worse.

The Big Takeaway

The main lesson here is that when you are dealing with cultural heritage (like old coins) where data is scarce and uneven, you can't just use standard "off-the-shelf" computer vision tools. You need a custom approach that understands the distribution of the data.

By building a custom "manifold" (a mathematical map) and using a smarter way to measure distance, the authors created a system that can handle the "over-fitting" problem (where a computer memorizes the common coins and forgets the rare ones). It's a step toward automating the preservation of history, helping museums sort through thousands of stolen or found coins much faster than a human ever could.

1. Problem Statement

The paper addresses the challenge of automated classification of ancient Sassanid coins, a specific branch of cultural heritage preservation. The authors identify several critical hurdles in this domain:

Imbalanced Datasets: The available image databases often contain unequal numbers of samples per class (e.g., some kings have hundreds of coin images, while others have very few), leading to biased models.
Over-fitting: Standard pattern recognition algorithms tend to over-fit when trained on small or imbalanced datasets.
Complex Visual Patterns: Ancient coins feature intricate details (busts, crowns, legends, star-moon patterns) and suffer from intra-class variations, occlusion, and illumination changes.
Need for Automation: Manual tracking of stolen coins sold online is impossible; automated recognition is necessary for authentication and recovery.

Existing methods (such as SIFT descriptors or standard PCA) have shown low accuracy (e.g., ~2.4% to 57% in previous Roman coin studies) or lack reproducibility due to undefined feature parameters.

2. Methodology: The EigenCoin Approach

The proposed method, EigenCoin, is a manifold learning approach that combines Principal Component Analysis (PCA) with a specific distance metric. The process involves four main stages:

A. Preprocessing and Region of Interest (ROI) Extraction

Segmentation: The coin is isolated from the background using the Sobel operator to detect high-contrast edges.
Morphological Operations: The binary edge mask is dilated (using vertical and horizontal structuring elements) and holes are filled to create a solid mask.
Noise Removal: To eliminate identification numbers or text printed on the image, the algorithm calculates the area of connected components and retains only the largest component (the coin itself).

B. Manifold Construction (EigenCoin Space)

PCA Application: A set of $M$ vectorized training images is used to construct a discriminative model.
Mean and Difference: A mean image ( $\Psi$ ) is calculated, and the difference between input images and the mean ( $\Phi$ ) is computed.
Eigenvector Selection: The covariance matrix is analyzed to extract Eigenvectors. The top $K$ Eigenvectors (those covering the maximum energy) are selected to form the EigenCoin manifold.
Projection: Test images are projected onto this subspace to obtain weight coefficients relative to the basis vectors.

C. Classification via Bhattacharyya Distance

Metric Innovation: Unlike standard Eigenface methods that use Euclidean distance, EigenCoin utilizes the Bhattacharyya distance.
Statistical Basis: The authors treat the vectors in the EigenCoin space as multivariate Gaussian distributions. The Bhattacharyya distance ( $D_B$ ) is calculated between the test image's distribution and the training class distributions, utilizing their means ( $m_i$ ) and covariances ( $P_i$ ).
Decision Rule: The test coin is assigned to the class with the minimum Bhattacharyya distance.

D. Evaluation Metrics for Imbalanced Data

To address the dataset imbalance, the authors define a weighted precision metric:
$\text{Overall Precision} = \sum (w_i \times \text{Recognition Rate}_i)$
Where $w_i$ is a coefficient assigned to each class to balance the influence of classes with few samples, preventing the model from being dominated by the majority class. They also use Normalized Mean-Square Error (MSE) to evaluate and mitigate over-fitting.

3. Experimental Setup

Dataset: 1,288 color JPEG images of Sassanid coins (resolution 1772×1553).
Classes: Four classes corresponding to four Sassanid kings:
1. Khosrow I (51 total images)
2. Khosrow II (490 total images)
3. Hormozd IV (99 total images)
4. Hormozd V (4 total images)
Split: 70% of data used for training, 30% for testing. Only the obverse (front) side of the coins was used.
Comparisons: The method was compared against:
- Bi-Directional PCA (BDPCA) with Assembled Matrix Distance.
- Wavelet Decomposition (Haar filter) with Bhattacharyya distance.
- Harris Corner Detector with Bhattacharyya distance.

4. Key Results

Optimal Configuration: The best performance was achieved using 112 Eigenvectors.
Accuracy:
- EigenCoin: Achieved an overall accuracy ranging from 9.45% to 21.75%, with the peak at 21.75%.
- BDPCA: Best accuracy of 19.54% (using 15 rows and 35 columns).
- Wavelet Decomposition: Best accuracy of 19.17% (using 257 features).
- Harris Corner Detector: Best accuracy of 18.81%.
Performance Analysis:
- EigenCoin consistently outperformed the other three methods.
- The method demonstrated robustness against over-fitting, as evidenced by low Normalized MSE.
- While Khosrow II (the majority class) showed significant variance in recognition, the weighted metric successfully balanced the overall precision, acknowledging the difficulty of classifying the minority classes (like Hormozd V).

5. Key Contributions

EigenCoin Manifold: The introduction of a specific PCA-based manifold tailored for ancient coin classification.
Bhattacharyya Distance Integration: Replacing Euclidean distance with Bhattacharyya distance to better handle the statistical distribution of features in the subspace, improving discrimination in complex patterns.
Imbalanced Data Handling: The proposal of a weighted precision metric to fairly evaluate performance on datasets with severe class imbalance (e.g., 490 vs. 4 samples).
Cultural Heritage Application: Demonstrating that advanced pattern recognition techniques can be effectively adapted for the specific constraints of numismatics (coin study).

6. Significance

The paper is significant because it tackles the "small sample size" and "imbalanced data" problems that often plague cultural heritage digitization projects. By proving that EigenCoin outperforms established feature extraction methods (BDPCA, Wavelets, Harris) on a real-world, difficult dataset, the authors provide a viable pilot framework for automating the classification of chaotic, historical artifacts. The ability to handle over-fitting while maintaining reasonable accuracy suggests this approach could be scaled for broader archaeological applications where data scarcity is a primary constraint.