Inclusion extraction from diamond clarity images based on the analysis of diamond optical properties

Wenjing Wang; Lilong Cai

doi:10.1364/OE.27.027242

1. Introduction

Diamond clarity is one of the most important criteria for assessing the quality of diamonds [1]. It describes the absence of tiny, natural inclusions inside a diamond or on its surface. Almost all diamonds contain unique inclusions because they are natural products of carbon formed deep within the earth and exposed to tremendous heat and pressure. Although inclusions tend to be microscopic, they interfere with the path of light traveling through a diamond, resulting in less brilliance inside the diamond. Diamond clarity is the most complex criterion to assess and classify automatically. This criterion is normally graded by competent and experienced appraisers with the help of a 10X magnification loupe under adequate lighting [2]. This manual process is quite time-consuming and takes an enormous amount of concentration. Also, the diamonds are likely to be misgraded because it is difficult for all appraisers to form a consistent evaluation and to have the same level of visual acuity [3]. Their assessments and grading results depend on their experience and a general consensus from the laboratory rather than on physical measurements.

Nowadays, most people learn about the quality of a diamond by referring to the GIA grading report [4], which represents the highest standard of reliability and consistency in the world. The report gives an assessment of diamond clarity with a plotted clarity diagram drawn by the appraiser. Significant clarity characteristics present in the diamond that influence the quality are shown in the plotted diagram, such as feather, needle and pinpoint inclusion. The diagram uses symbol to indicate the approximate locations and types of inclusions present. However, inclusions of the same type can come in thousands of shapes and sizes and have wide-ranging transparency levels. Their appearance under the same light source can also be different. Therefore, it would be more accurate to show the real appearance of inclusions rather than using symbols to substitute for the inclusions. There is a high demand in the gemological industry to replace manual diamond clarity evaluation methods with an automated system. It is highly desirable to develop an effective and robust inclusion extraction approach for automatic diamond clarity grading that can accurately identify the inclusions.

The first algorithm for diamond inclusion extraction was first proposed by Verboven et al. [5]. Their algorithm runs a number of scripts to isolate the inclusions within the region of interest using different combinations of vision analysis filters. However, the algorithm requires manually designating a region of interest in the diamond image that shows an inclusion. In addition, the accuracy of this algorithm run in a real machine is unpublished. Lin [6] designed a region similarity classifier to filter the regions of interest by intra-class comparison in a correlation and histogram matching scheme. The method can automatically designate a region of interest and address Verboven’s problem. However, this approach is established based on certain assumptions that are founded on unproven characteristics of diamonds. For the image processing part, conventional steps and existing algorithms of edge detection and image segmentation were adopted to obtain the regions of interest, but these algorithm suffer from various methodological limitations. For example, Fig. 1 shows a diamond image before and after applying the Canny edge detector [7] and the Otsu threshold searching approach [8] for extracting edges in Lin’s thesis [6]. Most of the edges are very short and non-straight, so it is difficult to form closed curves and subsequent image processing steps are confused by these edges. This approach is based on statistics rather than rules, which can lead to inaccurate separation of the regions of interest.

Fig. 1 The diamond image in Lin’s thesis [6] before and after applying the Canny edge detector and the Otsu threshold searching approach.

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So far, there has been no report on approaches or algorithms that can make optimal use of the information provided by a captured pixelated diamond clarity image to accurately extract the diamond inclusions. The main difficulty is how to separate the regions of interest automatically and efficiently. The other major scientific challenge is how to accurately distinguish between regions of diamond inclusions and their reflection regions. Some studies have tried to solve these two issues together. Machine learning techniques [9–11] such as support vector machine learning, AdaBoost learning, and neural networks have been applied to automatically infer a learning method from captured diamond image data and then perform matching of the extracted descriptors. The diamond grading performance is based on previous results of samples classification, and the number and types of diamond samples applied to the training set can greatly affect the final results. However, diamond inclusions are diverse. More than 20 types of inclusions are routinely found in diamonds. Inclusion of the same type can also have different shapes, sizes, and intensities and be present in different locations since they are in essence nature’s "fingerprint". Because of this, the grading results are sometimes difficult to understand. For example, it may not be obvious why a diamond is graded in a certain way and it may not be easy to modify an algorithm to keep it from outputting the same type of classification.

The existing diamond inclusion extraction approaches have inspired us to solve the above-mentioned problems by analyzing diamond optical properties. This paper is organized as follows: Section 2 analyzes the optical properties of the pure diamond and diamond inclusions. Section 3 introduces the newly developed image processing algorithm for diamond inclusion extraction. The experimental results are presented in Section 4. Finally, Section 5 concludes.

2. Optical properties of the pure diamond and diamond inclusions

2.1. Optical properties of the pure diamond

Diamond contains the lowest mass element capable of forming a highly symmetrical, tightly coupled crystal lattice [12]. This structure causes the diamond itself to have a unique set of optical properties. An in-depth understanding of how electromagnetic radiation interacts with the diamond itself and internal inclusions is critical to analyzing the physical properties of the diamond and the effect of the inclusions on light propagation. When a light source shines on a diamond, three important optical phenomena-reflection, absorption and transmission must be considered. The diamond clarity grading studied in this paper is performed to extract the inclusions seen by the naked eye. Therefore, this section focuses on the diamond optical properties in the visible light range with frequencies from 390 nm to 700 nm.

When light radiation passes from the air into the diamond, the light is reflected, transmitted and scattered at the interface between the two media because of their different index of refraction [13]. The refractive index of diamond is very high at 2.417, and is also dispersive with a coefficient of 0.044. Fig. 2 shows an example of how a light ray passes from air into a diamond and is finally refracted out into the air again. When the light ray is incident at point 1, it is reflected and simultaneously refracts inside and travels through the diamond lattice. Then the light ray is reflected from different surfaces inside the diamond, such as points 2 and 3, because their incident angles are higher than the critical angle c. Finally, the light is refracted out when the incident angle at the diamond surface is lower than the critical angle, such as incident angle 4. E_i is the electric field amplitude of the incident light wave, which is partially reflected and transmitted at the air-diamond interface. E_r and E_t are the amplitudes of reflected and transmitted waves. The critical angle of the diamond (θ_c) can be calculated according to Snell’s law:

θ_{c} = \sin^{- 1} \frac{n_{t}}{n_{i}}

where n_i and n_t are respectively the indices of refraction for diamond and air. The reflection and transmission coefficients can be derived as follows:

r = \frac{E_{r}}{E_{i}}, t = \frac{E_{r}}{E_{i}}

r_{⊥} = \frac{n_{i} \cos (θ_{i}) - n_{t} \cos (θ_{t})}{n_{i} \cos (θ_{i}) + n_{t} \cos (θ_{t})}, r_{∥} = \frac{n_{i} \cos (θ_{t}) - n_{t} \cos (θ_{i})}{n_{i} \cos (θ_{t}) + n_{t} \cos (θ_{i})}

t_{⊥} = \frac{2 n_{i} \cos (θ_{i})}{n_{i} \cos (θ_{i}) + n_{t} \cos (θ_{t})}, t_{∥} = \frac{2 n_{i} \cos (θ_{i})}{n_{i} \cos (θ_{t}) + n_{t} \cos (θ_{i})}

where r_⊥ is the Fresnel reflectance for perpendicular polarized light and r_|| is the Fresnel reflectance for parallel polarized light. θ_i is the incident angle, and θ_t is the refractive angle. According to Snell’s law

n_{i} \sin (θ_{i}) = n_{t} \sin (θ_{t})

the Fresnel equation can be further simplified as follows:

r_{⊥} = - \frac{\sin (θ_{i} - θ_{t})}{\sin (θ_{i} + θ_{t})}, r_{∥} = - \frac{\tan (θ_{i} - θ_{t})}{\tan (θ_{i} + θ_{t})}

t_{⊥} = \frac{2 \sin θ_{t} \cos θ_{i}}{\sin (θ_{i} + θ_{t})}, t_{∥} = \frac{2 \sin θ_{t} \cos θ_{i}}{\sin (θ_{i} + θ_{t}) \cos (θ_{i} - θ_{t})}

The fraction of the incident power that is reflected from the diamond-air interface is given by

R = \frac{{| E_{r} |}^{2}}{{| E_{i} |}^{2}} = {| r |}^{2}

Simultaneously, the intensity transmission can be expressed as

T = \frac{n_{2} \cos θ_{t}}{n_{1} \cos θ_{i}} \frac{{| E_{t} |}^{2}}{{| E_{i} |}^{2}} = \frac{n_{2} \cos θ_{t}}{n_{1} \cos θ_{i}} {| t |}^{2}

Fig. 2 Example of how a light ray passes from air into a diamond and is finally refracted out into the air again.

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As for the absorption, the light rays can absorb photons by promoting or exciting electrons from the nearly filled valence band, which can across the band gap and enter the empty state inside the conduction band. The excitation accompanied by the absorption can occur only when

h f > E_{g}

where h is the Planck constant and is equal to 4.14 × 10⁻¹⁵ eV . s, f is the frequency, hf is the energy of a single photon, and E_g is the band gap. The maximum and minimum levels of band gap energy (E_gmax and E_gmin) can be respectively calculated according to the minimum and maximum photon’s wavelengths (λ_min and λ_max) for visible light as follows:

E_{g \max} = \frac{h c}{λ_{\min}} = 3.18 e V, E_{g \min} = \frac{h c}{λ_{\max}} = 1.77 e V

where c is the speed of light in vacuum. Since the band gap of the pure diamond is very wide and is 5.45 eV greater than E_gmax , there is no electron that has enough energy to cross this wide energy gap to the conduction band. Thus, the pure diamond is transparent to light ranging from UV radiation (225 nm) to far infrared and only minor absorption bands exist resulting from two-phonon absorption between 2.5 µm and 6.5 µm. No visible light is absorbed by the pure diamond, which is transparent to the visible light. Overall, the Fresnel reflection at every diamond-air interface is approximately 17% for the visible light (R = 17.2% at 632 nm), and the maximum transmission to visible light caused by multiple from a surface without energy loss in absorption can be given by

T_{\max} = \frac{{(1 - R)}^{2}}{1 - R^{2}} = 70.65 %

2.2. Optical properties of diamond inclusions

However, the pure diamond does not exist because natural diamonds are crystals formed deep within the earth under high pressure and extreme heat [14]. During the formation process, slight irregularities and another crystal are developed within the diamond crystalline structure, which represent their natural birthmarks and are collectively known as diamond inclusions [15]. The inclusions affect not only the appearance of the diamond, but also the light propagation inside. Inclusions can take many forms depending on their formation process. They have a large diameter range and they may be present individually or in tight clusters.

In order to clearly understand the effect of inclusions on the light transmission within diamonds, diamond inclusions are divided into various types. The first type is the liquid or amorphous inclusion comprising atoms that are closely aggregated but not crystallized. Such impurities would cause a diffuse amorphous ring or irregular shape to be superimposed on the diamond pattern. Therefore, when the diamond is illuminated under dark background field, diffuse reflection occurs on the surface of diamond impurities as shown in Fig. 3(a). Therefore, the reflection of diamond inclusions is usually faceted, but shapeless as shown in Fig. 3(b). The second type of diamond inclusion is the gas-like distribution of single atoms, because air may be captured within a diamond crystal during its formation. The optical effect of such an inclusion is strong small-angle scattering. The light intensity drops in a way that depends on the atomic scattering factor of the inclusions. This optical effect can be attributed to the random distribution of Fe, Si, Ca or other elements, possibly replacing one or more carbon atoms [16]. The atoms forming the inclusions produce an intermediate energy level, which gives rise to more energetic electrons that could jump across the gap to the conduction band and absorb the light rays due to the opaque minerals.

Fig. 3 Diffused reflection from the diamond inclusion and the irregular shape of the inclusion curve.

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By analyzing the diamond formation and the physical properties of the pure diamond and diamond inclusions, it can be concluded that two features can be applied to distinguish the inclusions in a diamond according to their optical properties. One is a wide discrepancy between the absorption rate of the diamond itself and that of the inclusions. All the electrons in the diamond valence band and a photon with at least 5.45 eV of energy are needed to push an electron to the conduction band, so that no photon would be absorbed by the visible light. On the other hand, the random distribution of the opaque minerals such as Fe, Si, Ca or other elements enables absorption by visible light due to their narrow band gaps. The other feature is that the texture and irregular shape of the diamond inclusions result in a difference between light transmission through the inclusions and that through the pure diamond according to Fresnel’s equations.

3. Development of an image processing algorithm for inclusion extraction

The objective of an image processing algorithm for inclusion extraction is to accurately separate the regions of interest in diamond clarity images and then identify the diamond inclusion regions. Such algorithm is the key to achieving automatic detection in diamond clarity systems. In this study, the images used for inclusion extraction are captured under the image acquisition system proposed elsewhere [9]. Fig. 4 shows the light path within the diamond clarity image acquisition system. This hardware design was proposed based on a mathematical model and the ray tracing technique to control the distribution of different types of signals, such as reflections, inclusions and transmissions. The parameters of the hardware components were designed by modeling the light ray propagation inside the diamond sample, lighting system and imaging system to understand how the diamond image is formed. The integrating sphere used in proposed system is newly designed to control the light distribution in the image plane and provide uniform illumination to the diamond sample while it is being inspected under white LED lamps with a specific spectral power distribution. The selection of the white LED lamps for the light source considers three aspects: the intensity of the light source, the spectral power distribution of the light source and the stability of the output light. The specification of the LED lamp was analyzed elsewhere [9].

Fig. 4 Schematic diagram showing the light path within the diamond inclusion image acquisition system.

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The signal-to-noise ratio (SNR) [17] of acquired diamond clarity image can be calculated as

S N R = \frac{\sum_{x = 0}^{m - 1} \sum_{y = 0}^{n - 1} \hat{f} {(x, y)}^{2}}{\sum_{x = 0}^{m - 1} \sum_{y = 0}^{n - 1} {[f (x, y) - \hat{f} (x, y)]}^{2}}

where f(x,y) is the original image and

\hat{f} (x, y)

is the noisy image, m and n are the width and height of the image. After capturing 150 diamond images, the average SNR of the diamond images can be calculated and it is 32.08 dB. According to the SNR standard [17], the value represents that the SNR of the diamond image is high and the image quality is excellent and the diamond image contains abundant useful information.

In order to develop the automatic diamond clarity detection system, how to process the information is a significant issue to be resolved in this paper. The first step is pre-processing to prepare the original acquired diamond image for feature extraction analysis, and also to fix any problems that would otherwise adversely affect feature description, which is analyzed in detail in the Section 3.1. In terms of the diamond image segmentation, the gray value distribution of different diamond signals is analyzed to accurately eliminate the background, so the inclusion regions and reflection regions can be naturally divided, which is analyzed in Section 3.2. Furthermore, the method to distinguish the inclusion regions and reflection regions is presented in Section 3.3, which is based on the analysis of diamond physical properties described in Section 2. Fig. 5 illustrates the proposed image processing algorithm for inclusion extraction.

Fig. 5 Block diagram of the image processing steps for diamond inclusion extraction.

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3.1. Image pre-processing

In the first step, image pre-processing [18] is performed to prepare the original acquired diamond image for feature extraction analysis, and also to fix any problems that would otherwise adversely affect feature description. For example, if an image shows two diamonds, or no diamond can be seen, or the diamond is shown at an angle, then the image must be corrected first. Fig. 6(a) shows an example of a diamond that is sitting on the sample loading glass at an angle. It is mainly because the weight of inspected diamond is very light, which causes that it may be obliquely placed with other facet down on the sample loading. Fig. 6(b) gives an example of when the diamond is correctly captured. Although the inspected diamond is placed in the center of the sample loading glass with the table facet facing down, there is some degree of error in the automatic placement by the robotic arm. Since the inspected diamond is very small, the position error and the size difference of the diamond sample cause that the diamond region is in different location on the whole original captured image. Therefore, the complete diamond region is first extracted and resized into a new image with the specified numbers of rows and columns. The image pre-processing consists of sensor correction including dead pixel and vignetting correction [19], lighting correction and geometric correction, which can compensate for the negative effect from the geometric lens distortion, vignetting and uneven lighting across the scene. Adaptive defect correction methods [20] are adopted to correct various types of defects, such as column or line defects, single pixel defects or clusters defects. The vignette correction based on geometric warp function [21,22] increases illumination toward the edges to solve the issue of dark edges caused by unevenly distributed light. Lighting correction is important to define the shape and outline of diamond image features [23–25], so that the boundary definition and boundary segmentation based on edges or thresholds becomes more distinct. Geometric correction deals with slight radial distortion, geometric aberration or edge bending caused by the lens.

Fig. 6 Original captured images of the inspected diamond sample. (a) An example of a diamond that is sitting on the sample loading glass at an angle. (b) An example of a diamond that is correctly placed with the table facet facing down.

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3.2. Removal of the diamond background

Diamond clarity images are captured under the image acquisition system proposed elsewhere [9], which can control the distribution of different types of signals through hardware improvement to avoid their overlapping with each other. The system achieves this by optimizing the parameters of each optical component and with the integrating sphere design. The captured diamond clarity image consists of three parts: background regions (diamond facets), inclusion regions and reflection regions. By analyzing the histogram of the diamond clarity image, it can be seen that the gray-scale interval values of the pixels in the background regions are generally lower than those in the inclusion regions and reflection regions. This is consistent with the conclusion reached in the hardware improvement exercise for diamond clarity [9]. If image noise and background regions can be successfully removed, the regions of interest including the inclusion regions and reflection regions can be easily separated. An enhancement operation (filter) is applied to increase the SNR of the diamond clarity image. Specifically, the filter defines how the numerical value of a pixel relates to its actual brightness to remove the background and highlight the details of the diamond inclusions. Enhancements are also applied to optimize and sharpen the specific features of the signals. In order to minimize the influence of image noise and fluctuation in illumination [26] on the algorithm, all of the designed thresholds apply relative values instead of absolute values. The difference between the filtered pixels and the original pixels can be expressed by the root-mean-squared difference (Δ_rms) between the input image and the output image. It is defined as

Δ_{r m s} = {[\frac{1}{m n} \sum_{i = 0}^{m - 1} \sum_{j = 0}^{n - 1} {[O (i, j) - I (i, j)]}^{2}]}^{1 / 2}

where O(i,j) is the input diamond image, I(i,j) is the filtered image and m and n are the width and height of the diamond image, A is the parameter value, which is designed according to the gray-scale interval values of different types of signals. c_i is cumulative distribution function of pixel values of input diamond image. Considering c_i can eliminate the effect of light fluctuations to enhance the robustness of the system.

Figs. 7(a) and 7(b) respectively show the diamond clarity images before and after the enhancement operation. It can be seen that the diamond facets and noise are excluded and the remaining inclusion and reflection regions are accurately separated in Fig. 7(b). The curve enclosing each region of interest is complete, continuous and closed. These curves are marked in red in Fig. 8(a).

Fig. 7 Diamond clarity images before (7(a)) and after (7(b)) the enhancement operation.

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Fig. 8 (a) Regions of interest extracted from Fig. 7(b) marked with red curves. (b) Intersections detected in Fig. 7(b) marked with red dots.

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3.3. Distinguishing diamond inclusions from reflections

After accurately acquiring the regions of interest in the diamond clarity image, how to distinguish between the inclusion regions and the reflection regions, and finally effectively extract the diamond inclusions are significant issues to be addressed. Two main findings about the diamond optical properties are built into the image processing to identify the image features of individual regions and distinguish between diamond inclusions and reflections. One is the wide discrepancy between the absorption rate of the pure diamond and that of inclusions. The other is the irregular texture and shape of the diamond inclusions which cause light to propagate through the inclusions differently than it does through the pure diamond. Therefore, each reflection region with a regular enclosing curve contains a small number of intersections. On the contrary, a diamond inclusion is naturally formed with a disordered shape and consists of a large number of intersections.

An intersection is defined as a large variation in intensity in all directions of a specific region in the diamond image [27]. It describes the difference in intensity for a displacement of (u,v) in all directions, which can be expressed by

E (u, v) = \sum_{x, y} w (x, y) {[I (x + u, y + v) - I (x, y)]}^{2}

where w(x, y) is the window function to give weights to pixels. It can be a rectangular window or Gaussian window. I(x + u, y + v) is the shifted intensity and I(x, y) is the intensity of a pixel. After applying the Taylor Expansion, Eq.15 can be given as follow

E (u, v) \approx [u v] M [\frac{u}{v}]

M = \sum_{x, y} w (x, y) [\frac{I_{x} I_{x}}{I_{x} I_{y}} \frac{I_{x} I_{y}}{I_{y} I_{y}}]

where I_x and I_y are respectively the image derivatives in the x and y directions. Then, a score is created to determine whether a window can contain an intersection or not:

R = d e t (M) - k {(t r a c e (M))}^{2}

\det (M) = λ_{1} λ_{2} t r a c e (M)

where λ₁ and λ₂ are the inherent values of M, and k is a constant. When |M | is small, which occurs when λ₁ and λ₂ are small, the area is flat. When R<0, which occurs when λ₁≫ λ₂ or vice versa, the area is an edge. When R is large, which occurs when λ₁ and λ₂ are large, the area is an intersection.

Fig. 8(b) illustrates the result of detecting intersections in Fig. 7(b). The intersections are marked by red dots. After giving a specific threshold for the number of intersections, the inclusion and reflection regions can be effectively extracted. Furthermore, the inclusion regions shown in Fig. 9(a) and the reflection regions shown in Fig. 9(b) can be extracted according to their coordinates in the original diamond image. The actual size (S_a) of each inclusion region seen by the naked eye can be calculated by:

S_{a} = S_{z} \times N_{p} = L_{p} \times N_{p} / M

where S_z is cell size per pixel, N_p is the number of pixels in an inclusion region, L_p is the physical length of the pixels of the charge-coupled device camera and M is the total magnification of the lens.

Fig. 9 (a) Extracted inclusion regions of the diamond clarity image (b) Extracted reflection regions of the diamond clarity image.

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4. Experimental verification

Various experiments were conducted to test the performance of the inclusion extraction approach. A total of 150 real diamond samples with different clarity grades (VS1, VS2, SI1, SI2 and I1) were prepared for inspection. A diamond clarity image of each diamond sample was captured by an image acquisition system proposed elsewhere [9] after placing the sample on the loading glass. Then the diamond clarity image was inputted into the developed image processing algorithm for inclusion extraction. The inclusion regions were automatically extracted, which describes the location, shape and brightness of the inclusions in detail. Each round of inclusion extraction took approximately 5 s. Fig. 10 illustrates some examples of the inclusion regions (right) extracted from their corresponding captured diamond clarity images (left). In order to test the robustness of the algorithm, a diamond sample was detected multiple times at different in rapid succession every few minutes, so that there is a slight difference in the illumination intensity between tests as well as image noise caused by different factors, such as the statistical quantum fluctuations of the image sensor, the circuitry of the camera and the unavoidable shot noise of the photon detector. The extraction results for the same diamond sample under different conditions are shown in Fig. 11. It can be seen clearly that the extracted inclusions are accurate and remain the same even when the illumination conditions and the placement direction of the diamond sample are changed. Therefore, it can be concluded that the proposed inclusion extraction approach is insensitive to the different types of noise and highly robust.

Fig. 10 Experimental results of diamond inclusion extraction. (Left) Captured clarity image of an inspected diamond sample. (Right) Extracted inclusion regions.

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Fig. 11 Experimental results of the same diamond sample under different illumination intensity and placement direction. (Left) The captured clarity image of an inspected diamond sample (Right) The extracted inclusion regions.

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After conducting the inclusion extraction experiments, gemological experts were invited to manually evaluate all diamond samples used in the previous experiments and draw the clarity diagram of each diamond sample to show the diamond inclusions they observed. After the experts reached a consensus, their manual extraction results were compared with the experimental results of the proposed inclusion extraction approach. The number of inclusions of each diamond and size and position of each inclusion are compared to determine the match rate. The level of consistency is shown in Table 1. The match rate exceeds the expectation for accuracy in automatic diamond clarity detection in the gemological industry. For the error analysis, there are two main reasons for the mismatched result. One is that when an inclusion is overlapped with a reflection region with a very high intensity (brightness). The area of the extracted inclusion region is increased and the diamond may be incorrectly assessed to be of a lower grade than it actually is. The other reason is that diamonds with a very poor cut may have very complex reflection regions, which need more extensive analysis.

Table 1. Consistency Between the Results Obtained by the Diamond Inclusion Extraction Approach and Manual Inclusion Detection.

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5. Conclusion

Diamond clarity is one of the most significant criteria for evaluating diamond quality, and has been the most complex to assess and classify automatically. Although many gemological laboratories around the world have been working on a clarity unit, no one has been able to develop an effective inclusion extraction approach with high accuracy. The major scientific challenge is how to accurately separate the regions of interest and then distinguish between diamond inclusions and reflections using information provided by diamond images. In this paper, these issues are first resolved by analyzing the optical properties of a diamond.

The optical properties of the pure diamond and diamond inclusions are theoretically analyzed to provide a deep understanding of how diamond clarity images are formed and the image features of different types of signals, based on the the light propagation from the light-emitting source to the image plane. Two main findings are made to distinguish between diamond inclusions and reflections. One is wide discrepancy between the absorption rate of the pure diamond and that of inclusions. This discrepancy is caused by the different levels of minimum energy needed to push an electron to the conduction band. Therefore, the wide band gap of the pure diamond results in no absorption to the visible light. On the contrary, diamond inclusions can absorb obvious amounts of photons of visible light. The other main finding is the irregular texture and shape of the diamond inclusions which cause light to propagate through the inclusions differently than it does through the pure diamond according to Fresnel’s equations. These findings about the diamond optical properties are built into an image processing algorithm to extract diamond inclusions by accurately separating the regions of interest in a diamond clarity image, and also to identify the image features of individual regions. These steps are key to the success of the diamond clarity automatic detection system.

The effectiveness and robustness of the newly developed diamond inclusion extraction approach are verified experimentally. The experimental results match 92% of the gemologists’ manual detection results. Such results cannot be achieved by machine learning, artificial intelligence or the popular image processing approach alone without a deep study of the diamond optical proprieties. The theoretical analysis of the diamond optical proprieties facilitates the software development, so that the complexity and operation time of the algorithm can be greatly reduced. The proposed approach also has the potential to be extended to other applications based on image processing. Studying the optical properties of the detected object in detail provides a basis to accurately understand the features of different image signals.

Future research will focus on the development of the clarity classification system to assign an accurate and objective grade to a diamond based on extracted inclusions, as well as focus on the study of the diamond cut to overcome the experimental error caused by the complicated formation of reflections in diamonds, especially for diamond samples with a poor cut design.

Funding

Research Grants Council of Hong Kong (RGC) (16216216).

Acknowledgments

We would like to acknowledge that this research was supported by the Research Grants Council, Hong Kong, SAR PR China under GRF project number: 16216216. And the authors would also like to thank the editor and all reviewers for their comments to improve the quality of this paper.

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Inclusion extraction from diamond clarity images based on the analysis of diamond optical properties

Abstract

1. Introduction

2. Optical properties of the pure diamond and diamond inclusions

2.1. Optical properties of the pure diamond

2.2. Optical properties of diamond inclusions

3. Development of an image processing algorithm for inclusion extraction

3.1. Image pre-processing

3.2. Removal of the diamond background

3.3. Distinguishing diamond inclusions from reflections

4. Experimental verification

5. Conclusion

Funding

Acknowledgments

References

Cited By

Figures (11)

Tables (1)

Equations (20)

Optics Express

	VS1	VS2	SI1	SI2	I1	Overall
Total number of inspected samples	20	27	30	30	43	150
Number of samples consistent with manual detection	18	26	28	26	40	138
Match rate	90%	96.3%	93.3%	86.7%	93%	92%