A PCB image segmentation model based on rotational X-ray computed laminography imaging

Abstract

BACKGROUND:

The rapid development of industrialization in printed circuit board (PCB) warrants more complexity and integrity, which entails an essential procedure of PCB inspection. X-ray computed laminography (CL) enables inspection of arbitrary regions for large-sized flat objects with high resolution. PCB inspection based on CL imaging is worthy of exploration.

OBJECTIVE:

This work aims to extract PCB circuit layer information based on CL imaging through image segmentation technique.

METHODS:

In this work, an effective and applicable segmentation model for PCB CL images is established for the first time. The model comprises two components, with one integrating edge diffusion and l ₀ smoothing to filter CL images with aliasing artifacts, and the other being the fuzzy energy-based active contour model driven by local pre-fitting energy to segment the filtered images.

RESULT:

The proposed model is able to suppress aliasing artifacts in the PCB CL images and has good performance on images of different circuit layers.

CONCLUSIONS:

Results of the simulation experiment reveal that the method is capable of accurate segmentation under ideal scanning condition. Testing of different PCBs and comparison of different segmentation methods authenticate the applicability and superiority of the model.

Keywords

PCB CL image segmentation active contour model

1 Introduction

PCB plays a vital role in electronic system and is dominant in industry. The increasing demand for PCBs in industrialization warrants more complexity and integrity, which results in circuit layer and trace density getting increased. Inspection techniques with application to PCB are very important to ensure safety performance as there might be short circuits in internal circuit layers [1]. PCB inspection will also do help for regular maintenance to extend service life of aging devices and expensive electronic products that have lost the source files [2]. As electronic items penetrate our lives, the amount of e-waste has increased rapidly. PCB inspection can also contribute to PCB component classification, which facilitates to PCB waste recycling [3].

Bare PCB is usually made of high-density metal materials like copper and low-density insulation materials. PCB can be divided into 2-layer board, 4-layer board and other multi-layer boards of 10 layers or even 20 layers. Traditional manual inspection technique will damage the object and is difficult to identify the increasingly dense and trace of smaller width. PCB inspection usually adopts mechanical inspection [4]. Automatic optical inspection like automatic surface detection instrument can be used to inspect PCB, but it is incapable of detecting internal structures [5]. Ultrasonic imaging can also be used to inspect PCB defects, however, it is limited to testing simple PCBs [6]. Computed tomography (CT) and CL based on X-ray imaging are nondestructive testing techniques that are able to visualize the internal structures of the object, according to that different components have different X-ray attenuation coefficients [7–9]. CT is widely used in medical diagnosis [10] and industrialization [11]. CL is more flexible to acquire images of large flat samples with high spatial and contrast resolution while CT has higher risks of collision during the scan and rays not being able to penetrate the flat object. This is due to the special scanning geometry of CL. CL system has several types of scanning geometries including planar [12, 13], swing [14], rotary [15] and more complex geometries like spherical sinusoidal scan [16]. Over these years, rotational CL has been widely used in industrial nondestructive testing. The CL referred to in this article is X-ray rotational CL. The scanning geometry of the adapted CL set-up in this work can be referred to [15].

As CL scanning mode can lead to incomplete projection data and directly applying analytic reconstruction algorithm like Feldcamp-Davis-Kress (FDK) algorithm [17] for CL imaging will induce aliasing artifacts, it is challenging to segment PCB images based on CL imaging due to the aliasing and blurring. Researchers are trying to correct CL projections for filtering in pursuit of improving the 3-D image reconstruction [18]. In recent years, iterative reconstruction algorithms are being actively developed for CL imaging, which enable reduction of aliasing artifacts to some extent by improving regularizer [19, 20] with combination of the data features like edge property [21]. However, as iterative computation is large and the process is time-consuming, it is not applicable to use iterative reconstruction methods for engineering projects. Post-processing the images with combination of prior information after FDK reconstruction is worthy of exploration.

Due to the aliasing in reconstructed slices, pseudo structures from adjacent circuit layers will appear in the reconstructed slices of the current circuit layer, which brings great challenges to the image segmentation. In addition, slight metal artifacts and scattering artifacts will be induced [22, 23], resulting in low-contrast and intensity inhomogeneity. To tackle these problems, a fuzzy energy-based active contour model driven by local pre-fitting energy with edge diffusion l ₀ smoothing (FALPF-EDLS) is proposed to segment PCB images based on CL imaging in this paper. This model includes two parts. One part, the edge diffusion l ₀ smoothing, is to remove the pseudo structures and homogenize the intensities of the image. The other part is the fuzzy energy-based active contour model driven by local pre-fitting energy, which is to process the filtered images and output the segmentation results. Experiments on both synthetic data and real data are carried out to show the effectiveness of the proposed model for different types of PCBs in this paper. The simulation experimental results show that the proposed model has a good performance on the PCB CL image segmentation under ideal scanning conditions. The testing of 5 real PCBs with different sizes and layers has verified the applicability of FALPF-EDLS. The experiment on the reproduction of a complete PCB indicates the feasibility of FALPF-EDLS. Finally, the comparison experiment demonstrates the superiority of the proposed model.

The remainder of the paper is organized as follows. In Section 2, the related works are briefly illustrated. In Section 3, we describe the proposed model FALPF-EDLS in detail and analyze the superiority. In Section 4, experiments on both simulated data and real data are carried out, as well as the corresponding analysis and comparisons. Finally, conclusions and discussions of this work are given in Section 5.

2 Related works

PCB images are usually composed of circles and lines, of which are of simple shapes. Generally, the PCB circuit layers can be divided into three kinds of layers with different image characteristics: surface layer (top/bottom layer), copper layer (ground layer or power layer), and trace layer (signal layer). Copper layer and signal layer are internal layers. As are shown in Fig. 4, images of the second and third columns are the reconstructed slices of PCB copper layers based on CL imaging. As copper layer is usually covered by a large area of copper, a large area of pseudo structures from adjacent layers will appear in the reconstructed slices representing the copper layer, and these structures are easily mistaken for real structures. As are shown in the third and sixth columns of Fig. 4, the signal layers usually exist in complex PCBs that have narrow traces. The PCB CL images of signal layers are of low contrast, which also brings challenges to segmentation.

It can be seen from Fig. 2(a) that l ₀ gradient minimization [24] is an efficient smoothing filter for suppressing low-amplitude structures but it is still difficult to deal with relatively high-amplitude aliasing artifacts, which often occur in copper layers and trace layers. Besides, as can be seen in the second column of Fig. 2(b), the green curve (the pixel intensity distribution of l ₀ smoothing) in the diagram is far away from the blue curve (the pixel intensity distribution of pseudo ground truth (here after PGT)), which indicates that the image after l ₀ smoothing is in low-contrast. Edge information diffusion reconstruction (EIDR) model brought up in [21] utilizes reliable edge information of the inner slices and combines with SART [25] to reconstruct the internal structure. EIDR is effective in suppressing the inter-slice aliasing artifacts even relatively high-amplitude pseudo structures. However, as an iterative reconstruction method, EIDR is still time-consuming with large computation. The essential part for EIDR method is the edge-preserving diffusion (here after ED in this paper) procedure within slices. Similar to l ₀ gradient minimization, ED is also able to suppress aliasing artifacts even high-amplitude pseudo structures, and obtain relatively high-contrast results, as is shown in Fig. 2. However, as ED highly depends on faithful edges to suppress aliasing artifacts, it will fail if the edges of pseudo-structure are very clear or the edges of true structures are weak. It can be seen in Fig. 2(b) that the red curve (the pixel intensity distribution of ED) in the diagram is not smooth, which indicates that the image is with locally intensity inhomogeneity after ED processing. Combining l ₀ gradient minimization and ED will do help.

Image segmentation is an elementary task in the field of computer vision and is aimed to divide a given image into different regions where each region is homogeneous with regard to a certain feature [26]. As the aliasing artifacts in these images seriously interfere with subsequent segmentation, it is vital to remove the aliasing artifacts especially in the internal circuit slices for this work. Active contour model (ACM) [27, 28] is one of the most effective image segmentation models and has advantages in dealing with topological changes of contour curves. ACMs can be divided as edge-based ACMs and region-based ACMs. Edge-based ACMs like geodesic active contour model [29] highly rely on gradient information but they are sensitive to initial contour and have little effect on the weak edges and the noise interference. In contrast, region-based ACMs utilize the image features, like the image intensity, texture, to evolve contours. The Chan-Vese (CV) method [28, 30] based on Mumford-Shah (M-S) functional is a widely used region-based ACM that can handle objects with boundaries not necessarily defined by the gradient. However, CV segmentation model has high computational cost for assuming highly constrained models for pixel intensities within each region. Besides, it does not perform well on images with intensity inhomogeneity due to the assumption that the image intensities are statistically homogeneous. Fuzzy energy-based active contour (FEBAC) [30] method is a variation of the CV model and is proposed as a stable active contour with the resistance to noise with combination of the concept of fuzzy clustering. However, FEBAC cannot maintain the distance feature of the pseudo LSF without regularization term, and still needs to be improved for image segmentation with intensity inhomogeneity. Local binary fitting (LBF) [31] model is another variation of the CV model that can better deal with images with intensity inhomogeneity by extracting local information with a localized convolutional kernel function, based on the assumption that the intensities inside and outside the contour curve are constants within a small area. However, LBF is not sensitive enough to perform well on the images of low contrast. Fuzzy region-based active contours driven by weighting global and local fitting energy (FRAGL) [32] model is proposed based on the idea of LBF model and FEBAC model, where a fuzzy region energy is formulated by constructing a weighting hybrid fitting energy with local spatial image information, which is to approximate the image with intensity inhomogeneity. However, as can be seen from the third and fifth columns of Fig. 16, both LBF and FRAGL are not sensitive to the thin trace in PCB CL images. An active contour model driven by local pre-fitting energy (LPF) for image segmentation is presented in [33]. As is shown in the fourth column of Fig. 16, LPF shows good sensitivity to signal layer segmentation by locally computing average image intensities before the evolution of curve. Though the contour cannot evolve to the best place for the segmentation of copper layer, combining the advantages of LPF and fuzzy energy based active contour models will do help.

3 The proposed model

Based on the analysis above, we propose a fuzzy energy-based active contour model driving by weighted local pre-fitting energy for PCB CL image segmentation, with combination of edge-preserving diffusion and l ₀ smoothing pre-processing. In order to remove the pseudo structure in PCB CL images, we propose to combine edge diffusion and l ₀ smoothing (EDLS) for image preprocessing. As can be seen in Fig. 1(a), the proposed model includes two parts. The input is PCB CL image reconstructed by FDK algorithm. The image is firstly filtered by EDLS for removing pseudo structure and getting homogenized, and is then segmented by fuzzy energy-based active contour model driving by weighted local pre-fitting energy (FALPF). The detail of these two parts can be seen in Fig. 1(b) and (c). In this section, we will describe the proposed model in detail.

Fig. 1

(a) is the overall flowchart of the proposed model. (b) shows the processing steps of EDLS and (c) presents the process of FALPF.

3.1 EDLS

The aliasing of information among CL reconstructed slices will bring pseudo structures of adjacent slices to the images and cause the image contrast getting lower and intensity inhomogeneity, which makes it difficult for the segmentation. Therefore, it is necessary to suppress the aliasing artifacts and improve the CL image quality. l ₀ smoothing is effective for eliminating a manageable degree of low-amplitude structures, which can be used to deal with the CL aliasing artifacts. The optimization model can be expressed as $\min_{S} E^{l_{0}} (S; I) = \sum_{q} {(S_{q} - I_{q})}^{2} + κ Ct (S),$ (1) where $Ct (S) = # {q | | \partial_{x} S_{q} | + | \partial_{x} S_{q} | \neq 0} .$ (2)

In (1), I is denoted as the input image (the current result in the iterative process), S refers to the computed result. ∂_x S _q and ∂_x S _q are the gradients of pixel q along x and y directions respectively. # {} is the counting operator and Ct (S) is the gradient measure that counts q whose magnitude |∂_x S _q| + |∂_x S _q| is not zero. κ is a weight directly controlling the significance of Ct (S).

EIDR model can be computed by minimizing the following energy functional: $E^{eidr} (f) = \frac{1}{2} \int \frac{K (x, y, z)}{λ (x, y, z)} ({f_{x}}^{2} + {f_{y}}^{2}) dxdydz + \frac{β}{2} \int {(Rf (x, y, z) - p)}^{2} dxdydz .$ (3)

f (x, y, z) is the image to be seeking. f _x and f _y denote the gradients along x and y directions respectively. K (x, y, z) is used to control the propagation speed of the inner-slice edge information and λ (x, y, z) is the edge indicator whose value will be large for edge points while small for non-edge points. The weighting parameter β > 0 is to balance the two terms. p is the acquired projection data, and R is the forward projection operator. Obviously, (3) contains two energy functionals that the former energy functional is for ED and the latter is for the SART reconstruction.

As is mentioned in Section 2, l ₀ gradient minimization performs well in suppressing low-amplitude pseudo structures to some extent and homogenizing the intensity, but get images with lower contrast. ED is able to suppress high-amplitude pseudo structure but the intensity is inhomogeneous. The experimental result shown in Fig. 2 supports the claim, which has also been explained in Section 2.

Fig. 2

(a) shows a PCB CL slice (original image, ORI) and PGT, as well as the results after ED, l ₀ smoothing (LS), and EDLS. The display window = [–3,7]. (b) shows the pixel intensity distribution diagrams of ED (the first column), LS (the second column), and EDLS (the third column), along the row (the first row) and the column (the second row) corresponding to the orange dotted line in the ORI image of (a). (c) shows the segmentation results of FALPF, FALPF-ED, FALPF-LS, FALPF-EDLS and reference.

In order to suppress the pseudo structures and improve the image quality, we combine the advantages of ED and l ₀ smoothing propose EDLS to preprocess PCB CL images. The EDLS minimization problem can be written as follows: $\begin{matrix} \min_{S, \tilde{I}} E^{edls} (S, \tilde{I}; I), \\ E^{edls} (S, \tilde{I}; I) = \frac{1}{2} \int K (x, y) ({\tilde{I}}_{x}^{2} + {\tilde{I}}_{y}^{2}) dxdy \\ + \frac{β}{2} \int λ (x, y; t h_{1}, t h_{2}) {(\tilde{I} (x, y) - I)}^{2} dxdy \\ + \sum_{q} {(S_{q} (\hat{I}; κ) - {\hat{I}}_{q})}^{2} + κ Ct (S (\hat{I}; κ)) . \end{matrix}$ (4)

In (4), I is the current result, while $\tilde{I}$ denotes the edge diffusion image. ED is based on the finding that the inner-slice edges can be reconstructed rather accurately as the projection data corresponding to the X-ray paths are tangent to the inner-slice edges. Thus, in order to obtain reliable edge image, the edge function λ should be well defined. In our model, the edge function is defined as follows: $λ (x, y; t h_{1}) = {\begin{matrix} λ (x, y) = 10^{8} & if (x, y) ɛ {(x, y) | G (I (x, y)) \geq t h_{1}} \\ λ (x, y) = 10^{- 8} & if (x, y) ɛ {(x, y) | G (I (x, y)) < t h_{1}} \end{matrix},$ (5) $λ (x, y; t h_{1}, t h_{2}) = bwareaopen (λ (x, y; t h_{1}), t h_{2}),$ (6)

th ₁ and th ₂ are threshold parameters. bwareaopen (f ₀, th) is a small area elimination operator, whose function is to eliminate pixel regions with region area smaller than th in the binary image f ₀. Details of the numerical solution process for obtaining diffusion image $\tilde{I} (x, y)$ can be referred to [21]. $\hat{I} = \tilde{I} (x, y) + t h_{3} \cdot G (λ)$ , where G (λ) is the gradient of λ, th ₃ is a positive scalar. $S (\hat{I}; κ)$ refers to the result. Since the image contrast after l ₀ smoothing is not satisfying, we enhance on the diffusion image. The detail of the numerical solution for l ₀ gradient minimization can be referred to [24].

As is shown in Fig. 2(b), the curve in the EDLS diagram is relatively smoother than that of ED and is also relatively closer to that of PGT, which indicates that EDLS can effectively remove pseudo structure and keep the image in relatively homogeneous with higher contrast compared with ED and l ₀ smoothing (here after LS). Figure 2(c) shows the segmentation results by FALPF, FALPF-ED, FALPF-LS, FALPF-EDLS and the corresponding reference, which comes from PCB design source file and is for reference. Without preprocessing, the segmentation image obtained by FALPF is not accurate that the pseudo structures from adjacent layers are also preserved in the segmentation. The segmentation results of FALPF-EDLS is more accurate and clear comparing to the result of FALPF-ED and FAPLF-LS. EDLS performs better on both the intensity distribution of the filtered images and the segmentation results. The artifacts in the boxes are prone to segmentation errors. FALPF-EDLS performs best and looks the most similar to the reference.

3.2 FALPF

For the segmentation, we propose a fuzzy energy-based active contour model driving by weighted local pre-fitting energy to segment the image filtered by EDLS. We name it as FALPF. The energy function can be written as $\begin{matrix} \min_{u} E^{falpf} (u), \\ E^{falpf} (u) = λ_{1} \int_{Ω} {[u (x)]}^{m} g {(I (x) - c_{1}^{falpf})}^{2} dx + λ_{2} \int_{Ω} {[1 - u (x)]}^{m} g {(I (x) - c_{2}^{falpf})}^{2} \\ dx + a_{1} \int_{Ω} δ_{ɛ} (u - 0.5) | \nabla (u - 0.5) | dx + a_{2} \int_{Ω} \frac{1}{2} {(1 - | \nabla (u - 0.5) |)}^{2} dx, \end{matrix}$ (7)

The FALPF is established based on the FRAGL model, which is the variation of CV model with fuzzy clustering concept, as well as the modified version of FEBAC. FALPF uses 0.5 level set as the evolving curve based on the membership value u and the pseudo LSF u (x) is defined as: ${\begin{matrix} C = {x \in I : u (x) = 0.5} \\ in (C) = {x \in I : u (x) > 0.5} \\ out (C) = {x \in I : u (x) < 0.5} \end{matrix} .$ (8)

λ₁, λ₂ and α are positive constants. m is the weighting exponent for the fuzzy membership. g (x) is brought up in FRAGL as an edge detector to reduce noise and smooth the edge and can be expressed as follows: $g (x) = \frac{1}{1 + | \nabla K_{σ} (x) * I (x) |},$ (9) where K _σ (x) is a Gaussian kernel with standard deviation σ: $K_{σ} (x) = \frac{1}{{(2 π)}^{n / 2} σ^{n}} e^{- {| x |}^{2} / 2 σ^{2}} .$ (10) $c_{1}^{falpf}$ and $c_{2}^{falpf}$ are the weighted fitting energies: $c_{1}^{falpf} = w_{1} f_{o} + w_{2} f_{l}, c_{1}^{falpf} = w_{1} f_{b} + w_{2} f_{s} .$ (11)

Where the fuzzy fitting energies are $\begin{matrix} f_{o} = \frac{\int_{Ω} \int_{Ω_{x}} ω (x, y) I (x) {[u (x)]}^{m} dydx}{\int_{Ω} \int_{Ω_{x}} ω (x, y) {[u (x)]}^{m} dydx}, \\ f_{b} = \frac{\int_{Ω} \int_{Ω_{x}} ω (x, y) I (x) {[1 - u (x)]}^{m} dydx}{\int_{Ω} \int_{Ω_{x}} ω (x, y) {[1 - u (x)]}^{m} dydx}, \end{matrix}$ (12) $ω (x, y) = \frac{1}{1 + dis (x, y)},$ (13)

dis (x, y) denotes the spatial distance between pixel x and pixel y. The size of a local window is (2k + 1) × (2k + 1) where the radius of the local window k is the positive constant. In FRAGL, a weighting hybrid fitting energy with local spatial image information is proposed to approximate the image with intensity inhomogeneity. The weighted hybrid fitting energy is the combination of local binary fitting energy and the fuzzy fitting energy. We propose to use LPF instead to improve the local sensitivity. The pre-fitting energy can be expressed as follows: ${\begin{matrix} f_{m} (x) = mean (I (y) | y ϵ Ω_{x}) \\ f_{s} (x) = mean (I (y) | y ϵ Ω_{s}) \\ f_{l} (x) = mean (I (y) | y ϵ Ω_{l}) \end{matrix},$ (14) where Ω _s and Ω _l are defined by ${\begin{matrix} Ω_{s} = {t | I (y) < f_{m} (x)} \cap Ω_{x} \\ Ω_{l} = {t | I (y) > f_{m} (x)} \cap Ω_{x} \end{matrix} .$ (15)

As is mentioned before, Ω _x represents a small neighborhood centered at x with radius k. Ω _s is the region where the image intensities smaller than the average intensities in Ω _x, and Ω _l is the region with larger image intensities than the average intensities in Ω _x. f _s and f _s are the local average intensities in Ω _s and Ω _l.

a ₁ and a ₂ are positive parameters for the regularization term and a penalty term. The regularization term is the length of evolving contour and the penalty term is to keep the consistency between the signed distance and the pseudo LSF. The regularization term is the length of evolving contour and the penalty term is to keep the consistency between the signed distance and the pseudo LSF.

The sensitivity of the algorithm to local information is improved by introducing local pre-fitting weighted energy term on FRAGL. Besides, the robustness to initialization has also been improved by locally computing average image intensities before the evolution of curve. The detail of numerical solution to FALPF is similar to that of FRAGL, which can be referred to [32]. The proposed FALPF-EDLS model can be summarized as the following Algorithm 1.

ALGORITHM 1 The proposed model FALPF-EDLS
1. Initialize: κ, α, β, λ₁, λ₂, w ₁, w ₂, γ, ɛ, k, m, σ, th ₁, th ₂, th ₃, I
2. Compute the gradient of I: G (I (x, y))
3. λ (x, y):=λ (x, y ; th ₁, th ₂) by (5) and (6)
4. Update image by minimizing (4) with respect to $\tilde{I}$
$\tilde{I} = arg \min_{\tilde{I}} E^{edls}$
5. Compute $\hat{I} : = \tilde{I} + t h_{3} \cdot G (λ)$
6. Update image by minimizing (4) with respect to S
$S = arg \min_{S} E^{edls}$
7. Compute f _o and f _b by (12) and (13)
8. Compute f _s and f _l by (14)
9. Compute $c_{1}^{falpf}$ and $c_{2}^{falpf}$ by (11)
10. Update image by solving the optimization problem (7)

4 Experiments and results

4.1 Simulated experimental results

In order to better analyze the performance of the proposed FALPF-EDLS model, we generate the simulated PCB CL reconstruction data. The scanning parameters for CL simulating system are listed in Table 1. The phantom we adapted is shown in Fig. 3(b) and the equivalent coefficients of copper and insulating material are set to be 5.5661 and 0.5621. After reconstructed by FDK algorithm, we can then obtain the simulated PCB CL reconstructed slices as shown in Fig. 3(a). The simulation reconstruction volume includes 6 circuit layers.

Fig. 3

(a) Shows the three-view drawing of the simulated PCB CL reconstruction volume, and (b) is the original PCB phantom volume. The gray window of (a) and (b) are [–5.4537,10.3842] and [0.5621, 5.566120/04/2024], respectively. The size is 1000 × 1000 × 280 for both volumes.

Table 1

Scanning parameters for CL simulating system

Angle θ	40 degree
Source to objective table	23.299 mm
Source to detector distance	340.422 mm
Projection views	360
Detector unit size	49.5μm
Detector cells	1500×1500
Pixel size	5μm

Figure 4 shows the EDLS and the FALPF-EDLS results of 6 circuit layers of the simulated PCB CL image. The first column and the sixth column show the EDLS and FALPF-EDLS results of surface layers, the second column and the fifth column show the results of the copper layers and the third column and fourth column show the results of the trace layers. It can be seen that the proposed FALPF-EDLS model has a good performance on the simulated PCB CL images. The segmentation results are very close to the ground truth (GT).

Fig. 4

The results of EDLS and FALPF-EDLS.

Dice coefficient is used for calculating the similarity of two samples and the value ranges from 0 to 1. The dice coefficient between the segmentation result (SEG) and GT can be computed as follows: $Dice = \frac{2 * (SEG \cap GT)}{SEG + GT} .$ (16)

Figure 5 shows the results on the 4th circuit layer by CV, LBF, LPF, FRAGL, and FALPF-EDLS segmentation models. Both CV and FRAGL are limited to the image artifacts and get wrong segmentation. LBF and LPF have poor performance on the low-contrast image segmentation. Table 2 shows the dice coefficients of these different segmentation models. Our model has the best performance.

Fig. 5

The segmentation results of CV, LBF, LPF, FRAGL, and FALPF-EDLS.

Table 2

Dice coefficient for different segmentation models

Model	CV	LBF	LPF	FRAGL	FRAGL-EDLS
Dice	0.802699	0.829027	0.800220	0.752693	0.937655

Although there are obvious pseudo structures in the simulated PCB CL images, the edges of the simulated image are very clear. Thus, the image processed by EDLS is good enough for the subsequent segmentation. However, real PCB CL image is of much worse quality that the image is of low-contrast with weak edges. Our goal is to segment the real PCB CL images and obtain results that can provide reference for professionals.

The proposed FALPF-EDLS model has been tested and shows a good performance on simulated data, which means that under ideal scanning conditions (noise-free, no scattering, no harden artifacts, etc.), FALPF-EDLS model is able to suppress the images with aliasing artifacts caused by the incompleteness of scanned data, and obtain accurate segmentation results for these two categories: high-density metal and low-density insulation materials.

4.2 Real experimental results

In this part, we test 5 pieces of PCBs with different sizes and different number of circuit layers by FALPF-EDLS and present the experimental results. The PCB CL images are all at the size of 2000 × 2000. The angle θ of the adapted CL system is set to be 40.

4.2.1 Experimental results on 5 different PCBs

The physical images of these 5 PCBs are shown in Fig. 6 with the size indicated and the regions scanned marked by the red boxes. The regions scanned were chosen arbitrarily. The corresponding trace widths and layer numbers for each piece of PCB are listed in Table 3. The CL system scanning parameters for PCB 1–5 in Table 4. These PCBs are bare boards and are waste. PCB 1, 2 and 4 are complete circuit board. PCB 3 is a very small and thin but incomplete mobile phone circuit board. PCB 5 is a very thick but incomplete circuit board.

Table 3
Trace widths and layer numbers of PCB 1–5

PCB 1 2 3 4 5

Trace width (μm) 207 91 20 92 179

Layer number 4 8 10 20 20

PCB	1	2	3	4	5
Trace width (μm)	207	91	20	92	179
Layer number	4	8	10	20	20

Table 4

CL system scanning parameters for PCB 1–5

PCB	1		2	3	4		5
Target voltage (kV)	100		120	80	100	120	120
Power (W)	10	7	10	3	10		15
Pixel size (μm)	4.95		3.90	0.73	3.42	3.98	2.61
frame	1	2	2	2	2		2
Projection Views	720
Exposure time/projection	1 s

Fig. 6

The physical diagram of PCB 1–5. Each PCB is marked with its length, width and thickness. The regions scanned are marked by the red boxes.

Since the real data are in lack of ground truth and source file, here in the experiment of PCB 1, we add the corresponding PCB design images for reference. The images from the PCB design source file are not the ground truth corresponding to PCB CL images and can only be used as reference to tell whether the pseudo-structure is mistake for true. PCB 1 is a 4-circuit layer board, of which the internal layers are copper layers. We perform CL imaging on two regions of PCB 1 to obtain their internal structure images, respectively. For PCB 1 CL images, we can see from Figs. 7 and 8 that the PCB CL images suffer from heavy aliasing artifacts, which leads to the images are of low-contrast with high-amplitude pseudo structures, particularly for the copper layers. Results shown in red boxes and yellow boxes of Figs. 7 and 8 indicate that the proposed model has a good performance on the CL images with aliasing inter-slice information.

Fig. 7

The results of a set of PCB CL image for the region of the bottom red box of PCB 1 in Fig. 6.

We then scan the PCB 2–5 and obtain the PCB CL images. Figure 9 shows the results of the scanned region in PCB 2. Figure 10 shows the segmentation results of the region in the red box of PCB 3. Figures 11 and 12 show the results of the regions in the left and right red boxes of PCB 4 in Fig. 6, respectively. Figure 13 shows the results of the region in the red box of PCB 5 in Fig. 6.

Fig. 8

The results of a set of PCB CL image for the region of the upper red box of PCB 1 in Fig. 6.

Fig. 9

The results of a set of PCB CL images for PCB 2.

Fig. 10

The results of a set of PCB CL images for PCB 3.

Fig. 11

The results of a set of PCB CL images for PCB 4 (region of the left red box of PCB 4).

PCB 2 is a board large in size, small in thickness and trace width, with 8 circuit layers. It can be seen from the results that the proposed model shows a good performance on the CL images segmentation of PCB 2 that FALPF-EDLS model is able to obtain clear circuit structure and accurate connectivity information. Though some of the holes in the copper layer cannot be distinguished, the connectivity is accurate, which is the information we want to get from the copper layer. PCB 3 is a small board with 10 circuit layers though the width is only 0.75 mm. In order to obtain the inner structure of the circuit layer inside PCB 3, we decide to scan the object with lower voltage, lower power, and resolution less than 1μm. The segmentation results shown in Fig. 10 indicate that the FALPF-EDLS model is also applicable to thin and small PCB in mobile phone. PCB 4 is a circuit board with 20 circuit layers of 3 mm width, of which the wiring distribution is of high density. It can be seen from Figs. 11 and 12 that the FALPF-EDLS model perform well on the surface circuit layers. For the signal layers in Fig. 11 and copper layers in Fig. 12, though the segmentation is affected by the inter-slice aliasing artifacts, the results of the proposed model can still provide accurate information of the connectivity. PCB 5 is a thick board with 20 circuit layers in a width of 5 mm. We have to use a smaller pixel size (2.61μm) to visualize the board due to the limitation of the vertical resolution. As a result, the field of view is getting smaller, as is shown in Fig. 13. In this way, the objects in CL reconstructed images of PCB 5 are easier to be segmented. It can be seen from Fig. 13 that the segmentation results of PCB 5 CL images are very clear and accurate.

Fig. 12

The results of a set of PCB CL images for PCB 4 (region of the right red box of PCB 4).

Fig. 13

The results of a set of PCB CL images for PCB 5.

4.2.2 Experimental results on a complete PCB

In 4.2.1, we have verified the applicability of the proposed method to arbitrary CL imaging regions in different PCBs with different sizes, trace widths and layers. We then carry out the experiment on the CL data of a complete PCB. As is shown in Fig. 14(1), PCB 6 is a board of 4 circuit layers, at the size of 6 cm×9 cm×2 mm. The PCB parameters and the scanning parameters are listed in Table 5. We scanned 35 regions (red boxes in Fig. 14(1)) in PCB 6 under the scanning condition shown in Table 5 and obtained 35 sets of PCB CL data. All the PCB CL images we process are at the size of 2000 × 2000.

Fig. 14

(1) is the image of PCB 6. (2)-(5) are the segmentation results of 4 circuit layers in PCB 6.

Table 5

PCB and scanning parameters for PCB 6

Trace width (μm)	1000
PCB layer number	4
Target voltage (kV)	100
Power (W)	5
Pixel size (μm)	7.14
frame	1
Projection views	360
Exposure time/projection	1 s

Figure 15 shows the segmentation results of the scanned region A and region B of PCB 6 in Fig. 14(1). ORI-A and ORI-B are the CL images of 4 circuit layers of region A and region B in Fig. 14(1), respectively. In order to get the complete structure inside the PCB 6, the 35 regions we scan are overlapping. It can be seen in Fig. 15 that region A overlaps region B. We process these 35 sets of PCB CL data respectively by FALPF-EDLS model to obtain the segmentation results of 4 circuit layers in each scanned region, and then manually match them together. They outcome as Fig. 14(2)–(5).

Fig. 15

Segmentation results of the scanned region A and region B of PCB 6.

4.2.3 Comparisons

In this part, we carry out 5 experiments to segment the trace layer and the copper layer by different segmentation algorithms for comparison.

As is shown in Fig. 16, ORI-1 and ORI-2 are the ORI-3 of PCB 4 in Fig. 12 (the 1st row 3rd column in Fig. 12) and the ORI-10 in Fig. 12 (the 1st row 10th column in Fig. 12), respectively. The CV model gets the wrong segmentation results. The LBF model can only identify the holes which are of relatively high intensity. LPF is more sensitive and is able to distinguish the trace. However, LPF is still under-segmented for trace layer and gets wrong result for copper layer. The proposed model FALPF-EDLS shows obviously better segmentation performance of PCB CL images on both trace layer and copper layer.

Fig. 16

ORI-1 and ORI-2 are the PCB CL images of the 3rd and the 10th circuit layers of PCB 4 in Fig. 13, respectively. The 2nd–6th columns show the segmentation results of CV, LBF, LPF, FRAGL and FALPF-EDLS, respectively.

4.2.4 Parameters setting

For the EDLS method, if the edge information is not accurate, it will interfere the image structure information. Preserving pseudo structure edges will lead to more pseudo-structures leaving in the image, while removing the edge information of real structures, the real structure of the image will also be removed, resulting in wrong segmentation. Thus, the selections of th ₁ and th ₂ are very important. The gradient image is extracted from the normalized image. For surface layers, th ₁ is usually set as 0.9. For trace layers and copper layers, th ₁ ranges from 0.3 to 0.6. The value of th ₂ is set as 100. The smoothing parameter κ for l ₀ gradient minimization ranges at 0.001 to 0.003. β is set as 1 and th ₃ is usually set to 10.

Since FRAGL and FALPF are fuzzy energy based, we set the weighting exponent m is set as 2. k and σ are set to 6. λ₁, λ₂ and ɛ are all set to 1. α and γ are set to 0.5. w ₁ and w ₂ are the weighting coefficients and the selections of them very important for balancing the sensitivity of the proposed model. For surface layer, we choose w ₁ = 0.1 and w ₂ = 0.9. For trace layer, we usually choose w ₁ = 0.9 and w ₂ = 0.1. For copper layer, we usually choose w ₁ = 0.5 and w ₂ = 0.5.

5 Conclusion

In this work, we propose a model, FALPF-EDLS, for PCB segmentation based on CL imaging for the first time. The innovation of the FALPF-EDLS model lies in the following two points: 1.

Filtering the PCB CL images with combination of ED and l ₀ smoothing methods. Compared with the iterative methods, EDLS can remove the pseudo structure faster by post processing the images reconstructed by FDK.

A fuzzy energy based active contour model driven by weighted local pre-fitting energy is proposed to balance the sensitivity to the image information, which is then verified to be applicable to PCB CL image processing with different features.

We then present lots of experimental results on both simulated data and real data. It can be seen from the experimental results that the proposed model performs well in the simulated data. It is preliminarily verified that the FALPF-EDLS model has a good performance for PCB image segmentation with pseudo structures under ideal scanning condition. Then, we test on 5 PCBs with different physical sizes and number of circuit layers. The results show that the proposed model is able to extract accurate circuit signal connectivity, which can provide reference for professionals. This verifies the applicability of our method to CL images of different circuit boards. We also use CL to image all regions of an entire circuit board to achieve a nondestructive reproduction of the complete internal information. Finally, we compare the performance of different segmentation methods to show the superiority of this method.

The greatest significance of this work is that on the basis of the advantage of CL for arbitrary region imaging of PCBs with different sizes and number of circuit layers, the proposed model is able to process the images with aliasing artifacts caused by CL scanning mode. The real experimental results shown in this paper are not achievable to most current nondestructive inspection techniques, which is of great significance.

Similar to many image processing methods based on model mechanism, the FALPF-EDLS will be influenced by the parameters that it cannot be fully automated. Data-driven deep learning segmentation models are currently widely used. But for our problem, there are no relevant open datasets for model training, and PCB CL data preparation is a large workload. Besides, it requires hardware support for storage and computing. Using the data obtained from the proposed method in this paper, we will explore a data-driven intelligent model to process PCB CL data in the future.

Footnotes

Acknowledgment

This work was supported by the CAS Interdisciplinary Innovation Team under Grant JCTD-2019-02. This work was also supported in part by the National Natural Science Foundation of China (NSFC) under Grant 62271330, 61871275, 61827809, and 61971292.

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A PCB image segmentation model based on rotational X-ray computed laminography imaging

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULT:

CONCLUSIONS:

Keywords

1 Introduction

2 Related works

3 The proposed model

4.1 Simulated experimental results

4.2.1 Experimental results on 5 different PCBs

Table 3 Trace widths and layer numbers of PCB 1–5 PCB 1 2 3 4 5 Trace width (μm) 207 91 20 92 179 Layer number 4 8 10 20 20

5 Conclusion

Footnotes

Acknowledgment

References

Table 3
Trace widths and layer numbers of PCB 1–5

PCB 1 2 3 4 5

Trace width (μm) 207 91 20 92 179

Layer number 4 8 10 20 20