Fiber orientation measurement of fiber injection molded nonwovens by image analysis

Abstract

The fiber injection molding process is an innovative approach for the manufacturing of long fiber nonwoven preforms with little to no waste. An important property for the mechanical characteristics of the composite parts is the fiber orientation of the fiber injection molded nonwovens. In this paper a newly developed assemble method based on Fast Fourier Transform and improved Structure Tensor methods for the computation of the fiber orientation distribution in the local orientation by image analysis of transmitted light images is presented. For the computation of the fiber orientation, the Fast Fourier Transform and Structure Tensor methods are used. The new method is evaluated using simulated images and transmitted light images of real nonwovens to evaluate their accuracy. The computed fiber orientation distributions are compared to reference distributions by means of the Kullback–Leibler divergence. It is shown that the assemble method can perform accurate and reliable measurement of fiber orientation measurement and the modified Structure Tensor method improves results significantly compared to the current state of the art.

Keywords

fiber orientation nonwovens fiber injection molding image analysis Fast Fourier Transform Structure Tensor

Nonwoven-based composites represent a cost-effective alternative to endless fiber-reinforced composites for applications with lower mechanical requirements, such as claddings or floor panels.¹ Preforms for the manufacturing of composites are produced by cutting the contour from semi-finished products in the form of rolled goods, such as nonwovens and mats, followed by stacking and forming in a three-dimensional shape.² This leads to waste of material and therefor higher material costs.³

The fiber injection molding (FIM) process is a promising innovative process for the manufacturing of three-dimensional near net shape nonwoven preforms without the intermediate step of two-dimensional (2D) semi-finished products.³ The process allows the production of three-dimensionally formed long fiber semi-finished products without cutting waste by blowing fibers into a closed mold by means of an air stream.⁴ To better understand the process and monitor mold filling, a process monitoring system has been developed.⁵ For the monitoring system, the injection mold has been modified with two Plexiglas windows at the top and bottom sides. A digital camera is integrated beneath the mold to record the injection process. Additional lighting over the upper mold improves the visibility of the fibers and allows the capturing of transmitted light images of the final preform when the mold is fully filled. The transmitted light images of this monitoring system shall be used to evaluate the fiber orientation of the manufactured FIM nonwovens, as it is an important property of nonwovens that represents the directional mechanical properties of nonwovens. In addition, the mechanical properties of nonwovens can be improved by a fiber arrangement with one or more preferred orientations.

In related works, the fiber orientation is often represented by the so-called Orientation Distribution Function (ODF).⁶ The ODF is the probability that the fibers in one image are aligned in different orientations, which is defined as

ρ (θ) = \frac{n_{θ}}{\sum_{1}^{180} n_{θ}}, θ = 1, 2, \dots, 180

\sum_{1}^{180} ρ (θ) = 1, θ = 1, 2, \dots, 180

where

ρ (θ)

is the probability of a fiber with orientation θ and

n_{θ}

is the number of pixels in fibers with orientation θ.

The research of different methods for the measurement of fiber orientation distribution and anisotropy has been ongoing for a few decades. In recent years a great deal of research has focused on image analysis methods for fiber orientation analysis. Compared to traditional methods, image analysis methods require simple equipment and a short measurement time. In addition, they have been already widely used in industrial production, especially in the field of visual inspection. Based on image analysis theory, vision measurement methods in related papers can be divided into different types.

Among these methods, Fast Fourier Transform (FFT) is the most frequently used method.^7–12 In this method, the acquired images will be converted to the frequency domain. Then, the energy in the different orientations ranging from 1° to 180° will be integrated and compared with each other to get the final ODF. Tunák et al.^13,14 adopted window FFT to construct a blockwise FFT (BFFT) method. Firstly, the whole nonwoven image will be divided into multiple same-sized subwindows. Then, FFT will be processed to find the preferred orientation for each subwindow.

The Hough Transform is also a common image analysis method and some experts have made attempts to adapt it for orientation measurement.^15–18 In order to use the Hough Transform, the original nonwoven images should be added to a thinning procedure to prevent spectrum leakage. Analog to the FFT method, there is also a variation of the original HT where the image is divided into subwindows, which will be called blockwise Hough Transform (BHT) in the following.¹⁹

Van Vliet and Verbeek²⁰ first adopted the Structure Tensor (ST) to measure the properties of the orientation of materials. The ST, which was presented by Knutsson,²¹ improves the properties of the gray value gradient. Krause et al.²² used the ST to analyze fiber-reinforced materials scanned with computer tomography in two and three dimensions. ST methods are widely used for the analysis of different types of fibrous materials, such as biomaterials, nonwovens, composites and paper.

Besides the three main theories, there are also some different attempts. Pourdeyhimi and Dent²³ used a Flow Field (FF) to integrate the local gray value gradient of each pixel by some statistical method. Hong et al.²⁴ made use of a similar orientation estimator (the least mean square orientation measure algorithm) to measure the orientation of ridges within a fingerprint image. Pourdeyhimi et al.²⁵ also attempted to directly track (DT) the fibers to determine fiber orientation distribution. In this method, before tracking the fibers need to be thinned to one pixel width. Otherwise, tracking will be confused by multiple surrounding pixels. Besides fitting the line in Hough space, Jue et al.²⁶ also wanted to fit the edge lines of fibers in the image domain. These methods obtained good results when the input images have a very high resolution, such as those acquired by a microscope. Tunák et al.¹³ introduced the Image Moment Analysis (IMA) method for fiber orientation measurement of nonwovens and nano-fibrous layers and combined spectrum and moment approaches in the measurement of the fiber orientation section. Lijuan and Weidong¹⁸ addressed this method for the analysis of electrospun submicro-fibers. In contrast to the BFFT method, the evenly cut off subwindow will not be transformed into the frequency domain through FFT, but directly be analyzed by moment analysis to calculate the dominant orientations of each window. By considering the variability of image intensities along different directions surrounding each pixel, Quinn and Georgakoudi²⁷ presented a weighted orientation vector summation (WVS) algorithm that can detect fiber orientation simultaneously at each pixel within an image.

The fiber injection molded nonwoven images contain dense fibers and rovings with different width and length and possess a high basis weight (around 1250 g/cm³) compared to other nonwovens analyzed in the literature. Based on the specific measurement equipment and the structural characteristics of the analyzed materials in this work, among the introduced method some of them are not suitable for this work because of the measurement theory and principles they rely on. As for the results in related works,⁷ the original FFT methods that are based on the whole nonwoven images can accurately estimate the orientation of the dominant orientations but will overestimate the variance of estimated ODFs. The BFFT method can overcome this problem under the premise of ensuring the same accuracy. Therefore, instead of the original FFT, the BFFT method will be further analyzed and improved in this paper. Hough Transform methods compare the energy of accumulator points in each orientation to calculate the final ODF. When the fibers are very dense, there will be serious energy leakage (too many artificial significant accumulator points) in the Hough space, which is caused by the thinned fiber and roving structure by using the Hough Transform method. Therefore, Hough Transform methods are not considered for this work. The ST is a very versatile method that can measure the orientation of each pixel, which is a supplement for the results of BFFT, but it can only get the global ODF of the analyzed image. However, it is sensitive to the local structure variety, which needs images with high resolution and a large magnification factor. In addition, the ST method can only evaluate a few fiber pixels in a thin edge zone. Therefore, the ST method will be adopted but improved in this work. The line fitting and fiber tracking methods directly in the image plane need smooth edges of fibers. Therefore, the analyzed images in the methods presented in the related papers are acquired by a microscope. However, the industrial camera in an on-line vision inspection system cannot reach the same resolution as a microscope, so these methods will also be excluded from this work. Measuring the image directly by IMA is inaccurate because of the centrifuged fiber structures in the subwindows. So, when it is used directly to analyze complex web structures, the measurements usually have lower precision. However, based on the algorithm in Tunák et al.,¹³ it is successfully used to analyze the preferred orientation based on the spectrum of each subwindow. The reason for the success is that, before moment analysis, the center of gravity of the spectrum can be transformed to the geometric center of the image. For WVS, based on the evaluation results in Quinn and Georgakoudi,²⁷ the accuracy is not as good as FFT but its computational time is shorter than FFT. As the computational time of FFT is short enough to meet the requirement, there is no need to adopt the WVS in our approach. An overview of all the presented methods from the state of the art is given in Table 1.

Table 1.

Overview of state of the art with the presented methods, evaluated materials and the image acquisition equipment used

Method	Evaluated materials	Image acquisition equipment
FFT Pourdeyhimi et al.⁷	Nonwovens	Camera
FFT Ghassemieh et al.⁸	Nonwovens	Scanning Electron Microscope (SEM)
FFT Enomae et al.⁹	Papers	Microscope DG2; SEM
FFT Yongping et al.¹⁰	Nonwovens	–
FFT Marquez¹¹	Tissue construct	Camera
FFT Sander and Barocas¹²	Fibrin tissue analogs	SEM
BFFT Tunák et al.¹³	Nonwovens	SEM
HT Pourdeyhimi and Kim¹⁵	Nonwovens	Camera
HT Bin et al.¹⁶	Nonwovens	SEM
HT Lijuan and Weidong¹⁸	Electrospun fiber membranes	SEM
BHT Bayan et al.¹⁹	Collagen fibers	Second Harmonic Generation (SHG)
ST Van Vliet and Verbeek²⁰	Hydrocarbons	Camera
ST Krause et al.²²	Composites	Computer tomography
FF Pourdeyhimi and Dent²³	Nonwovens	Camera
FF Hong et al.²⁴	Fingerprints	Unknown
DT Pourdeyhimi et al.²⁵	Nonwovens	Camera
IMA Tunák et al.¹³	Nonwovens	SEM
IMA Lijuan and Weidong¹⁸	Electrospun fiber membranes	SEM
WVS Quinn and Georgakoudi²⁷	Collagen fibers	SEM

FFT: Fast Fourier Transform; BFFT: blockwise Fast Fourier Transform; HT: Hough Transform; BHT: blockwise Hough Transform; ST: Structure Tensor; FF: Flow Field; DT: directly track; IMA: Image Moment Analysis; WVS: weighted orientation vector summation.

Based on the analysis of the existing methods, the research gap that this work focuses on is the analysis of nonwovens with high basis weight and complex structural properties within a digital image acquired by an industrial camera. So, in this paper, an assemble method has been developed for fast and non-invasive measurement of the fiber orientation distribution and local orientation with a focus on fiber injection molded nonwovens.

Development of methods for fiber orientation calculation

In this work, an industrial camera was used to acquire nonwoven images. Because of the limit of image resolution, the images were preprocessed to enhance the local structure of fibers and rovings. The original BFFT method can efficiently and accurately measure the global ODF of nonwovens. However, in the original BFFT method the calculated orientation distributions of each subwindow are used to calculate the overall ODF with the same factor. So, in this work, it was improved by assigning adaptive weights to each subwindow. In addition, the original BFFT method cannot provide the orientation of each foreground pixel, which causes an information loss of fiber orientation. To overcome this deficit, in this work a new method called Structure Tensor Thinning (STT) based on the ST method was developed.

The assemble measurement method consists of three main parts, as shown in Figure 1: image preprocessing, BFFT and STT. In the first step, the acquired images are cropped, denoised, enhanced and segmented by an adapted image preprocessing workflow. Then, by using BFFT an accurate global ODF can be calculated quickly and reliably. In this work, we improved this method with the weighted summation of preferred orientations of all image blocks for obtaining the global ODF. Finally, the images are measured by the newly developed STT method, which can provide the local orientation of each pixel and the global ODF based on the local information. The global ODFs determined by these two different methods can be compared with each other.

Figure 1.

Processing workflow of the assemble method for the determination of the fiber Orientation Distribution Function. CLAHE: Contrasted Limit Adaptive Histogram Equalization; BFFT: blockwise Fast Fourier Transform; FFT: Fast Fourier Transform; GC: Gaussian Curvature; ODF: Orientation Distribution Function.

Image preprocessing

Before the image is analyzed with the fiber orientation measurement methods, some preprocessing procedures must be done to enhance the contrast of detailed structures. The three main steps of preprocessing are image denoising, image enhancement and binary segmentation. For this preprocessing different filters are integrated to achieve these three desired functions. Firstly, the color image will be cropped to a square shape and converted to a gray scale image. For intuitive analysis, in this work bright (white) pixels represent the fiber and dark (black) pixels represent the background. Then, the new edge-preserving Gaussian Curvature filter, developed in recent years, is adopted to achieve a good denoising effect without smoothing the edges of fibers, which leads to the loss of the detail edge structure of fibers and rovings. This curvature filter is a generic and parameter-free algorithm, which makes it robust to different applications and the user does not need to tune too many parameters. In addition, in comparison with other types of curvature filters, for instance Mean Curvature filters or Total Variation filters, the Gaussian Curvature filter can better retain the major structure and reduce blurring.²⁸ The most important part in the preprocessing is the integrated contrast enhancement method, which is a combination of two contrast enhancement filters: Contrasted Limit Adaptive Histogram Equalization (CLAHE)²⁹ and Local Radon Transform. On the one hand, CLAHE enhances the contrast between the web structure and background. On the other hand, because of the narrow shape of the adopted masks, Local Radon Transform enhances the contrast on the detail edge area. In addition, as an optional procedure, a background removing algorithm can be adopted to further harmonize the first-order intensity of images. Then, the enhanced gray scale image is binarized by Local Adaptive Thresholding. The threshold is calculated by using local first-order statistics. After binarization, Connectivity Analysis is used to remove the small areas with too few pixels, and morphological ‘Closing’ or a fractional integral can be used as an optional procedure to smooth the remaining fiber structure. The detailed flow of image preprocessing is shown in Figure 1 and the settings of the parameters of the necessary procedures in this work are shown in Table 2.

Table 2.

Parameter settings used for image preprocessing

Filters	Parameters
Curvature Filter	Type 2 (Gaussian Curvature), 25 loops
CLAHE	Contrast enhancement limit is 0.01
Local Radon Transform	$σ = 2$ , evaluate square areas between $3 \times 3$ and $5 \times 5$ pixels
Local Adaptive Thresholding	Gaussian mask with $7 \times 7$ pixels, sensitivity (area fraction) is 0.65
Connectivity Analysis	4 connectivity, pixels number limit 250 pixels

CLAHE: Contrasted Limit Adaptive Histogram Equalization.

In Figure 2, the results of image preprocessing by original histogram equalization and the newly developed preprocessing methods are illustrated. Based on the double-contrast enhancement method (CLAHE) and local contrast enhancement method in our image preprocessing method, the detailed structure of fibers and rovings in nonwoven images are much clearer than the results based on the original histogram equalization. This significantly improves the measurement of the orientation of fibers.

Figure 2.

(a) Original transmitted light image of a fiber injection molded nonwoven sample of 400 mm × 400 mm with resolution of 2000 × 2000 pixels. (b) Image after the original histogram equalization. (c) Gray value image after the presented preprocessing. (d) Binary image after the presented preprocessing.

Improved blockwise Fast Fourier Transform

As discussed before, the BFFT method can efficiently and accurately measure the global ODF of nonwoven images. In addition, FFT methods are robust to different types of fibrous materials. Therefore, in this work BFFT is adopted for an efficient and accurate first overview of the ODF of nonwoven fabrics.

In Tunák et al.,¹³ each dominant orientation of a valid subwindow is assigned with the same weight (uniform weight). However, this is only reasonable when the fiber density is low and fibers are parallel aligned. In FIM nonwovens, the fiber density is very high and fiber alignment very complex, which makes the fiber structures in different subwindows very different from each other. Therefore, regardless of the specific fiber structure in each subwindow, assigning the same weight to calculate dominant orientations from different subwindows is not reasonable.

The assignment of weights should consider fiber density and their specific alignment. The fiber density is represented by the area fraction. The specific fiber structure is considered by the ratio of the long axis and the short axis. In Figure 3 the relation between them is shown. This means that when there are more fibers with dominant orientation in one subwindow, the ratio is larger than the ratio of a subwindow with fewer fibers of dominant orientation. In this work, a constant a was set as the correlation coefficient of the ratio of dominant fibers and the ratio of the long and short axes. The adaptive weight of one dominant orientation is defined as

W_{i} = \frac{n_{i} \times a \times (l_{i} / (l_{i} + s_{i}))}{N}

where

W_{i}

is the weight,

n_{i}

is the area fraction in the ith subwindow,

l_{i}

is the length of the long axis,

s_{i}

is the length of the short axis and

N = \sum_{i = 1}^{t} n_{i}

, with tbeing the number of valid subwindows.

Figure 3.

Moment analysis of the binary spectrum: (a) subwindow 1 and (b) its spectrum; (c) subwindow 2 and (d) its spectrum.

The whole determination of the fiber ODF with the improved approach is described in Algorithm 1, which shows the pseudocode of the implementation. For the results of this paper the implementation has been executed in MATLAB. The workflow of the computation corresponds to the steps described in Figure 1.

Algorithm 1. Improved BFFT

Input:

Enhanced gray scale image or binary image I, size of subwindow L

Code:

Evenly splitting the whole image, number of subwindows $N_{sub - window} = I / L^{2}$

Initial set of valid subwindow $M \in Ø$

for $i \in {1, \dots, N_{sub - window}}$ do

Multiple subwindow $S_{i}$ with hamming window function W

FFT of $S_{i} \times W$ , moment analysis of calculated spectrum

Check the validation of each subwindow by fractional area $ρ_{i}$ and ratio of long axis to short axis $r_{i}$

If the subwindow is valid $M M \cup {dominantorientation θ_{i}, ρ_{i}, r_{i}}$

end for

Weighted sum of dominant orientation in M

Output:

global $ODF$ of image I

Structure Tensor Thinning

In this section the detailed algorithm of the newly developed Structure Tensor Thinning (STT) method is presented. The major change of STT compared to the ST are the multiple iterations of thinning and orientation measurement. In every loop except the last, firstly, the ST and corresponding orientation of each pixel are calculated by the ST. Secondly, the edges or edge areas are detected and the orientation of pixels belonging to these areas are stored. Thirdly, fibers are thinned by removing the pixels in the edge areas. Finally, the remaining parts of each fiber are smoothed and will be the input image for the next loop. In the last loop, there is no thinning procedure, the remaining web structure is evaluated by the ST and the calculated orientation of all remaining foreground (pixels and roving) pixels will be stored. Through this algorithm, despite the width of fibers and rovings, the orientation of each pixel belonging to fibers can be measured. The algorithm of STT is given in Algorithm 2 as pseudocode.

In addition, before the calculation of global ODFs, there are three steps to search the overlap areas of different fibers. Since STT is based on 2D images, the areas where the fibers in different planes overlap cannot be accurately analyzed. The orientation measurement results of pixels in the overlap areas are not only inaccurate but also disturb the accuracy of the further calculated global ODF of nonwovens. In order to solve this problem, an overlapping area positioning and removal procedure is adopted. Firstly, the skeleton of the fibers is calculated by the medial axis transform algorithm. In this work, the 8 connectivity in the 2D image is used in this algorithm, which means that all eight neighboring pixels are considered for the tracking (see Pourdeyhimi et al.²⁵). Then, the branch points are found by morphological analysis. Finally, a certain number (here a square area in the size of 20 × 20 pixels) of fiber pixels surrounding these points are determined and their orientation information is neglected.

Algorithm 2. STT

Input:

Binary Image I, loops number N, size of mask for overlap areas removing l

Code:

Initial set of orientation map $M \in Ø$

for $i \in {1, 2, \dots, N - 1}$ do

Calculate structure tensor of pixels in I

Extract the edge pixels set $E_{i \in {1, 2, \dots, N - 1}}$

Add the orientation $θ_{i}$ of found edge pixels to $M M \cup θ_{i}$

Remove the edge pixels from current image $I I / E_{i}$

end for

Extract the skeleton of webs in orientation map S

Find the branchpoints set B of skeleton S

Remove the fiber pixels set of the square area P surrounding B, the reminded $M' M P$

Statistic the orientation of foreground pixels in $M'$

Output:

global $ODF$ of image I, orientation of each foreground pixels M

Experimental evaluation of fiber orientation measurement techniques

In this section, the evaluation test images and data analysis methods used to evaluate the developed methods are presented. On the one hand, the fiber orientation measurement method should accurately measure the ODF of different types of nonwovens. The accuracy means not only the dominant peak orientation but also the variance of each peak. On the other hand, it must reliably and robustly measure the ODF based on different types of fiber distribution function as well as nonwoven types, such as the fiber form or the web structure. By considering these requirements, the test image sets are constructed.

Data smoothing filter

In order to obtain accurate overall trends and eliminate local fluctuations in the measured ODF, in general, in related works a data smoothing procedure has been adopted. There are two major methods: one transforms the ODF in a 1-degree bin or higher range bin, mostly 5-degree or 10-degree;⁷ the other uses a local smooth filter, such as moving average or kernel regression.¹³ The first method loses too much information of the ODF and sometimes artificially enlarges the measurement error, especially for the measurement of dominant orientations. Therefore, in this work the kernel regression with a 7 degree span Gaussian kernel is used to smooth the measured ODF.

Evaluation indexes

Another relevant aspect is how to evaluate the similarity between different ODFs. In related works, the dominant orientation (peak orientation)⁷ and entropy of the ODF¹⁹ were used for the comparison of differently computed ODFs. Both are distribution characters of a single ODF. To compare the similarity between two ODFs (for example, the measured ODF and the reference ODF), different indexes should be compared separately and there is no unified standard that takes all indexes into account. Therefore, in this work the Kullback–Leibler (KL) divergence³⁰ is adopted as a standard to compare similarity between different ODFs. In mathematical statistics, the KL divergence (also called relative entropy) is a measurement of how one probability distribution is different from a second. For two probability distributions P and Q, the KL divergence is defined as

\begin{matrix} D_{KL} (P | | Q) = H (P, Q) - S (P) \\ = - \sum_{x \in X} p (x) log q (x) + \sum_{x \in X} p (x) log p (x) \end{matrix}

where

H (P, Q)

is the cross-entropy of P and Q, and

S (P)

is the entropy of P.

Simulated images

In practice, it is almost impossible to get the true ODF of real nonwovens. Therefore, a series of simulated images with different human-controlled ODFs was generated. In this work, we refer to the ‘arcs replaced by straight line’ idea, which was presented by Pourdeyhimi et al.⁶ The planar structure of simulated images should be as close to the real situation as possible. After analysis of the nonwovens in this work, five important structural properties are represented by simulated images, which are length, width, crimp, density and orientation distribution modal of fibers. Aimed to satisfy these requirements, our simulated images have been constructed. By using this algorithm simulated images with 2000 × 2000 pixels and different structural properties have been constructed for evaluating the accuracy and reliability of different orientation measurement methods. Each fiber in a simulated image is constructed separately to meet the requirements of different fiber forms. Then these fibers are rotated based on the given ODF. Next, they are randomly placed on the simulated image for a near uniform distribution. Finally, based on this known structural information, the true ODF is calculated as the reference in the evaluation of our approach. The pseudocode for the generation of these simulated images is given in Algorithm 3.

Algorithm 3. Construction of simulated images

Input: Fiber number N, fiber form $a (1 : long; 2 : short)$ , percent of crimp fibers $b \in [0, 1]$ , dominant orientations, variance of each orientation $σ_{i \in {1, 2, \dots, 5}}$ .

Code:

Calculate the expected Probability Distribution Function (PDF) $P_{i}$ of each dominant orientation by given $θ_{i}$ and $σ_{i}$

Calculate the PDF P of image $P \sum^{P_{i}} / max (i)$

Initial set of generated fibers $F \in Ø$

Initial simulated image $I \in zeros$

for $j \in {1, 2, \dots, 180}$ do

In orientation j calculate the fiber number $n P (j) \times N$

for $k \in {1, 2, \dots, n}$ do

Construct the fiber j_k{pixel number n, width d, dominant orientation j, form s (1:straight; 2:crimp)}

By given aand b

Randomly place fiber $j_{k}$ in image $I I \cup j_{k}$

$F F \cup$ $j_{k}$

end for

Calculate the real $ODF$ by weighted summation of fibers in F

Output:

global $ODF$ , simulated I

In order to evaluate the required characteristics mentioned before, three sets of simulated images have been generated. One set of images consists of short and crimped fibers, one set of images consists of long and straight fibers and a third set of images consists of long and crimped fibers. In each set the distribution models of fibers in different images are different as shown in Figure 4. In each set there are five different ODF models with different numbers of dominant orientations and variances. Table 3 shows the number of dominant orientations and the variance of each of these dominant orientations (peak) in parentheses for the different models.

Figure 4.

Simulated images with 2000 × 2000 pixels.. Image set 1 with short, crimp fibers and (a) one, (b) two and (c) three dominant directions. Image set 2 with long, straight fibers and (d) one, (e) two and (f) three dominant directions. Image set 3 with long, crimp fibers and (g) one, (h) two and (i) three dominant directions.

Table 3.

Structural parameters of simulated images in different image sets

		Model (number of dominant orientations, (variance of each peak))
		Model 1	Model 2	Model 3	Model 4	Model 5
Set 1	Short, crimp	1 (10)	2 (10, 10)	2 (10, 20)	2 (20, 20)	3 (10, 10, 10)
Set 2	Long, straight	1 (10)	2 (10, 10)	2 (10, 20)	2 (20, 20)	3 (10, 10, 10)
Set 3	Long, crimp	1 (10)	2 (10, 10)	2 (10, 20)	2 (20, 20)	3 (10, 10, 10)

The simulated images in actual nonwoven fabrics usually have an ODF with a maximum of two peaks. Therefore, the maximal number of peaks is controlled as three, which is already more complex as expected in real cases. Also, to evaluate the reliability of the methods, five different images have been generated with the same number of peaks but different orientations.

Real images

For the evaluation of the orientation measurement methods in this work, there are also three sets of real nonwoven images that are used to evaluate the ODF measurement methods, as shown in Figure 5. Image acquisition has been carried out using the mold integrated camera system presented by Moll et al.⁵ In this setup the camera UI-3290E from the company IDS (Obersulm, Germany) with a 4104 × 2174 pixel CMOS sensor and a Tamron M111FM08 lens has been used. Aperture has been set to f/22 in order to get the maximum depth of focus.

Figure 5.

Real nonwovens images of (a) a fiber injection molded sample (Set A), (b) a needled mat sample with additional weave (Set B) and (c) a powder mat sample (Set C) with sample size of 400 mm × 400 mm and resolution of 2000 × 2000 pixels.

These three sets consist of different types of nonwovens. The first set, A (images A1–A5), consists of five samples of fiber injection molded nonwovens with a basis weight of around 1250 g/cm² made of a 2400 tex glass fiber produced on a FIM test rig at wbk Institute of Production Science. The second set, B (images B1–B5), contains five samples of a needled glass fiber mat with 610 g/m² basis weight including a second layer of a coarse weave produced by P-D Glasseiden GmbH (Oschatz, Germany). Hence for this weave, the ODFs of nonwovens images in Set B should have two peaks at 0° and 90°. Set C (images C1–C5) contains five powder mats with a basis weight of 450 g/cm² with very good surface distribution also produced by P-D Glasseiden GmbH. The orientation distribution of fibers in Set C is more uniform than the nonwovens in Sets A and B. The nonwoven samples in all sets have a size of 400 mm × 400 mm. These obvious structure features of real nonwoven images have been used to evaluate the accuracy of the measurement methods.

The calculations were carried out on a personal computer equipped with an i7-8565U CPU (1.80 GHz), 16.0 GB RAM and Windows 10 Pro using MATLAB R2018b. For the evaluation of the real images with a resolution of 2000 × 2000 pixels the preprocessing took 216 s, the BFFT method 250 s and the STT method 540 s. The given values for the computational time are average values from the evaluation of all images in Sets A–C. As already described by Tunák et al.,¹³ the size of the subwindows affects computing time significantly.

Measurement results of the evaluated images

In this section the evaluation results based on simulated and real images by BFFT and STT are illustrated and discussed.

Simulated images

Firstly, the simulated images have been evaluated to study the influence of subwindow size and the effect of weighting the subwindows for the BFFT method. Figure 6(a) illustrates the KL divergence of the measured results by BFFT with 40 × 40, 50 × 50 and 100 × 100 pixels for the subwindow. The affiliation of the image numbers to the image sets and models can be taken from Table 4. The KL divergence in Figures 6 and Figure 7 is calculated from the smoothed measured ODF and the corresponding reference ODF. It can be noticed that the KL divergence is higher for larger subwindows than for smaller ones, which means that a smaller subwindow size leads to a more precise determination of the fiber orientation distribution. For all three sets the evaluation of the model with three peaks has the largest error between theoretical ODF and the computed one, whereas the model with only one peak has the best result. The accuracy also improves with a larger variance of fibers. It has to be noted, however, that the structural characters of nonwovens are normally very complex, so no general rule can be given for the calculation of a reasonable subwindow size. Our experience is that the size of subwindows should be decreased as the fiber density increases and the width of the fiber and roving decreases.

Figure 6.

Evaluation of parameters for the blockwise Fast Fourier Transform method: (a) influence of subwindow size; (b) effect of the weighting factor. KL: Kullback–Leibler.

Figure 7.

Measurement of (a) image 23 (set 1), (b) image 48 (set 2) and (c) image 73 (set 3) with BFFT and STT compared to reference.

Table 4.

Image number of simulated images in different image sets and models

		Image numbers
		Model 1	Model 2	Model 3	Model 4	Model 5
Set 1	Short, crimp	1–5	6–10	11–15	16–20	21–25
Set 2	Long, straight	26–30	31–35	36–40	41–45	46–50
Set 3	Long, crimp	51–55	56–60	61–65	66–70	71–75

Figure 6(b) shows the KL divergence of the results measured by BFFT with a subwindow size of 40 × 40 pixels and adaptive weight for each subwindow and, respectively, no weight (as in Tunák et al.¹³). By using an adaptive weight, the measured results are more accurate than the results without any weight. However, it is worth mentioning that the introduction of the new adaptive weight to the BFFT will also make the BFFT more sensitive to the web structure. Therefore, based on the evaluation of these two parameters, it is recommended that before the measurement of a new type of nonwoven fabric they should tuned.

Then, the simulated images have been analyzed by BFFT with $40 \times 40$ pixels subwindow size and by STT with 15 loops. In addition, the KL divergence between the calculated ODFs and real ODFs of each image were calculated. Kernel regression was used for all ODFs for smoothing. Based on the results, ODFs with three dominant orientations and relatively large variance can be accurately and reliably measured by BFFT and STT. From the diagrams in Figure 8 it is obvious that the ODFs measured by the STT and BFFT accurately fit the overall trend of reference ODFs (dominant orientations and variance). As mentioned previously, the KL divergence was calculated from the smoothed measured ODF and the reference ODF, which leads to a worse result than comparing the actually measured ODF. The accuracy of dominant directions by the BFFT method with weighting factor is around 1°, which is equal to the existing FFT²⁷ and BFFT methods.¹³ It can also be observed that the 0°/180° direction is slightly overestimated by STT. However, as shown in Figure 7, the accuracy of the ST has been greatly improved by the newly developed STT in this work, which has reached almost the same accuracy level as the BFFT. The accuracy of dominant directions is also around 1 °, which is much better than the original ST, which only had an accuracy of around 10°.

Figure 8.

KL divergence between measured and reference ODFs of measurements with (a) BFFT and (b) STT.

The average and standard variances of KL divergence of each of the five images are illustrated in Figure 8. Both methods deliver good results with only a small error for image Sets 1 and 3, but a little worse results for image Set 2 with long straight fibers. The worse results for Set 2 can be explained by the placement of straight fibers next to each other, which leaves few background pixels between the fibers and therefore complicates the calculation of the fiber orientation. Higher variance of the preferred orientation of the fibers (Models 3 and 4) thus leads to better accuracy. Comparing the two methods, it can be stated that BFFT measures the ODF with a slightly higher accuracy than STT.

Real images

The measured results by BFFT of real images are shown in Figure 9. For Set A, a clearly favored fiber orientation in the 90° direction was computed. Based on the subjective impression, this is a comprehensive result. The measured ODFs of nonwoven images of type B has two obvious 0° and 90° peaks. This can be attributed to the included weave, which can easily be seen in Figure 5. As expected, the measured ODFs of nonwovens images of type C are more uniformly distributed.

Figure 9.

Measurement by blockwise Fast Fourier Transform of (a) samples A1–A5, (b) samples B1–B5 and (c) samples C1–C5.

Figure 10 shows the measured ODFs by STT of real images. For all three nonwoven sets the same main fiber orientations as those computed with BFFT were determined. For Set A, however, the preference for the 90° direction is not as pronounced. In contrast, a slight preference for the 90° direction has been found for Set C.

Figure 10.

Measurement by STT of (a) samples A1–A5, (b) samples B1–B5 and (c) samples C1–C5.

In addition, Figure 11 shows the local orientation measurement for every pixel of the image. For Set A no clear pattern in the location of the preferred fiber orientations can be seen. For Set C no distinct pattern can be seen either, as the fibers are randomly distributed as claimed by the manufacturer. In contrast, the display of the local orientation of a Set B sample clearly shows the weave of this nonwoven type.

Figure 11.

Local orientation measurement for (a) image A1, (b) image B1 and (c) image C1.

The data in Table 5 show the average KL divergence between measured ODFs of images within a single set and images from different sets. The average KL divergence between measured ODFs of images within a single set is much smaller than that of images from different sets. As the different samples within one set have similar structural features and, especially in the case of Sets B and C, the same fiber orientation, we can derive from the small KL divergences within one set that the methods allow accurate measurements. Regarding the variety of the evaluated sets it can be claimed that BFFT and STT methods are not sensitive to the type of nonwoven fabrics. They can reliably measure different types of nonwovens with different structural characters. At the same time, they can distinguish the nonwovens with different fiber orientation distributions.

Table 5.

Average Kullback–Leibler (KL) divergence between measured Orientation Distribution Functions of images in one set and images from different sets

	Set A	Set B	Set C	Sets A and B	Sets A and C	Sets B and C
Mean KL divergence
BFFT	0.0243	0.0106	0.0152	0.8607	0.4796	0.2660
STT	0.0036	0.0042	0.0063	0.2540	0.0846	0.1445

BFFT: blockwise Fast Fourier Transform; STT: Structure Tensor Thinning.

Conclusion

In this work, the algorithms of an improved BFFT and ST were adopted as the basis for a newly developed assemble method. At first, BFFT was improved by assigning an adaptive weight to each subwindow. BFFT was used to measure the overall orientation distribution of nonwovens. Then, based on the idea of ST, a new method called STT was developed to estimate the local orientation of each pixel in a nonwoven image. Meanwhile, the overall orientation distribution has also been calculated from this local information as a reference of the ODF obtained from BFFT.

Based on these results, it has been proved that BFFT and STT can clearly distinguish the different ODFs between different types of nonwovens. The evaluation with simulated images and known fiber orientation distributions showed that, by weighing the subwindows based on fiber density and specific alignment of the fibers, the BFFT method was improved compared to the existing methods. The newly developed STT methods have shown a high accuracy determining the dominant directions of fibers, improving the accuracy of state of the art ST methods significantly. However, as the 0 °/180° directions are slightly overestimated by this method, further research will be required. The evaluation of different real images shows that the type of nonwovens has no influence on the developed orientation measurement assemble schema. Because the measurement is based on the orientation of each pixel, the measured ODFs of STT are smoother and more robust than BFFT. BFFT is sensitive to the setting of different parameters. For the evaluation of these parameters a combination of both methods is recommended. For the measurement of a new type of fabric, the measured ODF by STT can be used as a reference to choose the right parameters for BFFT. Once the measured ODF by BFFT is reasonable, in future measurement of nonwoven fabrics can be efficiently measured with less required computing time.

The findings of our study indicate that the newly developed assemble method can be integrated in our equipment to accurately and robustly measure the ODF of different types of nonwoven fabrics. On the one hand, these calculated indexes can be used to control the mechanical properties of produced fiber injection molded nonwovens. On the other hand, they could be used to analyze and further guide the improvement of the production process.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This publication was partly written within the framework of the Profilregion Mobilitätssysteme Karlsruhe, which is funded by the Ministry of Science, Research and the Arts in Baden-Württemberg. The other part was supported by the German Research Foundation (DFG: Deutsche Forschungsgemeinschaft; project no. 439709829).

ORCID iD

Patrick Moll

References

Stegschuster

Schlichter

. Perspectives of web based composites from RCF material. IOP Conf Ser Mater Sci Eng 2018; 406: 1–6.

Cherif C. Textile materials for lightweight constructions. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016.

Fleischer

Teti

Lanza

, et al. Composite materials parts manufacturing. CIRP Ann 2018; 67: 603–626.

Förster E. Verfahren und Vorrichtung zur Herstellung von dreidimensional ausgeprägten Formteilen sowie Formteil, Deutschland, 2003.

Moll

Schäfer

Coutandin

, et al. Method for the investigation of mold filling in the fiber injection molding process based on image processing. Procedia CIRP 2019; 86: 156–161.

Pourdeyhimi

Ramanathan

Dent

. Measuring fiber orientation in nonwovens: Part 1: simulation. Text Res J 1996; 66: 713–722.

Pourdeyhimi

Dent

Davis

. Measuring fiber orientation in nonwovens: Part III: Fourier transform. Text Res J 1997; 67: 143–151.

Ghassemieh

Acar

Versteeg

. Microstructural analysis of non-woven fabrics using scanning electron microscopy and image processing. Part 2: application to hydroentangled fabrics. Proc IMechE 2002; 216: 199–207.

Enomae

Yoon-Hee

Akira

. Nondestructive determination of fiber orientation distribution of paper surface by image analysis. Nord Pulp Paper Res J 2006; 21: 253–259.

10.

Yongping

Zengbo

Ruqin

. Application of Fourier transform techniques in the measurement of structural parameters in fabrics and nonwovens. J Chin Text Univ 1998; 24: 18–22.

11.

Marquez

. Fourier analysis and automated measurement of cell and fiber angular orientation distributions. Int J Solid Struct 2006; 43: 6413–6423.

12.

Sander

Barocas

. Comparison of 2D fiber network orientation measurement methods. J Biomed Mater Res A 2009; 88: 322–331.

13.

Tunák

Antoch

Kula

, et al. Estimation of fiber system orientation for nonwoven and nanofibrous layers: local approach based on image analysis. Text Res J 2014; 84: 989–1006.

14.

Tunák

Antoch

. Monitoring homogeneity of textile fiber orientation. Text Res J 2018; 88: 1226–1243.

15.

Pourdeyhimi

Kim

. Measuring fiber orientation in nonwovens: the Hough Transform. Text Res J 2002; 72: 803–809.

16.

Bin

Xiaoming

Yuening

, et al. The influence of process parameters on needle punched nonwovens investigated using image analysis. RSC Adv 2017; 7: 5183–5188.

17.

Bugao

Ling

. Determining fiber orientation distribution in nonwovens with Hough Transform techniques. Text Res J 1997; 67: 563–571.

18.

Lijuan

Weidong

. Orientation image analysis of electrospun submicro-fibers based on Hough transform and Regionprops function. Text Res J 2017; 87: 2263–2274.

19.

Bayan

Levitt

Miller

, et al. Fully automated, quantitative, noninvasive assessment of collagen fiber content and organization in thick collagen gels. J Appl Phys 2009, pp. 105: 102042 .

20.

van Vliet L and Verbeek P. Estimators for Orientation and Anisotropy in Digitized Images. In: ASCI '95: Proceedings of the first annual conference of the Advanced School for Computing and Imaging ; Heijen, the Netherlands, May 16 – 18, 1995. (ed van Katwijk J), Heijen, May 16-18, pp. 442–450. Delft: ASCI.

21.

Knutsson H. Representing local structure using tensors. In: 6SCIA: Proceedings of the 6th Scandinavian conference on image analysis, Oulu, [Finland], June 19-22, 1989. (ed Pietikäinen M), pp. 244–251. Oulu: Pattern Recognition Society of Finland.

22.

Krause

Hausherr

Burgeth

, et al. Determination of the fibre orientation in composites using the structure tensor and local X-ray transform. J Mater Sci 2010; 45: 888–896.

23.

Pourdeyhimi

Dent

. Measuring fiber orientation in nonwovens: Part IV: flow field analysis. Text Res J 1997; 67: 181–187.

24.

Hong

Wan

Jain

. Fingerprint image enhancement: algorithm and performance evaluation. IEEE Trans Pattern Anal Mach Intell 1998; 20: 777–789.

25.

Pourdeyhimi

Ramanathan

Dent

. Measuring fiber orientation in nonwovens: Part II: direct tracking. Text Res J 1996; 66: 747–753.

26.

Jue

Bugao

Hanchao

, et al. Measuring fiber orientations in nonwoven web images using corner detection by Bézier fitting curves. Text Res J 2018; 88: 2120–2131.

27.

Quinn

Georgakoudi

. Rapid quantification of pixel-wise fiber orientation data in micrographs. J Biomed Opt 2013, pp. 18: 046003 .

28.

Gong

Sbalzarini

. Curvature filters efficiently reduce certain variational energies. IEEE Trans Image Process 2017; 26: 1786–1798.

29.

Pizer

Amburn

Austin

, et al. Adaptive histogram equalization and its variations. J Electron Imag 1987; 39: 355–368.

30.

Kullback

Leibler

. On information and sufficiency. Ann Math Stat 1951; 22: 79–86.