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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This paper presents a novel, real-time defect detection system, based on a best-fit polynomial interpolation, that inspects the conditions of outer surfaces. The defect detection system is an enhanced feature extraction method that employs this technique to inspect the flatness, waviness, blob, and curvature faults of these surfaces. The proposed method has been performed, tested, and validated on numerous pipes and ceramic tiles. The results illustrate that the physical defects such as abnormal, popped-up blobs are recognized completely, and that flames, waviness, and curvature faults are detected simultaneously.

Real-time visual inspection systems have improved over the last few years, ensuring a high standard of product quality in the mass production systems of industry. This is compounded by the fact that manufacturing industries are strongly motivated to use high-precision fault and defect detection systems with minimum development, low installation and maintenance costs, and a reduction in avoidable, time-consuming effort. Due to these requirements, applying a powerful inspection system with the ability to inspect and detect all kinds of faults is of significant interest. To create a complete, real-time defect detection system, it is essential to know all the faults that result in defects. In terms of product quality control, surface geometry and physical properties are often classified into four groups:

Defects, such as: welds, spots, blobs, cracks, and scratches in the ceramic-tile industries;

Roughness, such as residual polishing-marks in the car industries;

Waviness, although not as common as roughness, has a measurement. Measuring waviness in a bearing ball is one example.

Flatness, roundness, or curvature, which is an error on the shape of products. Flatness faults of stones or ceramic tiles are typical examples.

These defects are classified as irregular patterns on these surfaces upon inspection. This paper gives a background to the problem through summarizing related works and problem statement in the subsections below. Section 2 presents, in detail, the novel methodology adopted to resolve the problem. Section 3 renders the validation and the measurement accuracy of the proposed method for various lines and ellipses. Section 4 explicates the results of the proposed method, which was tested in real-time on ceramic tiles and pipes. Finally, the paper is wrapped up by a comparison, discussion and an overall conclusion.

Rosati

A typical visual inspection system contains a camera, image-processing software, and a manufacturing process control system [

Previous works concentrated their efforts on capturing and analyzing the outer surfaces of spheres and cylindrical objects by locating the camera above these objects [

Any gain, however, should be seen in a wider context. If the camera captures outer surface from the side, it will not be able to see scratches, holes and small spots on the outer edges. Therefore, the presented method is proper to assess outer surface defects that change the curvature of surfaces and visible to the camera; especially for flatness defects, waviness blobs and welds on the edges of outer surfaces.

In analogue view, all edges with different slopes seem smooth. Even all curves are easy to recognize, but in the digital view of an image, lines with different slopes have various breaks. Edges of images have various line segments, such as a curve, a circle, and a straight line [

In the pre-processing step, the image should be smoothed to decrease noise. A simple smoothing filter, such as a mean or median filter, is applied. Thereafter, the edges of the image are extracted using a canny edge detector [

The edges of the image source from the pre-processing step are sent to a feature extraction. These edges are called a digital image, but the source image does not match exactly because of resolution limitations. Therefore, this step matches a digital image to a source image and helps provide more accurate results. The aim of this step is to find the closest pixels in a digital image that are near to source image. In the proposed method, the coordinates of edges in an image are saved in

The average of each category illustrates the pixels the closest to the source image. For instance,

From the previous step, the critical-pixels are collected as data points. These data points are used in polynomial interpolation. In mathematics, a polynomial is an expression of finite length, constructed from variables (also known as in determinates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomial interpolation is a generalization of linear interpolation, and linear interpolation is a method of curve-fitting using linear polynomials. As mentioned, all extra edges of canny edge detection can be omitted, and only the edge of outer surface remains for processing.

Assume we have n critical-pixels after applying canny edge detector on the outer surface; therefore we have _{1}_{1}_{n}, y_{n})_{i})_{i}_{1}, f(x_{1}))_{n}, f(x_{n}))_{th}_{k}_{k}_{+1}

There is only one interpolating polynomial of degree, _{1} … _{n}^{(n)}

Curvature refers to any number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. The curvature of a circle is equal to the reciprocal of the radius:

On the other hand, the curvature of circles has an inverse proportion with the radius; increasing radius decreases curvature. Therefore, a circle with a large radius has a small curvature, and

The curvature of point ^{2}^{2}_{n}

To validate the accuracy of the proposed method, three lines with different slopes are selected, as shown in

The line graph of Line (a) is depicted in

The results of Line (b) and Line (c) are shown in

To complete the validation, two ellipses are selected. The ellipse is selected because the curvature of two corners of the ellipse is more than in other parts. In

In order to validate the inspection of the proposed system, an automated visual inspection system is proposed. The system is developed by a CCD camera with a maximum frame rate of 30 Hz. Furthermore, the distance between the camera lens and objects on the conveyor belt is 18 cm approximately. The light resource is a fluorescent lamp which illuminates a conveyor belt with an approximate 565 lx intensity from the top of the conveyor. As a result, most of reflection returns to the top of the inspected item and little light is visible to the camera. Therefore, the camera will be able to capture from high reflective surface. Moreover, a portable laptop with 2.2 GHz processor and 2 GB RAM is used to process the captured images.

The layout of a real-time system that investigates the ceramic tile edges is shown

The software was developed in Visual Studio with OpenCV (image processing library) and ALGIB (mathematics library). The interface application is depicted in ^{−1} curvature. To increase the precision of the result, the setting of the camera was changed to a higher resolution (1,280 × 720 pixels), and the accuracy was increased to approximate +0.33 mm^{−1} curvature. In addition, the speed of using proposed algorithm in our system in an image with a resolution of 864 × 480 pixels is 0.31 s that increased to 0.43 s in images with 1,280 × 720 pixels. This speed indicates our system is quite rapid for real time inspection in ceramic tiles factory. This system can measure the flatness and waviness of ceramic-tiles as well; however, other defects, such as blobs and welds, are found more easily than curvature defects.

In contrast,

It is inferred that the curvatures of critical-pixels on the surface of the tile are less than 1.50E-06, which means it is a non-defective tile. This result depicts that the proposed method is able to classify non-defective tiles from flatness-defective tiles.

The proposed method was also tested on the outer surface of a steel pipe, which has high light reflection in a captured image. The layout of the steel pipe inspection system is illustrated in

Since color, shadow, and reflection of light influence the image, the proposed system has been tested for several steel and coloured pipes. All experimental results indicate that the proposed method is robust, even for reflective and colorful, multi-curvature surfaces. Moreover, the results illustrate that not only is the proposed method able to assess blob defects in pipes, but it is also reliable to inspect waviness and flatness.

The proposed method has been tested on various ceramic tiles and pipes. The results illustrate that this method has the capability of sufficiently detecting the surface defects. Furthermore, it is possible to define the range of valid curvature defects. For example, if it is essential to inspect the outer surface meticulously, the interpolation-error mentioned before, ^{−1} deviation. The difference between the proposed method and related work is that our method can find blob, weld, flatness and waviness defects simultaneously which is not seen in related work. However, the precision of detecting blobs, welds and spots is not as good as that of related work, but the accuracy of finding flatness defect on wavy edge is improved compared to related works.

A real-time visual inspection method for curvature and wavy edge defect detection of outer surfaces was proposed. The approach described an enhanced feature extraction method based on polynomial interpolation to detect flatness and waviness defects on outer surfaces. The proposed method introduces a novel method which finds critical pixels of an image; then, by utilizing polynomial interpolation, the curvatures of outer surfaces are assessed. It is noteworthy in the proposed method; the camera inspects the outer surface of items from the side. Therefore, less surface reflection is captured by the camera, and it is thus suitable for capturing images from reflective surfaces, although in this situation, small holes, scratches and cracks are hidden from the camera. Results of the proposed method, which has been tested on different graphical lines, ellipses, real tiles and pipes, indicate that it is able to measure curvature defects and wavy edges for various surfaces, such as colorful or reflective surfaces. Moreover, the outcome of testing 200 colorful and reflective ceramic tiles and pipes illustrates that the method is capable of measuring and inspecting the curvature of surfaces with different levels of precision. Furthermore, it is able to detect physical defects such as flatness, waviness, welds or blobs on the border of items simultaneously, which outweighs previous contributions in defect detection.

The authors would like to thanks Ministry of Higher Education Malaysia and Universiti Kebangsaan Malaysia for providing facilities and financial support under Grants No. FRGS/1/2012/SG05/UKM/02/12 and PTS-2011-054.

More experimental results of ceramic tiles and pipes with different defects are shown in this section. The results of various defects on different ceramic tiles and pipes show that the proposed method is stable in blob, weld and curvature defects. In contrast, it is unable to detect cracks and scratches on the outer surfaces. In

Furthermore, defective ceramic tiles are assessed. For example,

Camera captures image from side of pipe. The first image shows a non-defective pipe, and the second image depicts a pipe with curvature and blob defects.

Overview diagram of proposed method.

Example of finding critical-pixels. The grid shows pixels in a digital image: (

The curvature of point

Three lines with different slopes showing different gradients: (

The curvature diagram of Line (a) in

The curvature graph of Line (b) in

The curvature diagram of Line (c) in

Two horizontal ellipses with different heights. Ellipse (

The line graph shows the curvature values of Ellipse (a).

The line graph shows the curvature values of Ellipse (b).

Layout of ceramic tile inspection system to capture the surface defects from the side.

Close up of the ceramic tile inspection system layout.

Ten defected points detected on the surface of a ceramic tile.

Source image of flatness defected tile.

Edges of source image after applying canny edge detector on source image.

Critical-pixels of ceramic tile that has flatness defect.

The curvature diagram of flatness defected tile.

Source image of a non-defective ceramic tile.

Edges of ceramic tile after applying canny edge detector on source image.

Critical-pixels of a non-defective ceramic tile.

Curvature diagram of a non-defective ceramic tile.

Layout of pipe inspection system with respective placements of a camera, pipe, and computer.

Real image of a reflective pipe showing a small blob on the surface.

The small blob is shown on the surface of the pipe after applying the canny edge detector.

Critical-pixels of pipe with blob defect on the outer surface.

The curvature diagram of a blob defective pipe.

Non-defective ceramic tile after using canny edge detection.

Curvature diagram of a non-defective ceramic tile.

Edge of ceramic tile with a small weld defect in the middle.

Curvature diagram of a ceramic tile with weld defect on the middle.

Flatness defected ceramic tile after using edge detection.

Curvature diagram of flatness defect ceramic tile.

Real image of a pipe showing a curvature defect on the surface.

Curvature diagram of a pipe with curvature defect.

The results of the proposed method for lines and ellipses.

Line (a) | 2.1E-05 | 8.3E-06 | 5.4E-06 | 4.5E-06 |

Line (b) | 6.8E-05 | 2.7E-08 | 1.0E-05 | 1.4E-05 |

Line (c) | 6.9E-04 | 3.8E-06 | 1.4E-04 | 0.00015 |

Ellipse (a) | 0.20264 | 0.07476 | 0.04859 | 0.05732 |

Ellipse (b) | 0.01579 | 0.00778 | 0.00702 | 0.00379 |