Essay: Enhanced Image Segmentation for Non-Destructive Testing Using Fuzzy Logic

Abstract

This research aims to develop an algorithm suitable for automated systems to interpret and make decisions on metal imperfections. Utilizing Non-Destructive Testing (NDT) images, our method employs advanced image processing techniques to analyze these imperfections. Given the degraded quality of metals and the small size of defects, NDT images can be challenging to inspect, often subject to human error and subjective interpretation. Our approach translates the discrimination power of the human eye into an efficient algorithm, surpassing previous methods based on entropy and histogram thresholding. For improved precision, we propose a segmentation approach based on fuzzy logic, tailored to NDT-specific information.

Introduction

Non-Destructive Testing (NDT) is defined by the American Society for Non-destructive Testing (ASNT) as the evaluation of the physical condition of an object without impairing its functionality. NDT techniques utilize probing energy forms to determine material properties or identify material discontinuities, whether surface, internal, or concealed. These methods are crucial in inspecting materials used in machinery and structures to detect possible faults like corrosion, cracks, and other imperfections, ensuring safety and reliability. NDT inspection technology underpins safety assessment and explosion prevention technology for boilers and pressure vessels. Numerous methods exist for conducting NDT and obtaining images, but fewer are available for their analysis. Previous algorithms have not yielded satisfactory results due to the low contrast between defective and sound regions in NDT images. Thus, we propose an algorithm to segment these images into non-overlapping, meaningful regions, enhancing interpretability and reliability.

Image Segmentation in NDT

Image segmentation is fundamental to object recognition and computer vision, enabling applications such as image retrieval, visual summaries, and image-based modeling. Segmentation partitions an image into meaningful regions according to specific criteria. Formally, segmentation is the partition of a set $F$ into connected subsets SiS_iSi​ such that the homogeneity predicate P(Si)P(S_i)P(Si​) is true for all regions and P(Si∪Sj)P(S_i \cup S_j)P(Si​∪Sj​) is false when SiS_iSi​ and SjS_jSj​ are neighbors. Various segmentation approaches exist, including classical, statistical, fuzzy, and neural methods. Our method, based on second-order fuzzy correlation, utilizes a modified co-occurrence matrix to extract local information from the image. Fuzzy logic, which mimics human reasoning, effectively handles the vagueness inherent in human perception and language, making it ideal for this application.

Basic Concepts

Co-occurrence Matrix

The co-occurrence matrix is a statistical method for texture extraction, calculating how often pairs of pixels with specific values occur in a given spatial relationship within an image. For a grayscale image $I$ of dimensions $M\times N$ with $L$ grey levels, the Gray Level Co-occurrence Matrix (GLCM), defined by Haralick, is a square matrix $G$ of size $L\times L$. The $(i,j)$th entry of $G$ represents the probability of a pixel with intensity $j$ occurring around a pixel with intensity $i$. Various definitions of the co-occurrence matrix are possible depending on the spatial relationship considered, such as in any of the eight possible directions (N, S, E, W, or the four diagonals).

Fuzzy Set Theory

Introduced by Zadeh, fuzzy set theory models problems involving imprecise data and diffuse categories. Unlike classical sets, which use a characteristic function mapping from the universal set $U$ to {0,1}, fuzzy sets are defined by a membership function mapping $U$ to the interval [0,1]. This allows for varying degrees of membership, reflecting the uncertainty and vagueness of real-world data. A fuzzy subset $A$ of a universe $X$ is a collection of ordered pairs (x,μA(x))(x, \mu_A(x))(x,μA​(x)), where μA(x)\mu_A(x)μA​(x) denotes the degree of membership of element $x$ in $A$. This concept is crucial for handling the incomplete and unreliable information provided by NDT.

Membership Function

The membership function quantifies the participation of each input in a fuzzy set, associating weights with inputs for processing. These rules, often linguistic, use input membership values to influence the fuzzy output sets’ conclusions. Input membership functions can take various forms, such as triangles, trapezoids, or bell curves, depending on the system’s requirements. In this research, we employ an S-shaped membership function, which is particularly useful for image thresholding due to its adaptability and precision.

Implementation

The proposed segmentation method consists of five phases:

1. Generation of the Modified Co-occurrence Matrix
2. Calculating the 2D S-type Membership Functions
3. Determining the Second-Order Fuzzy Correlation
4. Measuring Ambiguity for Each Gray Level and Identifying the Threshold Level for Segmentation
5. Producing the Final Image Output with Thresholding

Procedure

Modified Co-occurrence Matrix

A grayscale image’s pixel intensity ranges from 0 to 255, and its histogram plots the number of pixels at each intensity level. In practical applications, histograms are often unimodal, making threshold selection challenging. Our algorithm uses spatial information to produce a transformed co-occurrence matrix, effectively handling unimodal images by emphasizing significant features and enhancing contrast. This method accounts for the rate of change of gray level and edge values, providing more accurate segmentation.

2D S-Type Membership Function

The 2D S-type membership function adapts the standard S-function to handle real-life, two-dimensional images. By modifying parameters, we transform the function to better represent the image’s characteristics. This function calculates fuzziness for each pixel intensity, identifying the threshold with minimal ambiguity.

Fuzzy Correlation

Fuzzy methods offer stability under uncertain conditions and simplicity in achieving desired image enhancement effects. The proposed method uses fuzzy correlation to threshold the image histogram, extracting essential information. The correlation between local properties, such as edginess or texture, helps identify significant features and enhance segmentation accuracy.

Measure of Ambiguity

Ambiguity measures the difficulty in classifying a pixel as part of the object or background. By defining initial regions and classifying pixels based on fuzzy membership values, we maximize contrast between the object and background. The optimal threshold corresponds to the gray level with maximum ambiguity, ensuring precise segmentation.

Thresholding

Thresholding partitions pixels into foreground and background based on their gray levels. The identified threshold separates object pixels from background pixels, resulting in a segmented image that clearly delineates the object from its surroundings.

Experimental Results

We implemented the proposed algorithm in MATLAB and tested it on several poor-quality NDT images. The results demonstrate that our method produces segmentation results close to the ground truth, with a high rate of satisfactory outcomes. In most cases, the algorithm accurately identified the appropriate threshold, validating its effectiveness.

Conclusion

This research presents a novel technique for segmenting NDT images, leveraging fuzzy logic to enhance precision and reliability. Experimental results indicate that the proposed method performs well across various gray level digital images, with results closely matching ground truth data. Although the algorithm occasionally fails to produce the optimal threshold, its overall performance is robust and reliable.

Future Scope

Future research can refine the algorithm to improve accuracy and extend its application to multiple thresholds for images with complex histograms. Additionally, the method can be adapted for use in recognition systems and other color models, expanding its utility in various domains.

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Based on 2017-7-27-1501177594 but rewritten.