# Weak-Edge Extraction of Nuclear Plate Fuel Neutron Images at Low Lining Degree
## 1 Introduction
This algorithm is easy to implement and effectively removes salt-and-pepper noise, but its localization accuracy for edges is not good. Machine-learning algorithms have become the new direction of edge-detection research. In particular, deep learning [13; 14; 15] is used to automatically extract the deep features of images for better edge results. Despite the superior performance of deep learning methods, they require a large number of samples for training, and their computational complexity is high and time-consuming. However, there is no relevant research on edge detection algorithms for neutron images. The above methods are suitable only for certain images, such as visible images, so they cannot be applied to neutron images effectively. Neutron images are affected by the substance attenuation coefficient and the inevitable noise effects of the environment; the grayscale contrast between the fuel element cladding and background is poor, and the edges are weak and blurry, so roof-type weak edges occupy a substantial proportion. If the traditional algorithm is applied directly to the edge detection of the plate fuel pellet and its cladding, only strong edges can be detected, while weak edges are missed or fractured, and it is easy to produce incomplete and discontinuous edges. In the research [16], the authors discovered that, biologically or physically, the edges in images could be characterized as locations where the Fourier components are maximally in phase agreement. This phenomenon is known as phase congruency (PC). As a low-level image feature, because of its invariance to illumination and contrast and consistency with the human visual system [17], PC is favored and applied widely in image vision tasks, including image quality assessment [18], multi-modal image analysis [19], pattern recognition, object detection [20], and image registration [21]. Edge detection using the PC model can detect distinct types of edges, including roof-type weak edges and step-type strong edges, in images of arbitrary brightness and contrast without bias, owing to its contrast invariance. To overcome the limitations of traditional edge detection algorithms, this paper proposes to use the PC model for neutron image edge extraction. A detail-enhancement algorithm based on the classical perceptual field model was utilized to improve contrast at weak edges. A bilateral filtering algorithm was applied for denoising and preserving edge information, owing to its robustness to noise and friendliness toward edge details. Using the phase congruency model with six directions, an enriched edge map of the denoised image was generated, enabling more weak edges to be detected accurately even in low grayscale contrast. The non-maximum suppression further guaranteed accurate localization and prevented edge breakage. The edge outcomes were further optimized by eliminating erroneous edges and noise interference using mathematical morphological operations. To examine the effectiveness and feasibility of the proposed method, it was compared with conventional approaches using subjective and objective evaluation metrics.