# Contrast-Invariant Edge Detection: A Methodological Advance in Medical Image Analysis
## 1 Introduction
Medical images enable doctors to intuitively analyze the internal organ structure of the body, thus assisting them in diagnosing diseases and formulating treatment plans. In the process of medical image-assisted diagnosis, edge detection is a key technology: the precision and reliability of its edge detection are crucial in the whole diagnostic process [8; 9]. Accurate, complete, and stable medical image edge detection results can help doctors quickly and accurately locate the lesion area and identify key information such as perimeter, dimensions, and form of the lesion [10]. This helps doctors to not only make quick diagnostic decisions but also provide an accurate basis for subsequent treatment plans. For example, in the diagnosis of tumor diseases, edge detection can determine the growth site and range of the tumor, providing an important reference for the scope of surgical resection, to avoid excessive resection or incomplete resection. Traditional edge detection methods mainly rely on the first- and second-order derivatives of the image and identify the edges in the image by detecting the changes in the gray values. The Roberts operator uses local differences based on first-order derivatives to detect edges. It calculates the gradient magnitude for edge detection by utilizing the difference between two adjacent pixels in the diagonal direction. The Roberts operator is highly sensitive to noise and lacks directional information [11]. Prewitt and Sobel operators are both based on first-order derivatives [12]. The Prewitt operator measures the gradient using two 3 \(\times\) 3 convolution kernels, which are used to calculate the horizontal and vertical gradients separately. The structure of the Sobel operator and the Prewitt operator is similar, the difference being that it has different weights. Prewitt and Sobel are simple and effective but sensitive to noise [13]. The Laplacian operator is a second-order derivative-based method that determines edges by detecting changes in the second-order derivatives, and it is often combined with Gaussian filtering to detect edges due to it being very sensitive to noise [14]. The Canny operator is among the more commonly employed methods. The Canny initially conducts Gaussian smoothing on the image for noise reduction. Subsequently, it calculates the gradient magnitude and direction of each pixel. Finally, it acquires the ultimate edges through non-maximum suppression and double thresholding [15]. The Canny operator employs the first-order derivatives of an isotropic Gaussian kernel and is regarded as the theoretically ideal way for detecting isolated edges contaminated by additive white Gaussian noise [1]. In recent years, in the medical field, scholars have proposed many different methods of edge detection for the characteristics of medical images. [PERSON] et al. [16] proposed an edge detection method based on Gaussian gradient for retinal Optical Coherence Tomography (OCT) images. They utilized the convolution result of a Gaussian function and its first-order derivative as a kernel, and the method was able to efficiently extract the boundary information in retinal OCT images. [PERSON] et al. [17] proposed a productive edge detection technique B-Edge. The B-Edge algorithm calculates the gray threshold and adjusts the intensity. It adopts a triple-intensity threshold automatic selection method to cover the gray range and determines the edge pixels through horizontal and vertical scanning, thus improving edge connectivity. [PERSON] et al. [18] proposed an MRI edge detection method based on Semi-Translation Invariant Contourlet Transform (STICT) and Fuzzy C-Means (FCM) clustering, and finally, the Canny operator is used to recognize the edges. The method performs well in improving image quality and edge detection accuracy. [PERSON] et al. [19] adapted the improved Canny operator for medical ultrasound images. They replaced the Gaussian filter with an adapted median filter and a weighted smoothing filter.