# Research on Wavelet Transform Modulus Maxima and OTSU in Edge Detection
## 1 Introduction  
Edge detection is an important process in techniques, such as image analysis and processing, computer vision and pattern recognition, with the aim of detecting information about the shape of objects in an image [1; 2; 3; 4; 5]. In the real world, there are four situations in which edges can be formed in an image: (1) discontinuities in depth, (2) discontinuities in surface orientation, (3) different materials of objects in an image and (4) different lighting in a scene. Edges often locate in an image where there are significant changes in grey scale, colour and texture [6], so the edges of an object can be determined by detecting gradients. Commonly used algorithms for edge detection include [PERSON], Prewitt, Sobel, Laplace and Canny. These detection methods are easy to implement, demonstrate many advantages when detecting images with relatively simple backgrounds and are widely used in many industries [7; 8]. However, when dealing with images with complex backgrounds [9], they are not sufficient recovering much high-level semantic information, which means they have some shortcomings. The wavelet transform is a time-frequency domain analysis method that has the ability to characterize the local features of a signal. The singularities of the wavelet-transformed signal are closely related to the location where the signal apparently changes. [PERSON] [10] applied the wavelet transform modulus maxima method to image processing, which determined the damage of the object caused by external forces or environmental conditions in the image. [PERSON] [11] used this method to successfully denoise tunnel monitoring, providing a basis for tunnel health diagnosis; [PERSON] [12] used an improved wavelet transform mode maxima method to subdivide and fuse two edges obtaining the clearer andbetter connected edge information; and [PERSON] [13] embedded a 1-bit watermark in wavelet transform mode maxima to achieve rotation, scaling and panning of the image, improving the robustness of the watermarking technique. [PERSON] [14] used wavelet transform modulus maxima based on Bayesian threshold estimation to effectively remove noise in MEMS. In an article by [PERSON] [15], he mentioned a huge disaster caused by a melting glacier, which greatly affected the livelihood of the local people. By using high-resolution images provided by commercial and government satellite constellations, the analysis of the disaster can be completed in a short period of time when manpower and technology are available, and if changes in glacier melting or mountain sliding are detected early through the monitoring of remote sensing images at an early stage, and timely warnings are given, unnecessary damage can likely be avoided. This demonstrates the importance of a range of image technologies such as edge detection in the field of remote sensing. In the process of applying wavelet transform modulus maxima, thresholds need to be set to remove pseudo-edges in gradient images, but manual setting requires repeated debugging and is not efficient. OTSU method can use the maximum inter-class variance of the image to automatically calculate the threshold and improve the debugging efficiency. Using the OTSU, [PERSON] [16] carried out threshold segmentation on the real image data and predicted the segmentation results based on the Monte Carlo statistical method; [PERSON] [17] used OTSU to segment plant images to discriminate between healthy leaves, unhealthy leaves and other backgrounds, and could identify the infected parts of leaves; [PERSON] [18] used OTSU to pre-process and segment brain MR images and extracted many important features from the segmented images; [PERSON] [19] used OTSU to work out the FSW extrema coefficients and obtain the edges of the image by connecting the edge points using the predicted edges; and [PERSON] [20] used OTSU and watershed marker-controlled technique to distinguish between single cells and groups of cells. [PERSON].