Image Edge Detection with Signal Processing Approach

Abstract

Edge detection is one of the most important techniques used for segmentation within an image. In addition, edge detection is a technique that enables object detection by determining the edges of objects. There are signal processing techniques under edge detection algorithms. In this article, edge detection algorithms, methodology and signal processing part will be mentioned briefly.

Introduction

The detection of the edges of the objects in the images creates a solution for us in most scenarios. As we know, images consist pixels which are digital signals, pixels are express in numbers and they can be displayed in a matrix. Each row and column in the matrix represents one pixel. If our image consists 3-dimension color space like BGR, RGB, HSV one element of the matrix has 3 different value. For example, we have worked 16x16 image. It has 64x64x3 values if the image contains colors that different than black and white. Black and white images are represented with one channel. This means more space complexity exits if we work with colored images.

Edge detection algorithms are based on detecting and manipulating differences between each pixel. In here “difference” means different values of pixels. If there is a sudden change between pixels, there is a high probability that there will be an edge. Because of the nature of different objects, pixel values are different from each other. In this scenario, although, the edge detection process is worked on single-channel images, (black and white) transforming a multi-channel image into a single-channel image will result in data loss because it reduces the data that each pixel carries. (lossy compression)

Methodology

Because the images are composed of matrices, matrix operations are used to detect the edge. Using the step unit step function, we can begin to perceive the edge. Generally, edge detection is classified gradient based and Laplacian-based. Gradient method is based on “mask” operation in digital signals. It calculates horizontal and vertical directions of image’s edges. The Laplacian-based edge detector uses computing the second order derivative expression.

If there is no blur in the photo, there will be a sharp transition as it appears on the left. This is equal to the function u(t) that appears. According to the variable “t” edge can be found where the change is in the picture. Otherwise, naturally, some blurs can exist. Generally, the cause of blur is the quality of the photo, noise, flicker. Special algorithms have been developed to eliminate this blur. The use of the unit step function works in theory, while in some cases it is necessary to use more precision valued functions. One of them is the “Sigmoid” function. Sigmoid is now widely used in areas such as deep learning and machine learning as the activation function. On the other hand, we need to blurry images. Because every change in the photo may not mean an edge. For example, if we want to detect an outfit, we don’t want to accept the shadows in the outfit as an edge. So, we use “Fuzzy Logic based Edge Detection” technique to do it.

In a frame, received from CNN education of Andrew Ng, he explains the detection of edge with vertical and horizontal convolution. Here, the left-bottom matrix represents our image. On the middle side matrix is the matrix required for edge detection. This is a function and finds vertical or horizontal edges according to its value. In the result, the last image represents a convolution mask for edge detection.

Mehmet Cagri Aksoy — 2018

References

• Edge Detection with a PreprocessingApproachMohamedAbo-Zahhad1, Reda RagabGharieb1, Sabah M. Ahmed1,Ahmed Abd El-BasetDonkol
• Methods of Image Edge Detection: A ReviewDharampal and Vikram Mutneja*Shaheed Bhagat Singh State Technical Campus, Ferozepur, Punjab, India
• International Journal of Computer Applications (0975–8887) Volume 51 — №8, August 2012 12 Image Edge Detection based on Soft Computing Approach Pushpajit A. Khaire PG Student, Department of Computer Science & Engineering, Shri Ramdeobaba College of Engineering & Management Nagpur Nilesh singh V. Thakur. Phd, Department of Computer Science & Engineering Shri Ramdeobaba College of Engineering & Management Nagpur
• Precise Edge Detection Method Using Sigmoid Function in Blurry and Noisy Image for TFT-LCD 2D Critical Dimension Measurement Seung Woo Lee, Sin Yong Lee, and Heui Jae Pahk