Methods of edge detection

Computer vision is a crucial field of artificial intelligence that enables computers to understand and interpret visual information from images or videos. It is gaining significant attention as this is becoming a new medium of communication between users and computers. Computer vision can be seen in facial recognition and fingerprint recognition in our smartphones.

Moreover, this technology is becoming a part of vehicles, relying on computer vision for their autopilot and full self-driving capabilities. Companies such as Tesla take advantage of computer vision for perceiving and comprehending the surrounding environment. 

Computer vision's impact also extends to domains such as improved medical diagnosis, surveillance, and security, revolutionizing these areas with its underlying principles. One such principle, which is the foundation of many other applications, is edge detection. 

What is edge detection? 

The concept of edge detection refers to extracting the location of the edge points of any image, mapping out an edge map. An example can be seen down below:

This extraction is done through the detection of variance in the intensity of an image. Usually, the edges are detected by the variation of gray levels in the image, but the noise can hinder that in the image. In image processing, edges are considered a special type of feature known as a singularityPoints in an image where there are abrupt changes or discontinuities in intensity values.. The abrupt changes or discontinuities are identified by examining the gradients, which measure the rate of change in intensity. At the edges, the gradient values highly vary, indicating the presence of a significant transition in the image intensity.

In simpler terms, edges in an image are points where there is a sudden shift in brightness or color. These points are identified by looking at the rate of change becoming extremely high, leading to high gradient values. By detecting these abrupt changes in the gradient, we can identify and locate edges in an image. As mentioned, edge detection is an essential component in image processing and is used in various methods, such as:

• Pattern recognition

• Image segmentation

• Scene analysis

In this Answer, we’ll be looking at the different methods for edge detection.

Methods of edge detection

There are now several methods for detecting edges which are achieved in different ways. Let’s discuss them one by one.

Gradient operators

Gradient operators are simple techniques employed to detect edges. They leverage the concept of calculating the first derivative, which can be computed through a convolution process. Now what is a convolution process?

Convolution is a powerful tool in image processing, allowing for various operations like blurring, sharpening, edge detection, noise reduction, and more. It enables the extraction of useful information from images. Different types of kernels can be used in convolution to achieve different effects, depending on the desired image processing task. The convolution process involves placing a filter (also known as a kernel) on each pixel of an image, multiplying the filter elements with the corresponding image pixels, adding the results, and repeating this process for all pixels. This generates a new image called the convolved output image.

Roberts cross

Roberts edge detection is a simple method used in images for detecting edges. It relies on the computation of gradient magnitudes utilizing a pair of small, simple filters known as the Roberts operators.

The Roberts operators consist of two 2x2 kernels, one for computing the gradient in the horizontal direction and the other for the vertical direction, shown below.

Sobel edge detection

The Sobel method is an edge detection technique used in image segmentation. It identifies edges by computing a 2-D spatial gradient, emphasizing regions with a high spatial frequencyRapid changes or variations in pixel intensity within an image, representing fine details or sharp edges. corresponding to edges. The Sobel technique is commonly used to estimate the absolute gradient magnitude at each point in a grayscale image. It involves using a pair of 3x3 convolution kernels, where one kernel is the other rotated by 90 degrees. This operation is similar to that of the Roberts Cross operator.

Prewitt edge detection

Prewitt edge detection is another popular method used for detecting edges in digital images. It is similar to the Sobel method and shares the goal of finding regions of significant intensity change that indicate edges.

The Prewitt operator involves the computation of gradient magnitude and direction using two 3x3 convolution kernels: one for detecting edges in the horizontal direction and the other for the vertical direction.

Furthermore, we have to calculate the gradient magnitude at each pixel by combining the horizontal and vertical gradients of the convolved output image using the Euclidean distance formula:

Canny edge detection

Canny edge detection is an advanced and widely used edge detection algorithm in computer vision and image processing known for its ability to produce high-quality edge maps with low noise.

The Canny edge detection algorithm consists of several steps, starting with the Gaussian smoothing and gradient calculation. The input image is convolved with a Gaussian filter (shown below) to reduce noise and remove small variations in pixel intensities.

The gradient magnitude and direction are calculated at each pixel using the first-order derivatives in the horizontal and vertical directions. After this, non-maximum suppression is applied, where the gradient magnitude of each pixel is calculated in the direction of the gradient. This process keeps only the highest values along the gradient direction, thinning the edges and removing non-maximal values. 

Then, double thresholding is performed by applying a high and a low threshold to the gradient magnitudes. Pixels with the calculated magnitudes above the high threshold are classified as strong edges, while those between the high and low thresholds are considered potential edges. Pixels below the low threshold are considered non-edges and are eliminated. 

Finally, edge tracking by hysteresis is applied, which aims to connect weak edges to strong edges based on their connectivity. This process helps preserve important edges that may have lower gradient magnitudes.

Marr-Hildreth detector 

The Marr-Hildreth edge detection algorithm, or the Laplacian of Gaussian (LoG) edge detector, is a method for detecting edges in digital images. It combines the concepts of Gaussian smoothing and the Laplacian operator to identify significant intensity variations corresponding to edges. A Gaussian filter is used to reduce noise and eliminate fine details, while the Laplacian operator highlights regions where the intensity changes abruptly, indicating the presence of edges.

Moreover, noise amplification is mitigated through zero-crossing detection. Zero-crossings represent locations where the Laplacian response shifts from positive to negative or vice versa. Additionally, thresholding can be applied to the filtered image to minimize false detections caused by noise. This ensures that only prominent and reliable edge information is retained.

Before we conclude our Answer, let's take a small quiz.

Conclusion 

As we can observe, through the advancements in deep learning and neural networks, computer vision continues to advance rapidly, pushing the boundaries of what is possible in visual understanding and interaction with computers.