C# How to: Image Edge Detection
Article Purpose
The objective of this article is to explore various edge detection algorithms. The types of edge detection discussed are: Laplacian, Laplacian of Gaussian, Sobel, Prewitt and Kirsch. All instances are implemented by means of Image Convolution.
Using the Sample Application
The concepts explored in this article can be easily replicated by making use of the Sample Application, which forms part of the associated sample source code accompanying this article. When using the Image Edge Detection sample application you can specify a input/source image by clicking the Load Image button. The dropdown combobox towards the bottom middle part of the screen relates the various edge detection methods discussed. If desired a user can save the resulting edge detection image to the local file system by clicking the Save Image button.
Edge Detection
Edge detection is the name for a set of mathematical methods which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The points at which image brightness changes sharply are typically organized into a set of curved line segments termed edges. The same problem of finding discontinuities in 1D signals is known as step detection and the problem of finding signal discontinuities over time is known as change detection. Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction.
Image Convolution
Convolution is a simple mathematical operation which is fundamental to many common image processing operators. Convolution provides a way of `multiplying together’ two arrays of numbers, generally of different sizes, but of the same dimensionality, to produce a third array of numbers of the same dimensionality. This can be used in image processing to implement operators whose output pixel values are simple linear combinations of certain input pixel values.
In an image processing context, one of the input arrays is normally just a graylevel image. The second array is usually much smaller, and is also two-dimensional (although it may be just a single pixel thick), and is known as the kernel.
Single Matrix Convolution
The sample source code implements the ConvolutionFilter method, an extension method targeting the Bitmap class. The ConvolutionFilter method is intended to apply a user defined matrix and optionally covert an image to grayscale.
Horizontal and Vertical Matrix Convolution
The ConvolutionFilter extension method has been overloaded to accept two matrices, representing a vertical matrix and a horizontal matrix.
Original Sample Image
The original source image used to create all of the edge detection sample images in this article has been licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license. The original image is attributed to Kenneth Dwain Harrelson and can be downloaded from Wikipedia.
Laplacian Edge Detection
Discrete Laplace operator is often used in image processing e.g. in edge detection and motion estimation applications. The discrete Laplacian is defined as the sum of the second derivatives Laplace operator Coordinate expressions and calculated as sum of differences over the nearest neighbours of the central pixel.
A number of matrix/kernel variations may be applied with results ranging from slight to fairly pronounced. In the following sections of this article we explore two common matrix implementations, 3?3 and 5?5.
Laplacian of Gaussian
The Laplacian of Gaussian (LoG) is a common variation of the Laplacian filter. Laplacian of Gaussian is intended to counter the noise sensitivity of the regular Laplacian filter.
Laplacian of Gaussian attempts to remove image noise by implementing image smoothing by means of a Gaussian blur. In order to optimize performance we can calculate a single matrix representing a Gaussian blur and Laplacian matrix.
Sobel Edge Detection
The Sobel operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Sobel operator is either the corresponding gradient vector or the norm of this vector. The Sobel operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation that it produces is relatively crude, in particular for high frequency variations in the image.
Unlike the Laplacian filters discussed earlier, Sobel filter results differ significantly when comparing colour and grayscale images. The Sobel filter tends to be less sensitive to image noise compared to the Laplacian filter. The detected edge lines are not as finely detailed/granular as the detected edge lines resulting from Laplacian filters.
Prewitt Edge Detection
The Prewitt operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation which it produces is relatively crude, in particular for high frequency variations in the image. The Prewitt operator was developed by Judith M. S. Prewitt.
In simple terms, the operator calculates the gradient of the image intensity at each point, giving the direction of the largest possible increase from light to dark and the rate of change in that direction. The result therefore shows how "abruptly" or "smoothly" the image changes at that point, and therefore how likely it is that that part of the image represents an edge, as well as how that edge is likely to be oriented. In practice, the magnitude (likelihood of an edge) calculation is more reliable and easier to interpret than the direction calculation.
Kirsch Edge Detection
The Kirsch edge detection method is often implemented in the form of Compass edge detection. In the following scenario we only implement two components: Horizontal and Vertical. Resulting images tend to have a high level of brightness.