Canny Edge Detector: Unveiling the Art of Visual Perception

By Fouad Sabry

What is Canny Edge Detector

This edge detection operator is known as the Canny edge detector, and it employs a multi-stage method in order to identify a large variety of edges that are present in images. In 1986, John F. Canny was the one who had the idea for it. Additionally, Canny developed a computational theory of edge detection, which explains the logic behind the effectiveness of the technique.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Canny edge detector

Chapter 2: Edge detection

Chapter 3: Sobel operator

Chapter 4: Gaussian blur

Chapter 5: Prewitt operator

Chapter 6: Image gradient

Chapter 7: Deriche edge detector

Chapter 8: Compressed sensing

Chapter 9: Histogram of oriented gradients

Chapter 10: Harris affine region detector

(II) Answering the public top questions about canny edge detector.

(III) Real world examples for the usage of canny edge detector in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Canny Edge Detector.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Apr 29, 2024

Book preview

Chapter 1: Canny edge detector

In order to detect a wide variety of edges in images, the Canny edge detector employs a multi-stage algorithm. John F. Canny created it in 1986. In addition, Canny developed a computational theory of edge detection to shed light on the efficacy of the method.

Canny edge detection is a method for drastically reducing the amount of data that needs to be processed by extracting useful structural information from various vision objects. It has found a lot of use in different kinds of computer vision systems. As Canny has discovered, the implementation of edge detection on various vision systems has similar requirements. As a result, a solution for edge detection that meets these needs can be applied broadly. In general, edge detection requires the following::

Low-error edge detection requires that as many of the image's edges as possible be successfully identified.

The operator-detected edge point must precisely locate the edge's geometrical center.

In order to avoid having multiple instances of the same edge being marked, image noise should be minimized.

Calculus of variations, a method for discovering the function that optimizes a specified functional, was the tool Canny used to meet these conditions. Canny's detector's optimal function can be approximated by the first derivative of a Gaussian distribution, which is defined by the sum of four exponential terms.

The Canny edge detection algorithm is one of the most precisely defined edge detection methods, and it offers both good and reliable detection. It quickly rose to prominence as one of the most widely used edge detection algorithms due to its effectiveness in satisfying all three edge detection criteria and its ease of implementation.

Canny edge detection algorithm can be simplified into five distinct stages:

Smooth the image with a Gaussian filter to get rid of the noise.

Determine the image's intensity variations.

To eliminate the false positives from edge detection, a gradient magnitude thresholding or lower bound cut-off suppression can be applied.

To identify possible edges, use a double threshold.

Hysteresis-based edge tracking involves finalizing edge detection by blocking out unconnected, weak edges.

Since image noise greatly impacts the accuracy of any edge detection result,, To avoid erroneous detection, noise must be filtered out.

Image smoothing, Convolution with a Gaussian filter kernel is used to alter an image.

The edge detector will be less affected by the blatant noise in the image after this process is applied.

The equation for a Gaussian filter kernel of size (2k+1)×(2k+1) is given by:

{\displaystyle H_{ij}={\frac {1}{2\pi \sigma ^{2}}}\exp \left(-{\frac {(i-(k+1))^{2}+(j-(k+1))^{2}}{2\sigma ^{2}}}\right);1\leq i,j\leq (2k+1)}

Here is an example of a 5×5 Gaussian filter, used to make the next picture, with \sigma = 1.

Note that the * indicates a convolution.

\mathbf {B} ={\frac {1}{159}}{\begin{bmatrix}2&4&5&4&2\\4&9&12&9&4\\5&12&15&12&5\\4&9&12&9&4\\2&4&5&4&2\end{bmatrix}}*\mathbf {A} .

It's crucial to keep in mind that the detector's efficiency will be impacted by the choice of Gaussian kernel size.

Inversely proportional to size, the less susceptible to noise the detector is, the.

Additionally, The larger the kernel size of the Gaussian filter, the larger the localization error when attempting to detect the edge.

A 5×5 is a good size for most cases, however, this will change depending on the circumstances at hand.

There are many possible orientations that an image's edge can point, Canny's algorithm for horizontal pattern recognition employs a quartet of filters, blurred edges both vertically and diagonally.

Operators for detecting edges (like Roberts), Prewitt, or Sobel) returns a value for the first derivative in the horizontal direction (Gx) and the vertical direction (Gy).

The angle and gradient of an edge can be deduced from this:

\mathbf {G} ={\sqrt {{\mathbf {G} _{x}}^{2}+{\mathbf {G} _{y}}^{2}}}

\mathbf {\Theta } =\operatorname {atan2} \left(\mathbf {G} _{y},\mathbf {G} _{x}\right) , where hypot is the inverse function and atan2 is the arctangent function with two arguments, and G can be calculated as a result.

The direction of the edge is rounded to one of four angles: vertical, horizontal, 30 degrees, and 75 degrees, horizontal, and the two diagonals (0°, 45°, 90°, and 135°).

For each color band, the angle at which an edge crosses will be fixed, for instance, θ in [0°, 22.5°] or [157.5°, 180°] maps to 0°.

Lower bound thresholding, also known as minimum cut-off suppression of gradient magnitudes, is a method of edge thinning.

To pinpoint the spots where the intensity value changes the most dramatically, a lower bound cut-off suppression is used. Each gradient image pixel's algorithm is:

Check the current pixel's edge strength against its edge strength in the up and down gradients.

As an example, if the current pixel is pointing in the y-direction, its value will be maintained if its edge strength is greater than that of all other mask pixels pointing in the same direction. When this doesn't happen, the value is lowered.

The algorithm, in some forms, separates the gradient directions into a handful of discrete categories before applying a 3x3 filter to the intermediate results (that is, the edge strength and gradient directions). If the magnitude of the central pixel's gradient is smaller than the magnitudes of its two neighbors, the central pixel's edge strength is suppressed (set to 0) at that pixel. Case in point, if the rounded gradient angle is 0° (i.e.

point is considered to be on the edge if its gradient magnitude is larger than the magnitudes at pixels in the east and west directions (assuming edge is in the north-south direction), if the rounded gradient angle is 90° (i.e.

the point is considered to be on the edge if the magnitude of its gradient is larger than the magnitudes at pixels in the north and south directions (assuming the edge runs east to west), if the rounded gradient angle is 135° (i.e.

if the point's gradient magnitude is larger than the magnitudes at pixels in the north-west and south-east directions (assuming the edge runs northeast to southwest), then the point will be considered to be on the edge, if the rounded gradient angle is 45° (i.e.

point is considered to be on the edge if its gradient magnitude is larger than the magnitudes at pixels in the north-east and south-west directions (assuming the edge runs northwest to southeast).

Implementations that are closer to the mark, Between two adjacent pixels that lie on opposite ends of the gradient direction, a linear interpolation is used.

For