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    Edge Detection: Exploring Boundaries in Computer Vision
    Edge Detection: Exploring Boundaries in Computer Vision
    Edge Detection: Exploring Boundaries in Computer Vision
    Ebook124 pages1 hour

    Edge Detection: Exploring Boundaries in Computer Vision

    By Fouad Sabry

    ()

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    About this ebook

    What is Edge Detection


    Edge detection is a collection of mathematical techniques that are aimed at recognizing edges, which are defined as curves in a digital image at which the brightness of the image changes abruptly or, more formally, contains discontinuities. The difficulty of discovering discontinuities in one-dimensional signals is referred to as step detection, and the problem of finding signal discontinuities over time is referred to as change detection. Both of these techniques are used to find discontinuities in signals. The method of edge detection is an essential tool in the fields of image processing, machine vision, and computer vision, notably in the areas of feature detection and feature extraction.


    How you will benefit


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


    Chapter 1: Edge detection


    Chapter 2: Digital image processing


    Chapter 3: Sobel operator


    Chapter 4: Roberts cross


    Chapter 5: Canny edge detector


    Chapter 6: Marr-Hildreth algorithm


    Chapter 7: Scale-invariant feature transform


    Chapter 8: Discrete Laplace operator


    Chapter 9: Scale space


    Chapter 10: Prewitt operator


    (II) Answering the public top questions about edge detection.


    (III) Real world examples for the usage of edge detection 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 Edge Detection.

    LanguageEnglish
    PublisherOne Billion Knowledgeable
    Release dateApr 29, 2024
    Edge Detection: Exploring Boundaries in Computer Vision

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      Book preview

      Edge Detection - Fouad Sabry

      Chapter 1: Edge detection

      Edge detection is a collection of mathematical techniques designed to find sharp transitions in brightness in digital images, sometimes known as edges. Finding discontinuities in one-dimensional signals is called step detection, while doing so in time-varying signals is called change detection. In the fields of computer vision, machine vision, and image processing, edge detection plays a crucial role, especially in the processes of feature identification and feature extraction.

      Capturing significant events and shifts in the world's attributes requires the detection of sudden changes in image brightness. Contrast changes in an image can be explained by a few standard assumptions about how images are formed:

      a depth discontinuity, Orientational breaks in surfaces, shifts in the material's atomic structure and

      subtle shifts in scene lighting.

      Applying an edge detector to an image can potentially produce a set of connected curves that represent the edges of objects, the edges of surface marks, and the edges of any breaks in the surface's orientation. In order to preserve the important structural aspects of a picture without over-complicating the processing, an edge detection method can be applied to the image to considerably reduce the quantity of data to be processed by filtering out information that may be deemed less relevant. If the edge detection process is effective, deciphering the image's information content may be much less of a challenge. However, such perfect margins are not always achievable from moderately complex real-world photos.

      Fragmentation, in which the edge curves are not connected, missing edge segments, and false edges not relating to relevant occurrences in the image all hinder the interpretation of edge data derived from non-trivial images.

      The detection of edges is a crucial first step in many types of image analysis, pattern recognition, and computer vision.

      Edges derived from a 2D representation of a 3D scene might be either viewpoint dependent or viewpoint independent, depending on how the 2D representation was created. Edges that are independent of the viewer's perspective often reveal information about the shape and texture of three-dimensional objects. An edge that depends on the viewer's perspective might shift as their position in the image does, reflecting factors like the occlusion of objects.

      The line where two adjacent blocks of color meet is an example of a common edge. As opposed to this, a line (which can be recovered by a ridge detector) may only consist of a few pixels of a distinct color on an otherwise uniform background. One edge may consequently exist on either side of a line.

      Although perfect step edges have been the subject of some research, natural photographs rarely yield truly perfect step edges. Instead, they are typically impacted by at least one of the following::

      focus blur due to depth of field and point spread function limitations.

      penumbral blur due to shadows cast by non-vanishing light sources.

      casting shadows onto a flat surface

      Several scholars have taken the easiest step beyond the ideal step edge model by describing the effects of edge blur using a Gaussian smoothed step edge (an error function).

      Thus, a one-dimensional image f that has exactly one edge placed at x=0 may be modeled as:

      {\displaystyle f(x)={\frac {I_{r}-I_{\ell }}{2}}\left(\operatorname {erf} \left({\frac {x}{{\sqrt {2}}\sigma }}\right)+1\right)+I_{\ell }.}

      Towards the left margin, the intensity is {\displaystyle I_{\ell }=\lim _{x\rightarrow -\infty }f(x)} , and right of the edge it is I_{r}=\lim _{x\rightarrow \infty }f(x) .

      The scale parameter \sigma is called the blur scale of the edge.

      The ideal value for this scale parameter is one that takes into account the image quality so that the image's genuine edges are not lost in the process.

      Consider the following one-dimensional signal as an example of why edge detection is not an easy process. It seems natural to assume that the fourth and fifth pixels in this example should be separated by a line.

      It would be less obvious that there should be an edge in the corresponding region if the intensity difference between the fourth and fifth pixels were smaller and if the intensity differences between the next bordering pixels were larger. In addition, there is a possibility of arguing that this case has multiple advantages.

      Therefore, it is not always easy to define a precise threshold for how much of an intensity difference there must be between two adjacent pixels for us to declare that there should be an edge between these pixels. As a result, unless the scene's objects are quite straightforward and the lighting can be carefully calibrated, edge detection may be a non-trivial task (see for example, the edges extracted from the image with the girl above).

      Many edge detection methods exist, however they can be broken down into either search-based or zero-crossing-based approaches. The search-based methods find edges by first estimating the local orientation of the edge, typically the gradient direction, and then looking for local directional maxima of the edge strength, which is typically a first-order derivative expression like the gradient magnitude. The zero-crossing based approaches often look for the zero-crossings of the Laplacian or the zero-crossings of a non-linear differential expression, both of which are generated from the picture, to locate edges. In most cases, a smoothing stage, often a Gaussian smoothing stage, is implemented as a pre-processing step before the actual edge detection is performed (see also noise reduction).

      Different smoothing filters are used and edge strength is quantified in slightly different ways among the reported edge detection algorithms. Since many edge detection strategies focus on calculating picture gradients, the filters employed to estimate such gradients in the x and y axes might vary widely between approaches.

      A variety of edge detection techniques are discussed in (Ziou and Tabbone 1998); Given the conditions of detection, localisation, and minimizing many responses to a single edge, John Canny explored the mathematical challenge of designing an effective smoothing filter. Under these conditions, he demonstrated, the best filter is a sum of four exponential terms. He also demonstrated that first-order Gaussian derivatives provide a good approximation to this filter. Given the presmoothing filters, edge points are defined as locations where the gradient magnitude attains a local maximum along the gradient axis, a concept that Canny previously presented. Haralick first suggested looking for the zero crossing of the second derivative along the gradient direction. A recent geometric variational interpretation of the operator, connecting it to the Marr-Hildreth (zero crossing of the Laplacian) edge detector, was discovered in fewer than two decades. Ron Kimmel and Alfred Bruckstein made that observation. Edge detectors with better performance than the Canny tend to necessitate either more computational time or more parameters.

      Vladimir A.

      Kovalevsky, and a ramp-dilution filter of his own design.

      In order to detect an edge between two neighboring pixels that are the same brightness but different colors, this technique ignores the luminance of the image and instead relies on the intensities of

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