Edge Detection
I want to read about edge detection because I was looking into style transfer and the topic of edge detection came up and it is something that I have always been interested in.
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Edge detection includes a variety of mathematical methods that aim at identifying edges, defines as curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as step detection and the problem of finding signal discontinuities 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.
The purpose of detecting sharp changes in image brightness is to capture important events and changes in properties of the world. It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are likely to correspond to:
- discontinuities in depth
- discontinuities in surface orientation
- changes in material properties and
- variations in scene illumination
In the ideal case, the result of applying an edge detector to an image may lead to a set of connected curves that indicate the boundaries of objects, the boundaries of surface markings as well as curves that correspond to discontinuities in surface orientation. Thus, applying an edge detection algorithm to an image may significantly reduce the amount of data to be processed and may therefore filter out information that may be regarded as less relevant, while preserving the important structural properties of an image. Edges extracted from non-trivial images are often hampered by fragmentation, meaning that the edges are not connected, missing edge segments as well as false edges not corresponding to interesting phenomena in the image - thus complicating the subsequent task of interpreting the image data. Edge detection is one of the fundamental steps in image processing, image analysis, image pattern recognition, and computer vision techniques.
Edges extracted from a two-dimensional image of a three-dimensional scene can be classified as either:
- viewpoint dependent edge: may change as the viewpoint changes, and typically reflects the geometry of the scene, such as objects occluding one another
- viewpoint independent edge: reflects inherent properties of the 3D objects, such as surface markings and surface shape
A typical edge might be the border between the block of red color and a block of yellow. In contrast a line (which can be extracted by a ridge detector), can be a small number of pixels of different color on an otherwise unchanging background.
Edges from real world images are normally affected by one of the following effects:
- focal blur caused by a finite depth-of-field and finite spread function
- penumbral blur cause by shadows created by light sources of non-zero radius
- shading at smooth object
Outside of images with simple objects or featuring well-controlled lighting, edge detection is not a trivial task, since it can be difficult to determine what threshold should be used to define an edge between two pixels.
There are many methods for edge detection, but most of them can be grouped into two categories: search-based and zero-crossing based. The search-based methods detect edges by first computing a measure of edge strength, usually a first-order derivative expression such as the gradient magnitude, and then searching for local directional maxima of the gradient magnitude using a computed estimate of the local orientation of the edge, usually the gradient direction. The zero-crossing based methods search for zero crossings in a second-order derivative expression computed from the image in order to find edges, usually the zero-crossings of the Laplacian or the zero-crossings of a non-linear differential expression.
As a pre-processing step to edge detection, a smoothing stage, typically Gaussian smoothing, is almost always applied. The edge detection methods that have been published mainly differ in the types of smoothing filters that are applied and the way the measures of edge strength are computed.
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