Line detection: Difference between revisions

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{{Short description|Algorithm}}

In image processing, '''line detection''' is an algorithm that takes a collection of ''n'' [[edge detection|edge points]] and finds all the lines on which these edge points lie.<ref name=":0">{{Cite book|title=Digital image processing and analysis : human and computer vision applications with CVIPtools|last=Umbaugh|first=Scott E.|date=2011|publisher=CRC Press|isbn=9781439802052|edition=2nd|___location=Boca Raton, FL|oclc=491888664}}</ref> The most popular line detectors are the [[Hough transform]] and [[Kernel (image processing)|convolution]]-based techniques.<ref>{{Cite web|url=http://www.mathworks.com/help/images/ref/hough.html|title=Hough transform - MATLAB hough|website=www.mathworks.com|access-date=2018-04-23}}</ref>

== Hough transform ==

The [[Hough transform]]<ref name="Caltech">{{Cite web|url=http://web.ipac.caltech.edu/staff/fmasci/home/astro_refs/HoughTrans_lines_09.pdf|title=Line Detection by Hough transformation}}</ref> can be used to detect lines and the output is a parametric description of the lines in an image, for example ρ = r cos(θ) + c sin(θ).<ref name=":0" /> If there is a line in a row and column based image space, it can be defined ρ, the distance from the origin to the line along a perpendicular to the line, and θ, the angle of the perpendicular projection from the origin to the line measured in degrees clockwise from the positive row axis. Therefore, a line in the image corresponds to a point in the Hough space.<ref>{{cite web|url=http://vision.stanford.edu/teaching/cs231a_autumn1112/lecture/lecture4_edges_lines_cs231a_marked.pdf |title=Finding lines: from detection to model fitting |first=Fei‐FeiFei-Fei |last=Li |date=10 October 2011 |publisher=Stanford Vision Lab}}</ref> The Hough space for lines has therefore these two dimensions θ and ρ, and a line is represented by a single point corresponding to a unique set of these parameters. The Hough transform can then be implemented by choosing a set of values of ρ and θ to use. For each pixel ({{var|r}}, {{var|c}}) in the image, compute r cos(θ) + c sin(θ) for each values of θ, and place the result in the appropriate position in the (ρ, θ) array. At the end, the values of (ρ, θ) with the highest values in the array will correspond to strongest lines in the image

== [[Kernel (image processing)|Convolution]]-based technique ==

In a [[Kernel (image processing)|convolution]]-based technique, the line detector operator consists of a convolution masks tuned to detect the presence of lines of a particular width n and a θ orientation. Here are the four convolution masks to detect horizontal, vertical, oblique (+45 degrees), and oblique (−45 degrees) lines in an image.