In general, the Hough transform is a method for finding geometry structures in images. This module uses the Hough transform for straight line detection. Extracted line segments can be used to construct rectangles or generally any other polygons. The transformation itself creates a raster image which is then used for finding line segments. The input of Hough transform is an image which contains only edges, or generally any lines, represented as raster map. It is not necessary but for practical reasons, these edges or lines should be thin e.g., those produced r.thin module or by i.edge module (Canny edge detector).
Lines can be mathematically represented in many ways. For this module, the following representation was chosen. Line is represented in polar coordinates where r is the distance between the line and the origin and Θ is the angle of the vector from the origin to the closest point. The equation follows.
r = x cos(Θ) + y sin(Θ)
When applying Hough transformation for streight lines, the point in the original image leads to a sinusoidal curve in the transformed image. Points in the original image belonging to one line result in sinusoids intersecting in one point in the transformed image (Hough space). The coordinates of this point describe the parameters r, Θ of the line and its value represents the number of points of the line.
In other words, points from the original image with x and y axes are transformed into the Hough space with r and Θ axes. We can say that the resulting (transformed) image is the Hough image. One point (pixel) in the original image is represented by a curve in the Hough image and one point in the Hough image defines a line in the original image by r and Θ parameters. One line in the original image is represented by an intersection of curves. More points (pixels) in one line lead to a higher value in the point of curves' intersection.
For further evaluation, it is necessary to extract local maximum values from the Hough image which correspond to significant lines of the original image. This way we obtain the desired lines in form of r, Θ coordinate pairs. However, we do not obtain the end coordinates of the original line segment (r, Θ are line parameters).
To extract significant lines from Hough image, r.houghtransform module uses the identify and remove Hough transform method described in [Fiala2003]. As mentioned above, it is needed to extract the local maxima representing the lines from the result of the Hough image. This task is compliated by the because presence of noise in the original image. The identify and remove Hough transform method provides not just the line parameters but also the actual coordinates of points as a byproduct. It is based on the idea of sequential removing peaks from the transformation result and eliminating the effect caused by the points of original image belonging to the removed peak.
Lines obtained by identify and remove Hough transform method had to be processed in order to get the actual line segments from the original image. Due to the noise in the original image, certain points can be included in the detected line although they do not belong to it. The subsequent step — extraction of line segments — has to ignore the outlying pixels. However, the main goal is to find separate line segments (pixels belonging to one line segment), so that the line segment is not interrupted. The method needs to tolerate also small gaps because some line segments can actually be interrupted, e.g. by vegetation. On the other hand, these gaps cannot be too frequent because many interruptions would indicate line segments which are probably not part of the feature. The serious line interruption means that there are two segments on one line in the image. As a result, the produced output can be more than one line segment for one detected line.
The Hough transform can be optimized by providing directions of edges [Galambos2000] (possible result of the Canny edge detector or other edge detection algorithm). These angles are used to search only pixels which are in the direction of the particular line. The r.houghtransform module uses exactly this approach.
It must be noted that line segment reconstruction does not have to be considered as a part of Hough transformation. The basic result of Hough transformation is the transformed image (Hough image). Thus, r.houghtransform module provides the posibilty to export also this image.
However, for implementation of the identify and remove Hough transform method, it is necessary and also very advantageous to create data structures instead of an image because of the need for backtracking the lines to the original image. As a result, r.houghtransform module combines Hough transformation and its identify and remove extension, so that the primary result are the line segments.
From the transformed image (Hough image), we can infer certain rules and symmetries, e.g. four peeks at certain positions may denote a rectangle. So possibly, some algorithms can use the Hough image to detect features in different ways than identify and remove Hough transform method. However, these algorithms are not part of r.houghtransform module, just the Hough image is provided.
The main purpose of the module is to detect line segments, so the output is a vector map which contains line segments found in the input raster edge map. The level of details is controlled by several parameters. The continuous straight series of pixels are interpreted as a part of a line when they are not too scattered (thus possible line width or line inaccuracy is limited). The algorithm tolerates small and not too often repeated gaps. As a result, the r.houghtransform module can produce more than one line segment for one detected line when the gap is too long. All the limits mentioned above as well as the minimum length of line segment can also be controlled by the user as well as the approximate number of all resulting lines.
The edge directions (e.g. the optional output of i.edge) can serve as an additional input to r.houghtransform module. The availability of edge directions reduces significantly the time needed for the computation without any negative effect on the result.
The optional output of r.houghtransform module is the image transformed into the Hough space (Hough image), i.e. the original output of the Hough transformation. It can be used for further processing and analysis if desired. The image is outputted as a raster map at coordinates (0,0). One image pixel is represented as one cell but the image does not have any geographical meaning (it is in Hough space). Note that Hough image does not contain all the information which is used to construct line segments (namely, the backtracking information). The color table of this image is set to gray scale with the black representing a zero. Note that the number of curves in this image is significantly reduced when you provide angle map as an optional input. So, if you want to get nicely looking image, you shall not provide angle map to r.houghtransform module.
Available at: r.houghtransform source code (history)
Latest change: Wed Feb 2 21:46:15 2022 in commit: 2e3dcb5eafe36d640aa68585be0192f07ca1eabb
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