text: This paper presents a region-partition based attraction field dual representation for line segment maps, and thus poses the problem of line segment detection (LSD) as the region coloring problem. The latter is then addressed by learning deep convolutional neural networks (ConvNets) for accuracy, robustness and efficiency. For a 2D line segment map, our dual representation consists of three components: (i) A region-partition map in which every pixel is assigned to one and only one line segment; (ii) An attraction field map in which every pixel in a partition region is encoded by its 2D projection vector w.r.t. the associated line segment; and (iii) A squeeze module which squashes the attraction field to a line segment map that almost perfectly recovers the input one. By leveraging the duality, we learn ConvNets to compute the attraction field maps for raw in-put images, followed by the squeeze module for LSD, in an end-to-end manner. Our method rigorously addresses several challenges in LSD such as local ambiguity and class imbalance. Our method also harnesses the best practices developed in ConvNets based semantic segmentation methods such as the encoder-decoder architecture and the a-trous convolution. In experiments, our method is tested on the WireFrame dataset and the YorkUrban dataset with state-of-the-art performance obtained. Especially, we advance the performance by 4.5 percents on the WireFrame dataset. Our method is also fast with 6.6 10.4 FPS, outperforming most of existing line segment detectors.
  @cite_26: 
  @cite_8: 
  @cite_9: Abstract The Hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve. The initial work showed how to detect both analytic curves (1,2) and non-analytic curves, (3) but these methods were restricted to binary edge images. This work was generalized to the detection of some analytic curves in grey level images, specifically lines, (4) circles (5) and parabolas. (6) The line detection case is the best known of these and has been ingeniously exploited in several applications. (7,8,9) We show how the boundaries of an arbitrary non-analytic shape can be used to construct a mapping between image space and Hough transform space. Such a mapping can be exploited to detect instances of that particular shape in an image. Furthermore, variations in the shape such as rotations, scale changes or figure ground reversals correspond to straightforward transformations of this mapping. However, the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes. This makes the generalized Hough transform a kind of universal transform which can be used to find arbitrarily complex shapes.
  @cite_21: This paper presents a new approach to the extraction of straight lines in intensity images. Pixels are grouped into line-support regions of similar gradient orientation, and then the structure of the associated intensity surface is used to determine the location and properties of the edge. The resulting regions and extracted edge parameters form a low-level representation of the intensity variations in the image that can be used for a variety of purposes. The algorithm appears to be more effective than previous techniques for two key reasons: 1) the gradient orientation (rather than gradient magnitude) is used as the initial organizing criterion prior to the extraction of straight lines, and 2) the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements.
  @cite_6: Voting in each column around an initial peak is considered to be a random variable.The optimal ? is determined by fitting and minimizing a 2nd-order curve.The optimal ? is determined by fitting and interpolating a sine curve.We calculate voting boundaries instead of searching for non-zero voting cells.The endpoint coordinates are determined by fitting instead of by solving equations. Line segment detection is a fundamental procedure in computer vision, pattern recognition, or image analysis applications. This paper proposes a statistical method based on the Hough transform for line segment detection by considering quantization error, image noise, pixel disturbance, and peak spreading, also taking the choice of the coordinate origin into account.A random variable is defined in each column in a peak region. Statistical means and statistical variances are calculated; the statistical non-zero cells are analyzed and computed. The normal angle is determined by minimizing the function which fits the statistical variances; the normal distance is calculated by interpolating the function which fits the statistical means. Endpoint coordinates of a detected line segment are determined by fitting a sine curve (rather than searching for the first and last non-zero voting cells, and solving equations containing coordinates of such cells).Experimental results on simulated data and real world images validate the performance of the proposed method for line segment detection.
  @cite_34: The Hough transform is a popular technique used in the field of image processing and computer vision. With a Hough transform technique, not only the normal angle and distance of a line but also the line-segment’s length and midpoint (centroid) can be extracted by analysing the voting distribution around a peak in the Hough space. In this paper, a method based on minimum-entropy analysis is proposed to extract the set of parameters of a line segment. In each column around a peak in Hough space, the voting values specify probabilistic distributions. The corresponding entropies and statistical means are computed. The line-segment’s normal angle and length are simultaneously computed by fitting a quadratic polynomial curve to the voting entropies. The line-segment’s midpoint and normal distance are computed by fitting and interpolating a linear curve to the voting means. The proposed method is tested on simulated images for detection accuracy by providing comparative results. Experimental results on real-world images verify the method as well. The proposed method for line-segment detection is both accurate and robust in the presence of quantization error, background noise, or pixel disturbances.
  @cite_0: This paper proposes a novel closed-form solution to complete line-segment extraction. Given a voting angle in image space, the voting distribution is analyzed and two functional relationships are deduced. Regarding the corresponding column in Hough space, voting along the distance axis is considered as being a random variable, and voting values in cells are considered as forming a probability distribution. Statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve. Direction, length, and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves. The midpoint of a line segment is determined based on the fitted linear curve. The method is tested on simulated and real-world images; results show that the proposed closed-form solution is feasible in the presence of quantization errors or image noise. HighlightsWe proposed a method for obtaining the complete set of line-segment parameters.The direction, length and width of a line-segment are extracted simul- taneously in a closed form.We provided a complete theoretical derivation of voting variance with respect to voting angle.The midpoint of a line-segment is determined by the coefficients of the fitted linear curve.Parallel, crossing, and aligned line-segments are discussed by analysing events in image space and Hough space.
  @cite_15: Hough transform (HT) is a well-known technique for extracting lines. However, it is difficult for most existing HT methods to extract line segments robustly from complicated images, mainly because the influence from various objects other than line segments are not taken into account. This paper proposes an accurate and robust evaluator that dynamically removes contributions of backgrounds and analyzes voting patterns around peaks in the accumulator space. In the experiments, four peak detection algorithms are tested against seven images completely automatically. Results show that our method is superior to existing methods in terms of accuracy and robustness while there are no clear differences in execution time. The proposed evaluator detects peaks after the HT and hence it can be applied to any HT that keeps the basic characteristics of the voting process.
  @cite_16: Abstract The Hough transform (HT) is commonly used in machine vision applications for detecting discontinuous patterns in noisy images. The process of using the HT to detect lines in an image involves the computation of the HT for the entire image, accumulating votes in an accumulator array and searching the array for peaks which hold information of potential lines present in the input image. The peaks provide only the length of the normal to the line and the angle that the normal makes with the x -axis. They do not provide any information regarding the length, position or end points of the line segments. However, the butterfly shaped [1] spread of votes in the accumulator array, generated by the process of peak formation, holds vital information like the length and position of the input line segment. Some authors [2] have used this property to develop an algorithm to determine the coordinates of the end points, the length, and the normal parameters of straight lines. A limitation of this method, making it unsuitable for application to a real machine vision problem, is that it would yield erroneous results if applied to an image consisting of anything more than a single line segment. Moreover, the precision of this algorithm is dependent on the sharpness of the peak. In this paper, new techniques which address the above mentioned shortcomings have been described. This paper details the method developed to provide complete line segment description for an image consisting of multiple line segments. In addition, the developed techniques are more robust and accurate than the previously proposed methods as they do not depend upon the sharpness of the peak.
  @cite_12: We propose a linear-time line segment detector that gives accurate results, a controlled number of false detections, and requires no parameter tuning. This algorithm is tested and compared to state-of-the-art algorithms on a wide set of natural images.
summary: In a long range of time, the hand-crafted low-level features (especially for image gradients) are heavily used for line segment detection. These approaches can be divided into edge map based approaches @cite_15 @cite_16 @cite_34 @cite_0 @cite_6 @cite_8 and perception grouping approaches @cite_21 @cite_12 @cite_26 . The edge map based approaches treat the visual features as a discriminated feature for edge map estimation and subsequently applying the Hough transform @cite_9 to globally search line configurations and then cutting them by using thresholds. In contrast to the edge map based approaches, the grouping methods directly use the image gradients as local geometry cues to group pixels into line segment candidates and filter out the false positives @cite_12 @cite_26 .