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.
['Zezhong Xu', 'Bok-Suk Shin', 'Reinhard Klette']
Closed form line-segment extraction using the Hough transform