134 
THE CONJUNCTION ANGLE MEASUREMENT 
USING THE HOUGH TRANSFORM 
Yury V. Visilter, Sergei Yu. Zheltov 
State Research Institute of Aviation Systems 
7 Victorenko St., Moscow 125319, Russia 
Tel. +7-095-1579748, Fax +7-095-1575097, E-mail zhl@fenix.niias.msk.su 
KEY WORDS: Angle Measurement, Image Processing, Hough Transform, Natural Parametrization, Least Squares 
Method. 
ABSTRACT 
This paper presents an image processing application for the welding quality control during the welding pipe 
manufacturing process. The conjunction angle automatic location and measurement were provided by a special two- 
stage modular algorithm. At the first stage, the Hough Transform with natural parametrization is used to detect and 
locate the lines of the angle. At the second stage, after the contour points are selected, the Least Squares Method is 
used to obtain the precise conjunction angle value. 
1. INTRODUCTION 
One of the most popular image processing areas of application is the manufacturing technical control. Usually, it is 
required to find different defects or measure some geometric characteristics using the images of a manufactured 
product. However, sometimes the technology process control is also provided by means of image processing. 
In the welding pipe manufacturing, the automatic control of the welding joint quality is a great problem. The 
important parameter that influences the joint quality is the "conjunction angle”, i.e. the angle between the metal sheet 
edges in the neighborhood of the welding point. The measurement and control of the conjunction angle can only 
occur during welding. So, this is a real-time image processing task. This poses hard computational requirements on 
the automatic angle measurement algorithm. 
Independently from this concrete industrial task, the conjunction angle is a specific geometric object in the gray level 
image, that has to be located and measured with high precision. In first approximation, the appropriate object model 
is the following: 
the object consists of two lines with the angle between them less than 10°; 
each object component (line) has a slope of less than 20° with respect to the horizontal direction; 
the lines cover the whole image width; 
the conjunction point is always out of the image (at the left) because of the image acquisition set-up. 
However, in practice, we must take into account that sometimes these lines are not exactly straight. They can have a 
curvature but not a very high one. 
Here, we present a two-step modular image processing algorithm for the solution of this task. It contains the location 
stage and the measurement stage. At the location stage, the object is detected and its parameters are coarsely 
estimated. This stage includes the Sobel contouring, Hough Transform (HT) and Hough accumulator analysis. The 
special fast HT with natural parametrization is used for computational efficiency and geometric flexibility. The 
analysis of Hough accumulator is realized with the use of its Lateral Histogram (LH). At the measurement stage, the 
Least Squares Method (LSM) is used after the preliminary selection of the line contour points. 
Below we describe this algorithm in detail. 
2. THE DETECTION AND LOCATION STAGE 
The classic HT is a well-known technique for the detection of straight lines in binary images. It transforms the initial 
image space (X , Y) to the parametric space (p , 9), called Hough space, where (p , 9) - normal parameters of a 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995