Randomized Hough Transform (RHT) in engineering drawing vectorization system

Abstract When the data is processed from the digitized drawThis paper presents how the recently presented Randomized IIough Transform (RHT) method can be used as a part of an engineering drawing vectorization system. The RHT algorithm is capable of recognizing and fitting straight line segments, circles, arcs and conic curve segments, in preprocessed images (eg. after noise removal, void filling). The thinning phase is not necessarily needed. The RHT method is based on the fact that a single parameter space point representing a curve in the image space, can be determined uniquely with a pair, triple, or generally n-tuple of points from the image. These point tuples can be chosen randomly and Hough transform like accumulation is used to detect curve parameters. Preliminary computer experiments using engineering drawings which contain line segments, circles with variable radius and other data, have shown that RIIT has reasonable performance in the line extraction task. It avoids problems which are faced with standard Hough transform (HT) techniques such as low parameter resolution, high storage and time complexities. A typical engineering drawing vectorization system consists of several preprocessing phases, the curve extraction phase and finally the vectorization phase [l, 2, 3,4]. Engineering drawings contain lots of different curves and symbols and due to their purpose must b e very accurately digitized. This leads to large data sets t o process. Almost all algorithms used in different phases have relatively poor time and storage complexities and are often iterative in nature. Especially the line or curve extraction phase is time consuming if done with some of the standard algorithms known within image processing field such as Hough transform. Engineering drawings contain lots of different curves and symbols and due t o their purpose must be very accurately digitized. This leads t o large data sets to process. ing towards the vector representation, the data set is reduced all the time. If the data set can be reduced as early as possible the amount of CPU time at later phases can be greatly reduced. The RHT algorithm can be used either on the raw image, just after the noise removal phase orland after the thinning phase. Due to the nature of the RHT it can extract the clearly detectable curves, eg. dominant curves, very rapidly from the large data set and later, after reducing the data set with thinning, the remaining detectable curve segments can be extracted. The RHT algorithm does not need any windowing techniques which also releases the vectorization phase from extra work. The algorithm can be used simultaneously to the whole area of the drawing or if needed only to some portion of it. Some small drawing components such as arrow heads, letters and small symbols cannot be extracted from the image data with RHT. This is because small objects, for example small line segments are not exactly lines on the square grid and cannot be recognized with H T techniques. In section 2, the RHT algorithm is briefly reviewed and some of its properties are discussed and in section 3 it is shown how the RHT fits in engineering drawing vectorization system. Finally some results are shown and some remarks are represented. The RHT algorithm reviewed The exact algorithm for extracting line segments, and variants of the basic algorithm applicable to extracting higher order curves, have been presented in [5, 6, 71. In the following we review the RHT in the case of straight line segments and refer t o details in our earlier work. The basis of the RHT in the line case lie in the fact that a single parameter space point representing a line in an image can be determined uniquely with a pair of points from the image. These points can be chosen using random sampling from the data set which is formed of all the binary image pixels which are considered 'on' pixels. The parameterized line can be expressed with a simple parametrization a