Detection ellipses by finding lines of symmetry in the images via an hough transform applied to straight lines

doi:10.1016/S0262-8856(01)00049-X

Image and Vision Computing

Volume 19, Issue 12, 1 October 2001, Pages 857-866

https://doi.org/10.1016/S0262-8856(01)00049-X Get rights and content

Abstract

Through the use of a global geometric symmetry, detection ellipses are proposed in this paper. Based on the geometric symmetry, the proposed method first locates candidates of ellipses centers. In the meantime, according to these candidate centers, all feature points in an input image are grouped into several subimages. Then, for each subimage, by using geometric properties again, all ellipses are extracted. The method significantly reduces the time required to evaluate all possible parameters without using edge direction information. Experimental results are given to show the correctness and effectiveness of the proposed method.

Introduction

One of the basic tasks in computer vision is the detection of straight lines, circles, ellipses, etc. from an image. The hough transform (HT) and its variants [2], [4], [6], [7], 10 are methods commonly used for line detection, but applying it to detect ellipses requires a five-dimensional array for the accumulator. Moreover, a great deal of computing time is needed to transform a feature point in an input image to many points in the parameter space. Several modified versions of HT have been proposed. Tsuji and Matsumoto [11] and Sewisy [9] first introduced the decomposition concept by the use of parallel tangents. Ballard [1] presented a method which simplifies the parameterization by deriving the ellipse center from the coordinates and tangent of an edge pixel. Illingworth et al. [12] and Illingworth and Kittler [3] proposed a better center finding process and used adaptive HT to estimate three other parameters. Tam Peter et al. [5] presented an approach which utilizes parallel edge points to deduce parameters. The methods mentioned above utilize gradient information to reduce the dimension of the parameter space, and the problem is broken down into multiple stages. But, estimates of the parameters of ellipses based on local geometric properties often suffer from poor consistency and locating accuracy because of noise and quantization error. To avoid these disadvantages, in this paper, we will present a new method that uses the global geometric symmetry of ellipses to reduce the dimension of the parameter space. In the proposed method, first a global geometric symmetry is used to locate all possible symmetric centers of ellipses in an image, and then all feature points are classified into several subimages according to these center points. Ellipses with different symmetric centers will lie in different subimages. Then the geometric properties are applied again in each subimage to find all possible sets of three parameters (the length of the major axis, the length of the minor axis and orientation) for ellipses. Finally, the accumulative concept of the HT is used to extract all ellipses in the input image. The remainder of this paper is organized as follows: Section 2 describes symmetric edge points about the straight line. Section 3 describes the proposed technique. Section 4 gives computer experiments. Section 5 presents a comparison of methods and Section 6 summary and conclusions.

Section snippets

Symmetric edge points about the straight line

Suppose that the points P(x, y), P₁(x₁, y₁) and P₂(x₂, y₂) lie on an ellipse, we locate the point (x_m, y_m) appearing on straight line l which passes through the two points P₁(x₁, y₁) and P₂(x₂, y₂) with these equations $x_{m} = 12 (x_{1} +x_{2}),$ $y_{m} = 12 (y_{1} +y_{2}).$ The symmetric points (x_s, y_s) of P(x, y) about this line l can be found using , , see Fig. 1. We have $x_{s} =x−2x_{m},$ $y_{s} =y−2y_{m} .$

Proposed technique

The proposed technique consists of two phases: detecting center with symmetric points and extracting ellipses with parameter's estimate.

Computer experiments

Image 1, see Fig. 4(a) (320×240), shows a real image of Egyptian coin. The extracted edge points of image 1 are shown in Fig. 4(b). After the scanning rightward is applied, Fig. 4(b) is transformed into another image ‘A’ shown in Fig. 4(c). Then, the HT is applied to detect vertical straight lines l_vi. There are 25 vertical straight lines, see Fig. 4(d). The symmetric edge points about the detected vertical straight lines in Fig. 4(d) are shown in Fig. 5(e). The vertical straight line l_v with

A comparison of methods

For comparison purposes, we apply the Tsuji's [11] method, Yuen et al.'s [12] method and Yip et al.'s [5] method to system 4(a) and Fig. 10(a). Table 1 summarizes the final result for these methods and proposed method. The CPU times for these methods and proposed method are indicated in Table 2.

Fig. 18 shows the experimental results of Yip et al.'s [5] method for detecting ellipses in an image 1 (Fig. 4(a)). Fig. 18(a) shows the edge-enhanced image of Fig. 4(a) using gradient edge operator with

Summary and conclusions

The method used the symmetric points to detect the center of an ellipse, then uses the geometrical properties of an ellipse to locate the boundary points of ellipse. This method can also be used to detect shapes, such as rectangles and circles. Furthermore, the proposed technique can be detected partially occluded ellipses. Computer experiments show that the proposed technique is effective and robust. Moreover, the gradient information is not used in the proposed technique. Finally, from Table 1

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View full text

Detection ellipses by finding lines of symmetry in the images via an hough transform applied to straight lines

Abstract

Introduction

Section snippets

Symmetric edge points about the straight line

Proposed technique

Computer experiments

A comparison of methods

Summary and conclusions

PR

CVGIP

Probabilistic and non-probabilistic hough transforms: overview and comparisons

IVC

The adaptive hough transform

IEEE Trans. Patt. Anal. Mach. Intell.

Modification of hough transform for circles and ellipses detection using a 2-dimensional array

PR

A new curve detection method

PR