KR102059726B1 - Circular Hough Transform Using Symmetric Pairwise Voting - Google Patents

Abstract

In the present invention, a circular hough transform based on symmetrical pair voting is proposed to robustly detect circular objects in images with noise, illumination, distortion, and obstruction. Experimental results show that the proposed method has a very short execution time and robust detection of circular objects even in the presence of image noise, lighting, distortion, and obstruction.

Description

Circular Hough Transform Using Symmetric Pairwise Voting}

The present invention relates to a circular object detection method using a circular hough transform (CHT), and more particularly, to a circular image in a given image by a circular hough transform based on symmetric pairwise voting (SPV). A method for detecting an object.

Circular object detection is one of the important tasks in computer vision systems. In particular, automatic defect inspection of mechanical parts, printed circuit boards, medicines, coins, sweets, etc., cell detection and tracking in the biological field, cancer detection in the medical field, pupil detection in the biometric field, ball tracking in the entertainment broadcasting field, etc. Circular object detection is an essential process.

A well-known method of detecting a circular object represented by an equation having three parameters represented by a center point and a radius is known as a Hough transform. Hough transform is a method of mapping from binary image space to huff space (parameter space). One-to-many mapping and many-to-one ) Can be classified as an event.

The present invention is characterized by detecting a circular object by using a many-to-one mapping in a method for detecting a circular object in an image.

이 되므로 매우 많은 계산량과 시간이 필요하다. 그리고 원의 중심 점과 반경의 값들이 가지는 범위에 해당되는 매우 큰 3차원의 허프 공간이 필요하다는 문제점이 있다. 이러한 문제를 해결하기 위하여 (2)단계에서 사상에 참여하는 에지 점의 수와 허프 공간의 차원을 감소시키는 방법들이 제안되었다. 콘커(Conker)는 그래디언트 방향을 이용하는 2대1 사상으로 원형 허프 변환을 제안하였다. 2×2 창 내의 두 점에서 그래디언트(Gradient) 크기의 차이인 r_c가 사전에 결정한 값보다 작은 경우에 그 두 점을 선택하여 다음과 같이 사상하였다: 2×2 창 내의 두 점 가운데 첫 번째 점에서의 그래디언트 방향을 θ_i로 두자. 만약

이면The general method of detecting circular objects with many-to-one mapping consists of five steps as follows: (1) The edge operator is used to convert from a given color or monochrome image space to binary image space. (2) Three parameters are calculated from three different edge points in binary image space and accumulated in corresponding cells in the huff space. (3) Step (2) is repeatedly performed for all edge points of the image space. (4) Find a case where a value accumulated in a specific cell of the huff space is larger than a predetermined threshold value. (5) If there is a cell whose cumulative value is greater than the threshold value, the circular object represented by the parameter corresponding to the cell is detected in the image space. This method shows excellent performance even in noise in the image space or partial occlusion of objects. However, if the edge score of binary image space is N, the number of combinations of edge points required in step (2)

This requires a lot of computation and time. In addition, there is a problem in that a very large three-dimensional huff space corresponding to a range having values of a center point and a radius of a circle is required. To solve this problem, in step (2), methods for reducing the number of edge points and the dimension of the hough space that participate in the mapping are proposed. Conker proposed a circular Hough transform with two-to-one mapping using gradient directions. If r _c , the difference in gradient size at two points in the 2 × 2 window, is smaller than a predetermined value, the two points are selected and mapped as follows: The first of two points in the 2 × 2 window Let's set the gradient direction at to θ _i . if

Back side

Given by, otherwise

Was given. Θ _i ≠ -θ _j and x _i ≠ x _j in equation (a), and θ _i + θ _j ≠ ± π and y _i ≠ y _j in equation (d). Huff space uses x-y for finding the center of the circle and x-r for finding the radius. The weight of the huff space was 1-r _c in the x-y space and (1-r _c ) × r (radius) in the x-r space. The disadvantage of this method is that when circular objects with the same center and different radii overlap, the circular objects are not detected, and additional convolution is used for clustering to densely accumulate cumulative weights in the huff space. The use of operators makes detection slower, Cao et al.

개의 두 점을 선택한다. 영상 잡음이나 에지 연산자의 영향으로 발생되는 그래디언트 방향의 오차를 고려한 원의 중심점 영역을 선정한다. 선택된 두 점으로부터 계산되는 원의 중심점이 이 영역에 포함되는 경우에만 사상에 참여시킨다. 허프 공간에서 국부 첨두치를 검출한다. 이진 영상 공간에서 이 첨두치에 해당되는 매개변수 값을 이용하여 원주 상에 존재하는 에지 점을 검출한다. 검출된 에지 점을 집합 S에서 제외시키고 위와 같은 방법을 반복한다. 허프 공간은 원의 중심점과 반경 그리고 누적 발생 빈도를 저장하기 위하여 4차원의 링크드 리스트(Linked-List)를 이용하였다. 이 방법의 단점은 선택되는 두 점들은 중심이 사전에 결정한 영역에 포함되든 아니든 투표에 참여해야 한다. 따라서 계산 복잡도를 줄이기 위해서는 랜덤 샘플링을 채택해야 한다. 그리고 반경이 서로 다른 원들의 중심이 동일한 경우에서도 원들을 검출하려면 하나의 원을 검출할 때와 동일하게 다시 영상의 모든 점들에서 반복적으로 두 점을 선택하고 사상하여야 한다. 따라서 계산의 복잡도는 감소되지 않는다.Goulermas et al. Used circles' equations in parametric form, similar to Conker's method. However, the following method is proposed to reduce the number of edge points mapped. A random set of M (M < N) edge points S is generated at all edge points N at random. And

Pick two points. Select the center point area of the circle considering the error in the gradient direction caused by the influence of image noise or edge operator. Participate in the event only if the center of the circle, calculated from the two selected points, is included in this area. Local peak is detected in the hough space. In binary image space, the edge value existing on the circumference is detected using the parameter value corresponding to this peak value. The detected edge point is excluded from the set S and the above method is repeated. Huff space uses a 4D Linked-List to store the center and radius of the circle and the cumulative frequency of occurrence. The disadvantage of this method is that the two points that are chosen must participate in voting, whether or not the center is in a pre-determined area. Therefore, random sampling should be adopted to reduce the computational complexity. And even in the case where the centers of the circles with different radii are the same, in order to detect the circles, two points must be repeatedly selected and mapped from all the points of the image as in the case of detecting one circle. Therefore, the complexity of the calculation is not reduced.

Pan et al. Used two randomly selected points in the edge image space and their gradient directions. Using a point and its gradient direction, the circle is represented as a single straight line in three-dimensional huff space (x, y, r). If the two selected points exist on the same circumference, the two straight lines corresponding to the two points in the three-dimensional huff space must intersect. The point where this intersection is projected vertically onto the (x, y) plane is the center point of the circle, and the height from the (x, y) plane to the intersection point is the radius. However, even if two points on the same circumference are selected due to image noise or shape deformation, two straight lines corresponding to the two points in the three-dimensional huff space often do not intersect. To solve this problem, calculate the value of the product of the Gaussian distribution based on the minimum distance between the two straight lines and the Gaussian likelihood function for the midpoint of those two points. This is the conditional probability that two given points are two points on the same circumference. The probability values are accumulated in a three-dimensional huff space corresponding to the mean of the midpoint and radius of the two points. Local peaks were detected by the mode-finding algorithm, and circular objects were finally detected in the image space.

The above methods use a random sampling method when selecting two points in a multi-to-one mapping to reduce the computational complexity than O (N ² ). There is no solution to selecting the maximum number of pairs when selecting two points by random sampling, and the performance is degraded when there is a complex background or noisy, according to Kalviainen Kiryati ( Kiryati et al. And the computational complexity is greatly increased to detect or not detect circular objects having the same center with different radii. In addition, even when different circular objects overlap or part of it is blocked by other objects, it cannot be detected efficiently.

(1) HK Yuen, J. Princen, J. Illingworth, and J. Kittler, "Comparative Study of Hough Transform Methods for Circle Finding," Image and Vision Computing, vol. 8, no. 1 , pp. 71-77, 1990.) (V. Leavers, "Survey: Which Hough Transform ?," CVGIP: Image Understanding, vol. 5, pp. 250-264, 1993.) 3 H. Kalviainen, P. Hirvonen, L. Xu, and E. Oja, "Probabilistic and Non-probabilistic Hough Transforms: Overview and Comparisons," Image and Vision Computing, vol. 13, no. 4, pp. 239-252, 1995.) (4) RS Conker, "A Dual P1ane Variation of the Hough Transform for Detecting Non-Concentric Circles of Different Radii," Computer Vision, Graphics, and Image Processing, vol. 43, pp. 115-132 , 1988.) (5) J. Goulermas and P. Liatsis, "Incorporating Gradient Estimations in a Circle-Finding Probabilistic Hough Transform,", Pattern Analysis and Applications, vol. 2, pp. 239-250, 1999.) (6) L. Pan, W.-S. Chu, JM Saragih, and FD la Torre, "Fast and Robust Circular Object Detection with Probabilistic Pairwise Voting (PPV)," IEEE Signal Processing Letters, vol. 18, no. 11, pp. 639-642, 2011.) (7) X. Cao and F. Deravi, "An Efficient Method for Multiple-Circle Detection," 3rd Int. Conf. On Computer Vision, pp. 744-747, 1990. (8) N. Kiryati, H. kalviainen, and S. A1aoutinen, "Randomized or Probabilistic Hough Transform: Unified Performance Evaluation," Pattern Recognition Letters, vol. 21, no. 13-14, pp. 1157-1164, 2000.)

The present invention is a circular huff transform (CHT) based on symmetrical pair voting (SPV) to detect circular objects in a given image. The present invention is a method of robustly detecting a circular object and increasing its detection speed by effectively removing points and noise that do not lie on the boundary of the circular object. The present invention is largely based on two-to-few mapping with symmetric pairwise mapping (SPM), symmetric pairwise weighting (SPW), and local peak-to-peak detection. It consists of original verification. First, symmetrical pairing is to analytically determine two-points selection criteria (TPSC) based on reflection symmetry in order to drastically reduce the number of two points participating in the voting process and to greatly improve its performance. This condition excludes two points on a single straight line in the image, two points on two parallel lines, and two points that satisfy the condition of rotational symmetry on the circumference. On the other hand, only two points that exist on the circumference and satisfy the reflective symmetry conditions on the horizontal or vertical scan line will participate in the mapping.

When the number of edge points in a binary image is set to N, the computational complexity is O (N ² ) in the conventional Hough transform, but O (αN) in the present invention. Where α is the sum of the horizontal size and the vertical size of the image, and α is generally much smaller than N. Therefore, the present invention is drastically reduced in execution time than the conventional method. Second, symmetric pair weighting is the accumulation of huff spaces for efficient detection even when circular objects of different sizes and non-overlapping, partially overlapping, completely overlapping, semicircle, etc. are partially hidden or deformed in a given image. The weight is used by stochastic combination of the reflection symmetry scale and the radius matching scale. In general, the direction of the gradient of the edge points existing on the boundary of the circular object due to noise, illumination, deformation, etc., has an error compared to the ideal case. Therefore, the center and the radius of the circular object calculated from two different points included on the boundary line of the same circular object have different values.

In order to reduce the influence of this error and to have a relatively robust detection performance, the symmetric pair weighting is used to probabilistically combine the reflection symmetry scale and the radius matching scale as cumulative weights of the huff space. Third, in order to quickly and efficiently detect the center and radius of the circle in the huff space, the huff space is transformed into a graylevel image, and the local peak value through segmentation and blob coloring is detected. A method of verifying whether a circle having a corresponding center and radius is located in a binary edge image space and finally verifying whether it is a circle or not.

The traditional method of detecting circular objects in a given color or monochrome image is to use a circular hough transform. In a two-dimensional plane, the circle equation has three parameters: (x ₀ , y _O ), the center point, and radius r.

At least three different points are required to determine these three parameter values. To this end, a given color or monochrome image is converted into a binary edge image. If the number of edge points included in the binary edge image is N, the computational complexity of the traditional circular hough transform is O (N ³ ) or O (N ² ) using a gradient. In general, an image including a circular object includes noise and light effects, or there are various types of objects composed of straight lines or curves in addition to the circular object. In addition, due to the effects of noise, changes in illumination, and roughness in processing objects, circular objects may not have the shape of a perfect circle, and their boundaries may not be clear, or may have the shape of a semicircle from the beginning. Moreover, there are cases where circular objects of different sizes overlap partially or entirely with each other or are partially hidden by other objects than the circular objects. In such cases, there is a need for a method of increasing the detection speed of a circular object and improving the detection performance.

First, the present invention intends to greatly increase the detection speed by greatly reducing the computational complexity O (N ² ) of the conventionally known circular hough transform without using random sampling. To this end, a method of removing points forming objects other than the circular object existing in the image including the circular object in advance is disclosed.

Second, due to noise or roughness, the boundary of the circular object is not clear, or partially obscured by objects other than the circular object, or in the case of a semicircle from the beginning. Even circular objects are to be detected efficiently.

Third, in the case where the circular objects have different radii and do not overlap each other in a given image, the circular objects are efficiently detected even in the case of partially overlapping and completely overlapping. Through this, the detection speed of the circular object is increased and the detection performance is improved.

In order to solve the above problems, in the circular object detection method using the circular hough transform of the present invention; The method calculates the center point of the circle in two-to-minority mapping, which greatly reduces the calculation complexity (α << N) from O (N ² ) to O (αN), and the two point selection condition. A symmetric pair mapping represented by (4) and an expression that is implemented on the horizontal and vertical scan lines of the image,

와

). 과,( here

Wow

). and,

Calculate the radius r _O using the above equation

Comprising the steps obtained by

Equations for robustly detecting circular objects in an image, such as noise, lighting, shape deformation, partial obstruction, etc .;

Symmetric pair weighting W _ij

,

, 그리고

로 표현되는 반사 대칭 척도와 반경 일치 척도를 확률적인 가중치와 결합하여 허프 공간의 가중치를 그래디언트 방향의 오차에 따라서 적응적으로 누적하는 대칭 쌍 가중과 이를 2-대-소수 사상으로 허프 공간에 누적하는 단계를 포함하고,Given here

,

, And

The symmetric pair weighting that adaptively accumulates the weights of the huff space based on the error in the gradient direction by combining the reflection symmetry scale and the radius matching scale represented by Including steps

The method of detecting a local peak in the huff space and verifying not only normal circular objects but also some obscured or deformed circular objects

It includes the step obtained by

It is a stepwise feature of the present invention to include all of the above steps.

In the circular Hough transform method using the symmetric pair voting method of the present invention, a new method for detecting a circular object in a given image is proposed. This method applies reflection symmetry to two-to-decimal mapping analytically to derive two point selection conditions, greatly reducing the number of two points participating in the mapping without random sampling. This greatly reduces the computational complexity O (N ² ) of the Hough transform from O (N ² ) to O (αN) (α << N), which greatly reduces the amount of computation and execution time. Furthermore, two points on each horizontal scan line can participate in the event independently of each other. Recently, multi-core CPUs or GPUs integrating homogeneous processors on a single chip are capable of high-speed parallel processing.

The proposed method enables Fork-Join parallel processing to distribute horizontal scan lines evenly among multiple cores or threads in a given image and process them independently. Using this method, the method proposed in the present invention can further shorten the calculation time.

The gradient direction is different from the actual value depending on the shape deformation of the object, lighting, image noise, and the performance of the edge operator. Due to this effect, the center point and radius of the circle calculated by Huff's error are different from the actual value. To calculate the center point and radius of the circle robustly against these effects,

In the present invention, the reflection symmetry is combined with the probabilistic weights to adaptively accumulate the weights of the huff spaces according to the error in the gradient direction. From the experimental results, the proposed method is very short in execution time and robustly detects circular objects even in the presence of image noise, lighting, and circular shape deformation.

1 is an example of D _ij = 0 , which is the case of two points to be removed from a symmetric pair mapping: FIG. 1A is an explanatory diagram illustrating the case of two points (ψ _ij = 0) on a single straight line.
FIG. 1B is the case where ψ _ij = 0 and ψ _ij = π at two selected points on two parallel lines, respectively, FIG. 1C is two points on the circumference (ψ _ij = π) that meet a straight line passing through the center of the circle. An explanatory diagram illustrating the case.
FIG. 2 is an explanatory diagram showing an example of two points on the circumference satisfying two point selection conditions D _ij ≠ 0 in a symmetric pair mapping.

Along with the accompanying drawings, circular object detection by a circular Hough transform method using a symmetric pair mapping vote (SPV) of the present invention will be described in more detail.

1 is an example of D _ij = 0 , which is two points to be removed from a symmetric pair mapping, and FIG. 1A is an explanatory diagram illustrating a case where two points (ψ _ij = 0) on a single straight line, and FIG. 1B is a parallel two In the case where ψ _ij = 0 and ψ _ij = π at two selected points on a straight line, FIG. 1C is an explanatory diagram for explaining the case where two points on the circumference (ψ _ij = π) meet a straight line passing through the center of the circle Fig. 2 is described together as an explanatory diagram showing an example of two points on the circumference satisfying two point selection conditions D _ij ≠ 0 in symmetric pair mapping.

SPV is largely composed of symmetric pair mapping (SPM) and symmetric pair weighting (SPW).

Symmetric Pair Mapping (SPM)

로 두자. 여기서

이고

인 편미분 연산자이다. 그래디언트의 크기

로 두고, 그래디언트의 방향

로 두자. θ의 범위는 (-π,π]이다.The size of a given image I (x, y) consists of H pixels horizontally and V pixels vertically. Gradient vector at any point (x, y) in the image

Let's leave it. here

ego

Is a partial differential operator. The size of the gradient

, The direction of the gradient

Let's leave it. The range of θ is (−π, π].

In a two-dimensional Cartesian coordinate system, the standard equation for a circle with center (x ₀ , y ₀ ) and radius r ₀ is

Differentiating equation (1)

to be. Where the slope m = dy / dx.

Two points are needed to calculate the center (x ₀ , y ₀ ) of the circular object from equation (2). The gradient size of these two points is g ≠ 0. There is a relationship between the gradient direction θ and m = -cotθ given in equation (2). Two different points are denoted by the subscript i and j for each variable.

Substituting two different points p _i and p _j and the gradient directions calculated from them into Eq. (2), the center of the circle (x _O , y _O ) is given by

Where D _ij = cotθ _j -cotθ _i . For Equation (1) to have a solution, D _ij ≠ 0 must be satisfied. 1 and 2, the following two point selection conditions (TPSC) are derived as follows.

이고

이다. 여기서

이다.Where k = i, j and δ are small positive constants. And

ego

to be. here

to be.

The present invention selects only two points on the horizontal line (α _ij = 0) or on the vertical line (α _ij = π / 2) for ease of multi-core based parallel processing. Using Equation (4) and α _ij = 0, TPSC of the present invention,

Where y _0i = y _i + (tanθ _i (x _j -x _i ) / 2) and y _0j = y _i + (tanθ _j (x _i -x _j ) / 2).

Calculating the radius r ₀ using equation (5)

,

, 그리고 p_0k = (x₀,y_0k)이다. 또한 α_ij = π/2인 경우에도 (x₀,y₀)와 r₀를 식 (5)와 (6)처럼 쉽게 유도된다.Becomes here

,

And p _0k = (x ₀ , y _0k ). In addition, even when α _ij = π / 2, (x ₀ , y ₀ ) and r ₀ are easily derived as in Equations (5) and (6).

Equations (3) and (4) or (4), (5), and (6) are called symmetric pair mapping (SPM).

The values calculated in equations (5) and (6) are accumulated in the huff spaces x-y and x-r using symmetric pair weights (SPW), respectively. The size of each huff space is equal to the size of a given image. In a binary edge image, if the edge points are evenly spread throughout the image area, the computational complexity of the symmetric pair mapping is O (αN). Where α is the sum of the horizontal size H and the vertical size V of the image, and α is generally much smaller than N.

Symmetric Pair Weighting (SPW)

)와 반경 일치 척도(

)를 확률적인 가중치와 결합하여 허프 공간의 가중치를 그래디언트 방향의 오차에 따라서 적응적으로 누적한다. 본 발명인 대칭적 쌍 가중 W_ij는 다음과 같이 주어진다.The gradient direction used in the 2-to-1 mapping is different from the actual value depending on the shape deformation of the object, lighting, image noise, and edge operator performance. Due to this effect, the center point and radius of the circle calculated by Huff's error are different from the actual value. In order to calculate the center point and the radius of the circle robustly against this effect, the present invention has a reflection symmetry scale (

) And radius match scale (

) Is combined with the probabilistic weights to adaptively accumulate the weights of the huff space according to the gradient direction error. The symmetric pair weighting W _ij of the present invention is given as follows.

,

, 그리고

이다. 수평선상에 존재하는 두 점들만 고려하는 경우에는

이다. 그리고 σ_c는 w_ij의 감도를 결정한다.here

,

, And

to be. If you consider only two points on the horizon

to be. And σ _c determines the sensitivity of w _ij .

와

인 경우이다. 이는 원주상의 두 점이 선택된 경우이다. 최소값은 원주상의 두 점이 선택되지 않는 경우가 된다. 일반적으로 랜덤 샘플링을 이용하는 다-대-일 사상에 기반한 허프 변환은 잡음이 거의 없는 고품질의 영상에 대해서 잘 동작하고 랜덤 샘플링을 이용하는 일-대-다 사상은 잡음이 강하고 저품질의 영상에 대해서 비교적 잘 동작한다고 알려져 있다.If w _ij shown in equation (7) has the maximum value in the given σ _c and r _o

Wow

If This is the case when two points on the circumference are selected. The minimum value is when two points on the circumference are not selected. In general, Hough transform based on many-to-one mapping using random sampling works well for high quality images with little noise, and one-to-many mapping using random sampling is relatively good for low noise and low quality images. It is known to work.

The present invention proposes a two-to-few mapping that uses TPSC without random sampling to take advantage of many-to-one and one-to-many mapping. In the present invention, the SPV combining the SPM and the SPW accumulates in all 3x3 cells including the corresponding cell in each Huff space corresponding to the center and radius calculated from Equations (3) and (4). As a result, the present invention confirmed that robust circular object detection is achieved, such as shape deformation, illumination, and image noise.

[Local peak detection and circular object verification]

In the huff spaces x-y and x-r, the local peaks are the final values corresponding to the center and radius, respectively. In order to detect a local peak in the huff space and finally detect a circular object in the image, the present invention performs the following process.

(1) Huff space is converted into a graylevel image.

(2) Perform segmentation.

(3) Blob Coloring

(4) Find the highest value in the detected blob area.

(5) Location of the circle in the binary edge image with the center and radius corresponding to the highest value.

(6) reliability at the located circle

이 되도록 한다. 그리고

는 이상적인 경우에 반경 r₀를 가지는 원주상의 에지 점들의 총수이다.Calculate Where N _d is the total number of edge points lying on the circumference in the binary edge image. n _r is a parameter that adjusts to detect partially hidden or deformed circles. This parameter is given by N _d

To be And

Is the total number of circumferential edge points with radius r ₀ in the ideal case.

Circular objects are finally detected in a given image using the symmetric pair mapping, symmetric pair weighting, and local peak-to-peak detection and circular object verification.

Claims (4)

A circular object detection method using a circular hough transform;
The method calculates the center point of the circle in two-to-minority mapping, which greatly reduces the calculation complexity (α << N) from O (N ² ) to O (αN), and the two point selection condition. A symmetric pair mapping represented by (4) and an expression that is implemented on horizontal and vertical scan lines of an image,

( here

Wow

). and,
Using the above formula, calculate the radius r ₀

Obtained by;
Equations for robustly detecting circular objects in an image, such as noise, lighting, shape deformation, partial obstruction, etc .;
Symmetric pair weights w _ij

Given here

,

, And

The symmetric pair weighting that adaptively accumulates the weights of the huff space based on the error in the gradient direction by combining the reflection symmetry scale and the radius matching scale represented by step;
The method of detecting local peaks in the huff space and verifying not only normal circular objects but also some obscured or deformed circular objects.

Obtained by;
Circular object detection method using a circular hough transform containing at least one delete delete A circular object detection method using a circular hough transform;
The method calculates the center point of the circle in two-to-minority mapping, which greatly reduces the calculation complexity (α << N) from O (N ² ) to O (αN), and the two point selection condition. A symmetric pair mapping represented by (4) and an expression that is implemented on horizontal and vertical scan lines of an image,

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Using the above formula, calculate the radius r ₀

Obtained by;
Equations for robustly detecting circular objects in an image, such as noise, lighting, shape deformation, partial obstruction, etc .;
Symmetric pair weights w _ij

Given here

,

, And

The symmetric pair weighting that adaptively accumulates the weights of the huff space based on the error in the gradient direction by combining the reflection symmetry scale and the radius matching scale represented by And a method of detecting a local peak in the huff space and a method of verifying not only a normal circular object but also some obscured or deformed circular objects.

Circular Hough transform method using a symmetric pair voting that combines all the steps obtained by the method and a method for detecting a circular object in the image using the same.

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