Title: Efficient and High-quality Ellipse Detection via Implicitly Excluding Most Useless Arc Groups and Enhancing Arc detection
Venue: NeurIPS 2025
Accepted: no
Keywords: ellipse detection

grid

edge extraction

edge-link
Abstract: Detecting ellipses from images is an fundamental problem in computer vision and pattern recognition, and plays an important role in many applications. This paper presents a new edge-link method for efficient and high-quality ellipse detection, where the two steps of edge-link methods are improved by our two presented novel measures respectively. The first is to adaptively adjust the search direction in linking edge pixels to generate arcs as consistently as possible. The second is to develop a novel measure for grouping arcs to check whether these arcs are from a same ellipse, which is by employing a grid to manage the arcs and designing a traversal path to visit grid cells continuously, through which most useless arc groups can be implicitly excluded for efficiency. This is different from existing methods that need explicitly check all possible arc groups. Based on these measures, we design an algorithm to detect ellipses as many as possible. Experimental results show that we can significantly improve both the accuracy and efficiency of ellipse detection, much superior to existing methods. Thus, we can significantly improve many applications.

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Abstract

Detecting ellipses from images is an fundamental problem in computer vision and pattern recognition, and plays an important role in many applications. This paper presents a new edge-link method for efficient and high-quality ellipse detection, where the two steps of edge-link methods are improved by our two presented novel measures respectively. The first is to adaptively adjust the search direction in linking edge pixels to generate arcs as consistently as possible. The second is to develop a novel measure for grouping arcs to check whether these arcs are from a same ellipse, which is by employing a grid to manage the arcs and designing a traversal path to visit grid cells continuously, through which most useless arc groups can be implicitly excluded for efficiency. This is different from existing methods that need explicitly check all possible arc groups. Based on these measures, we design an algorithm to detect ellipses as many as possible. Experimental results show that we can significantly improve both the accuracy and efficiency of ellipse detection, much superior to existing methods. Thus, we can significantly improve many applications.

1 Introduction

Ellipse detection is an important task in image processing, and required in many applications such as industrial inspection [1], medical image analysis [2], autonomous driving [3], and robot vision [4]. With regard to this, the edge-link methods [5, 6, 7, 8, 9, 10, 11] are prominent due to their efficiency and effectiveness, to be discussed in Sec. 2. These methods work by first extracting arcs with continuous edge pixels and then checking arcs in groups whether they are co-elliptical, called ellipse checks . The arcs from a same ellipse are called co-elliptical ones, and they are used to generate an ellipse.

Arc groups are always in a large number, so that arc grouping for ellipse checks dominates the efficiency. Considering that most arc groups are composed of arcs from different ellipses, which cannot be used to generate ellipses, called useless groups , many methods have been proposed to employ cheap calculations to exclude useless groups as soon as possible for efficiency, such as constraining the search region for arc grouping [5], leveraging convex hulls to group [9], building an adjacent matrix to represent the grouping relationships between arcs [8], and excluding many useless groups by constraints from characteristic mapping [12] or the Candy's theorem [13]. Even so, any arc group should be checked once and this still wastes much time on useless groups.

In this paper, we address the challenge of implicitly excluding most useless groups for efficiency. It is by using a grid to manage arcs and then visiting grid cells orderly from the center outward. For a visited grid cell, each arc contained in the grid cell tries to find other arcs for arc grouping in its

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constrained search region [5]. This corresponds to have grid cells paired for arc grouping. As the 35 constrained search region of an arc does not cover all grid cells in general, and a visited grid would 36 not be processed again after it is visited, this would have many grid cells not paired for arc grouping, 37 meaning their related useless arc groups are implicitly excluded. This will be discussed in detail in 38 Sec. 3. 39

We also present a measure to generate arcs as consistently as possible, by which ellipses can be more 40 effectively detected. This is by adaptively adjusting the search direction to link continuous edge 41 pixels to generate contours, to be discussed in Sec. 4.1. 42

Based on our two novel measures, we develop an algorithm to detect ellipses as many as possible, 43

where all formed arc groups are further checked by existing methods [9, 12] to exclude many more 44 useless groups and finally co-elliptical arc groups are used to generate their corresponding ellipses 45 with existing methods. As a result, we can detect many more ellipses and in a higher efficiency 46 and a higher quality than existing methods, as illustrated in Fig. 1 and demonstrated in Sec. 5. 47 Benefited from our improvements, many applications can be significantly promoted, as illustrated in 48 Appendix C. 49

2 Related work 50

Ellipse detection methods can be coarsely classified into three categories: Hough transform based 51 methods, edge-link based methods, and learning methods. Hough transform based methods [16, 17, 52 18, 19] take the ellipse detection task as a peak-finding process in a parametric voting space and use 53 the Hough transform on pixels for a solution. Unfortunately, they are expensive and prone to incur 54 incorrect results due to the complicated backgrounds and the lack of effective verification [20]. 55

Recently, some learning methods [21, 22, 23, 24, 15, 25] have been proposed for ellipse detection. 56 However, their potentials are limited by the difficulty of collecting high quality data for training, and 57 they are always inefficient as they need learn a lot of features for a complex model, as shown in Fig. 1 58 and Table 3 for the result of [15]. 59

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Till now, edge-link based methods are prominent for ellipse detection [5, 6, 7, 8, 9, 10, 26, 11]. They link discrete edge pixels into arcs for ellipse detection, where local continuity information of contours can be well exploited to suppress interference from outliers and noise, and therefore increasing the detection accuracy. In the following, we have edge-link methods discussed briefly by their three sub-tasks, arc generation, arc grouping and ellipse checks.

For arc generation, Kim et al. [27] extract short straight line segments to approximate arcs, Prasad et 65 al. [5] use curvature and convexity to extract smooth elliptic arcs, and there are two methods proposed 66 for better corner detection to promote arc extraction, the adaptive Ramer Douglas Peucker (RDP) 67 algorithm [28, 29] and a curvature-based method [30]. In implementing our method, we use the 68 adaptive RDP algorithm [28] to divide contours into arcs because it need not frequent parameter 69 adjustments. Based on the method of [8], Wang et al. [31] proposed a contrast-guided measure to 70 enhance the extraction of arcs, but the improvement in detection capability is limited. 71

For arc grouping, some constraints are proposed to quickly exclude useless groups using simple 72 computation, including arc-aware search regions [5], quadrant constraints [6], projection invariant 73

pruning [7], arc-support regions [14], characteristic mapping [12], the Candy's theorem [13] and 74 coherent chord computation [11]. As useless groups always take a very large portion of all possible 75 groups, these measures still take much time and prevent efficiency promotion. There are also some 76 data structures studied for improving ellipse detection by collecting the arcs that are very possibly 77 co-elliptical, including undirected graphs [9] and disjoint-set forests [10]. Even so, they need to 78 enumerate possible groups, and this still need check a large amount of useless groups. 79

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To check whether an ellipse is valid, a commonly used criterion is the ratio of inliers, defined as the proportion of arc points that fit the ellipse well [6, 7, 10]. When the ratio is high, it means the estimated ellipse is consistent with arcs. Other criteria include gradient consistency [10] and the completeness of ellipse [5, 7], which can filter out bad ellipses, but may prevent detection of imperfect ellipses in images. In our implementation, we use the measure of [9] for valid check of ellipses.

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Different from existing edge-link methods, we present an arc grouping method to implicitly exclude most useless groups, where arc-aware search regions [5] are used for grouping arcs that are possibly co-elliptical. To our knowledge, this is the first method that can implicitly exclude useless arc groups. Our method is orthogonal to existing methods and so easy to be integrated with them for improving ellipse detection. For example, the useless groups that are not implicitly excluded by our method can be further quickly excluded by characteristic mapping constrains [12]. As for arc generation, we will mainly use the measures of [9] but replace its strategy for contour extraction, where an adaptive strategy is developed to extract contours as smooth as possible for generating arcs consistently.

3 Grid-based arc grouping

Our measure for arc grouping is by using a grid to manage the arcs and then visiting grid cells by a traversing path, through which arcs are grouped for ellipse detection. In the following, we first introduce the steps of our measure and then discuss their implementation and the effectiveness on implicitly excluding useless groups. With an ablation study by four data sets, it is known that we can greatly reduce the arc groups to be checked in comparison with only using arc-search regions [5] for arc grouping, as listed in Table 1. This shows we can implicitly exclude most useless arc groups.

The steps of our measure are as follows. Firstly, a grid is generated by the bounding box for all extracted arcs. Then, arcs are recorded in the grid cells that contain or intersect with them. Finally, a traversing path is designed to visit cells sequentially from the center outwards gradually, by which each arc in the currently visited cell is taken as an active one to search for possible co-elliptical arcs (called inactive arcs ) in its improved arc-search region (to be discussed in Sec. 3.2) for arc grouping. As illustrated in Fig. 2, the active arc R 3 finds its inactive arc R 4 in its arc-search region in red to form a group. In this way, all possible co-elliptical arcs can be grouped. In summary, the algorithm for our arc grouping method is given in Alg. 1.

3.1 Grid resolutions

Clearly, the grid resolutions have much influence on the detection efficiency. A lower grid resolution means fewer cells, so that a cell would be larger to contain more arcs and prevent efficiency. In contrast, a higher grid resolution will lead to smaller cells containing fewer arcs, but this will generate more cells, also preventing efficiency. As an ideal expectation, if the arcs are evenly distributed in the grid cells for each grid cell to contain only one arc, the number of grid cells would not be large and a grid cell contains the fewest arcs, which would have ellipse detection in a high efficiency.

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Thus, we determine the grid resolution, NC x and NC y along the two axes, by Eq. 1, 116

where N arcs is the number of arcs, and r a = image_height image_width is the aspect ratio of the image.

With an investigation by many tests, such a grid resolution can always obtain good results and they are used in our implementation. Of course, arcs are generally in various lengths and distributed unevenly, which may influence the grid resolution in achieving high efficiency. As a future issue, we will further study these influences to optimize the grid resolution for high efficiency.

3.2 Improved arc-search regions

As discussed by Prasad et al. [5], an arc can only find its co-elliptical inactive arcs in a region, called an arc-search region . The arc-search region of an arc is bounded by the line connecting the two endpoints of the arc and two ray lines that are from its two endpoints and tangent to the arc, as illustrated by the red region for R 3 in Fig. 2. As we take the arcs of the visited grid cells each as active ones to find all their respective co-elliptical arcs, the visited grid cells would not be investigated in the following checks. Thus, our arc-search region for an arc should exclude the grid cells that have been visited. As illustrated in Fig. 2, the arc-search region of R 1 in the cell ⑤ should exclude the grid cells ① , ② , ③ and ④ , as the cell ⑤ containing R 1 is visited after these cells. Clearly, this reduces the arc-search region of R 1 and implicitly exclude the arc group of R 1 and R 3 . Such a reduced arc-search is called an improved arc-search region , as illustrated by the yellow region for R 1 , which excludes the light green cells ① , ② , ③ and ④ .

3.3 Traversing paths

For implicitly excluding useless groups as many as possible, we design a traversing path to visit grid cells from center outwards gradually. This is based on the following considerations:

In general, active arcs nearer to the center of the grid often have smaller arc-search regions than those farther away from the center, e.g., the arc-search region of R 3 is smaller than that of R 1 in Fig. 2. Thus, first checking the arcs nearer the center of the grid can more effectively avoid checking useless groups, as a smaller arc-search region is less possible to have useless groups. Of course, it is also possible for an arc near the boundary of the grid to have a smaller arc-search region when it is towards the outside. However, such cases seldom occur, and so would not interfere with our efficiency.

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With such a traversing path, the grid cells far away from the center would have their arcsearch regions improved, as discussed in Sec. 3.2. This is helpful for efficiency promotion. Otherwise, when the grid cells far away from the center are visited first, their arc-search region would be less improved, causing many useless groups generated. As illustrated in Fig. 2, if the grid cell containing R 1 is visited first, its arc-search region would be larger to include the light green cells, and so generating more useless groups.

As an investigation, we tested other traversing paths like the path from the outside inward and a zig-zag path, as illustrated in Fig. 3. The results show that using our path can generate much fewer arc groups than using the other paths. This shows the advantages of our designed traversing path for implicit exclusion of useless groups.

4 Improved ellipse detection

With our arc grouping measure, we present a new edge-link method for ellipses detection, where we mainly use the corresponding measures of [9] for arc generation and ellipse checks, and then take a new strategy for extracting ellipses as many as possible. The pipeline of our method is still by the steps for edge-link methods, extracting arcs, grouping arcs for ellipse checks and generating ellipses for co-elliptical arcs, as illustrated in Appendix A. For a complete introduction of our method for ellipse detection, we will first introduce the corresponding measures of [9] for arc generation, arc grouping and ellipse checks, and then discuss our improvements and our final algorithm for ellipse detection. Our improvements are as follows:

In arc extraction, we present a novel measure to improve contour extraction for generating arcs more consistently than using the corresponding measure of [9].

In arc grouping, our developed method in Sec. 3 is used, by which most useless groups can be implicitly excluded. Then, the collected arc groups could be further filtered by the characteristic mapping constraints [12] to more effectively obtain useful arc groups for ellipse checks.

In ellipse generation, we take another strategy that first generates ellipse candidates as many as possible and then removes the redundant ones. Thus, ellipses can be detected many more than existing methods.

4.1 Arc extraction

The arc extraction measure of [9] includes the following five steps. 173

Edge detection. The Canny's algorithm [32] is used to detect the edge pixels. For obtaining high 174 quality edges, Gaussian filtering with small kernels is applied to smooth out noise and bilateral 175 filtering is applied to smooth out textures. 176

Contour extraction. Continuous edge pixels are collected to obtain contour curves. Here, we 177 develop an adaptive measure to extract contours as smoothly as possible for generating arcs as 178 consistently as possible for helping ellipse detection, to be discussed later in this section. 179

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Contour segmentation. A contour may be composed of arcs from different ellipses. Thus, a contour should be segmented for arc extraction, which is by finding corner points, whose curvatures change abruptly in comparison with their respective neighboring points. More details are given in Appendix A.

Arc determination. The very short or very flat contour segments cannot be arcs of ellipses. They should be removed, and so the remained contour segments are the extracted arcs. Shen et al. [9] treat an arc as valid only when its length L satisfies L > L arc , and the aspect ratio B < B arc , where L arc and B arc are thresholds. Aspect ratio B = box _ width box _ height is used to describe the degree of flatness of the arc, where box _ width and box _ height are the longer side and the shorter side of the rotated rectangle with the minimum area bounding the arc.

In the above steps of [9] for arc extraction, there are some parameters. For the thresholds of these parameters to achieve good results, we set them by investigating the tested data sets, as done in existing methods [5, 7, 8, 30]. In our tests, we set θ arc = 49 ◦ , L arc = 52 and B arc = 29 .

With the above steps for arc extraction, we can obtain many more arcs for detecting ellipses as many as possible, especially those overlapped ones. This is superior to many methods like the learning based method [25], which mainly extracts the arcs on the outer contours of objects and so would miss many overlapped ellipses, as shown in Appendix B.

4.1.1 Improvement on contour extraction.

Contour extraction is to connect the edge pixels by the neighboring relationships between them to generate edges. Shen et al. [9] extracts an contour by randomly selecting an unused edge pixel as a seed to search for neighboring edge pixels iteratively until the contour cannot be extended, where the depth first search is used. After all edge pixels are used, it means all contours are extracted. As illustrated in Fig. 4(a), starting from the left most yellow pixel, a contour is generated. In the depth first search of [9], the search order is fixed as shown by the dashed lines with numbers in Fig. 4(a). With such a search order, from pixel P , the contour will be next connected to pixel Q , not to pixel S , as illustrated in Fig. 4(b). Thus, pixel P will be taken as a corner point in contour segmentation to generate shorter arcs.

For generating arcs as long as possible for improving ellipse detection, we change the search order for extending a contour as smooth as possible, which is by the angle difference from the search direction of the last extension. The neighboring pixels with the smaller angel difference will be searched more preferentially. As illustrated in Fig. 4(c), according to the last search direction from pixel R to P, our search order for extending the contour from P is determined by the changed ordered numbers. Thus, the contour is extended from P to S.

The measure of [9] for contour generation is by starting from a seed edge pixel with a depth first search. When the seed edge pixel is at the middle of an arc, this is unsuitable for extracting the arc completely. Considering this, we have two directions searched from each seed edge pixel for generating arcs as long as possible. For example, if pixel R is selected as a seed, the contour can be generated by search along two directions from R, as shown in Fig. 4(c).

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4.2 Arc grouping with valid checks

With the obtained arcs, we first use our method in Sec. 3 to collect arc groups. Afterwards, for the collected arc groups, we could use the characteristic mapping constrains [12] for a further exclusion of useless groups. At last, the remained arc groups are used for ellipse generation.

For a collected arc group, its arcs are used for generating an ellipse, where we mainly use the corresponding measures of [9]. At first, an ellipse is estimated for them by the Least-Squares fitting method. Then, it is checked whether the estimated ellipse is valid. The valid estimated ellipses are our detected ellipses.

For valid checks, it is by the measure of [9] using the ratios of inliers, which are computed by the following equation:

where g ∗ is the set of arcs in a group, p is an arc point, e is the estimated ellipse, dist ( p, e ) is the algebraic distance from point p to the estimated ellipse e , and Ind ( . ) refers to the indicator function.

When S ( e ) has a high value, it means the estimated ellipse is valid. For this, a threshold S arc is used for such a determination. By the suggestion of Shen et al. [9], we set S arc = 0 . 73 in our tests, and always obtain good results.

4.3 Our algorithm for ellipse detection

With the measures discussed in the above subsections, we design an algorithm to detect ellipses as many as possible. Here, we generate candidates as many as possible and then remove the redundant ones, as discussed in the following.

Generating ellipse candidates. Our ellipse candidate generation is by the following steps. Firstly, an ellipse is estimated for each arc, as an arc may form an ellipse itself. Here, the estimated ellipse with its S ( e ) less than S arc , is discarded. Secondly, an ellipse is estimated for any a pair of arcs, where one arc is active and the other is one of its inactive arcs. It is by investigating the possibly estimated ellipses for pairs ( arc i,active , arc j,inactive ) , j = 1 , 2 , 3 , · · · , where arc j,inactive are the inactive arcs in the improved arc-search region of the active arc arc i,active , and remaining the ones whose S ( e ) value is greater than S arc . In this way, if many arcs are co-elliptical, any two of them are used for ellipse estimation respectively. Clearly, this may cause redundant ellipses, but would not miss ellipses.

Removing redundant ellipses. We use two measures to remove redundant ellipses. Firstly, we guarantee that an arc can be used only once for ellipse detection. We queue up ellipse candidates by their S ( e ) values from the highest to the lowest, and iteratively select the ellipse with the highest S ( e ) values from the candidates which contains only unused arcs. Secondly, we merge similar ellipse candidates with the corresponding measure by [9], which computes a weighted L 2 difference between the ellipse parameters.

5 Results and discussion

To verify the effectiveness and efficiency of our method, we conducted extensive experimental studies and collected results on a personal computer installed with an Intel(R) Core i7-8700 CPU@3.2GHz and 48GB RAM, where we have a comparison with the state-of-the-art methods [5, 6, 7, 14, 8, 9, 10, 15, 12, 31]. Their source codes can be obtained from the internet except for the code of [31]. For the method of [31], we implemented it by ourselves. Prasad et al. [5] have their codes implemented in Matlab, Lu et al. [14] implemented in Matlab and C++, Wang et al. [15] implemented in Python, and the other methods implemented in C++. All methods run on the CPU except for [15], which runs on GPU GTX1080Ti.

Datasets. In our tests, we used four synthetic datasets for testing our effectiveness on ellipse detection and four real-world datasets for comparing with existing methods. The used synthetic datasets

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include the Occlusion/Overlapping dataset [5] and Concentric/Concurrent dataset [8]. The tested four real-world datasets are Prasad/Prasad+ dataset [5], and the Random/Smartphone dataset [6].

Evaluation metrics. Here, we use Precision, Recall and F-measure to evaluate the performance of an ellipse detector over a specific dataset.IoU is used to evaluate the similarity between a detected ellipse with an ellipse of ground truth.

5.1 Accuracy

We made tests on synthetic and real-world datasets, as discussed below. We also made tests on generated ellipses with various shapes, orientations and sizes in the supplementary materials, showing our superiority over existing methods.

Tests on the synthetic datasets. The results of the compared methods for the four synthetic datasets are shown in Table 2. Clearly, our method can always achieve the best results except the one for Precision metric on the Overlapping dataset, where Jiang et al. [10] has the best Precision result. This is because it is very rigorous in selecting ellipse candidates and reduces the ellipses to be generated in the cases when there are many overlapped ellipses, by which its Precision value is high. However, it would miss many true ellipses so that its Recall value is low. Some visualization are provided in the appendices.

Tests on the real-world datasets. The statistics on the real-world datasets are given in Table 3, where we use IoU = 0 . 8 as the threshold to validate ellipses, as suggested by [7]. For the details about comparison on detection performance with various setting of IoU, please see Appendix B in the supplementary materials. From the statistics in Table 3, it is known that our method always achieve the highest F-measure values than existing methods except for that Lu et al. [14] achieves better F-measure values than ours on Prasad and Prasad+. This is because the images of these two datasets are of low pixel resolutions, so that our arc generation with Gaussian filtering may have some elliptical arcs missed. When the images are of high pixel resolutions, as those in the datasets Random

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and Smartphone, our method can obtain better results than Lu's method. For further verification, we made tests with relaxing constraints on arc generation (referred to as *Ours in Table 3), where we have better F-measure values than [14] on Prasad and Prasad+ datasets. Overall, we can always obtain many more accurate ellipses while producing fewer wrong ellipses than existing methods, as illustrated in Fig. 1 and Fig. 5.

5.2 Efficiency

We made tests on the four real-world datasets to check our efficiency on ellipse detection. By the statistic data in Table 3, it is known that ours can be faster than existing methods except in handling the Prasad dataset, in which each image has very few ellipses, leading the generated matrices for the method of [8] to detect ellipses very small, so that [8] is the fastest in handling this dataset. This also makes [12] faster than ours. As for the other cases that have many ellipses in the image, ours is faster than them, especially ours+CM, which is by combining ours with the characteristics mapping constraints [12]. This shows our higher performance than existing methods.

6 Conclusions

Edge-link methods are prominent for ellipse detection. In this paper, we presented two novel measures to improve edge-linking methods, one for generating arcs more consistently and the other for saving a large amount of computation by implicitly excluding most useless arc groups. Meanwhile, we develop an algorithm to detect ellipses as many as possible by checking whether an arc or any a group of arcs can form an ellipse. Experimental results show that we can more efficiently detect ellipses, while obtaining many more ellipses and in a higher quality, than existing methods.

Limitation. Our method is dependent on arc extraction. When arcs are sufficiently detected, their corresponding ellipses can be almost detected by our method. Though we improve arc extraction, some arcs may be still missed to prevent ellipse detection, especially in handling the overlapped ellipses. As a future issue, arc extraction would be seriously investigated.

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A Some details for implementation of our method

Pipeline of ellipse detection. The pipeline of our method for ellipse detection follows the standard workflow of all edge-linking methods, as illustrated in Fig. 6. For an input image, we first extract the elliptic arcs, which involves edge detection, contour extraction and splitting. Then, we group the arcs that are likely from a same ellipse, where we use our grid-base method to implicitly eliminate most useless groups. Finally, we generate a candidate ellipse for each group, and apply further checks to remove redundant ones.

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Contour segmentation. After extraction of curves, we subdivide the curves into elliptic arcs using corner points. The corner point can have an abrupt change in the magnitude of curvature, or be related to direction bending. Here, we provide an explicit example of this procedure. As shown in Fig. 7, we calculate the angle θ i between the connected straight lines, and when θ i is greater than a threshold θ arc or its sign is different from θ i -1 , we mark the point as a corner point. We have θ arc = 46 ◦ in our experiments as suggested by [9].

Removing redundant ellipses. For the evaluation of redundant ellipses, we use the measure by [9] to compute the difference between two candidate ellipses, say e i and e j , Diff ( e i , e j ) , in the following formula,

where ( x ∗ , y ∗ ) are the center coordinates of these two ellipses, a ∗ and b ∗ are the lengths of the semi-major axis and semi-minor axis, respectively, δθ is the angle between the two semi-major axes of these two ellipses, and

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Diff ( e i , e j ) when one of the two ellipses is close to the circle. When two ellipses have a very low Diff ( e i , e j ) , meaning they are very similar and regarded as redundant ones. Here, we use a threshold Th d = 9 . 8 for determining redundant ellipses, as suggested by [9].

B Additional experimental results

Details of used datasets. We test on four synthetic datasets, the Occlusion dataset and the Over420 lapping dataset proposed in [5], and the Concentric dataset and the Concurrent dataset constructed 421 by Meng et al. [8]. The Occlusion dataset and the Overlapping dataset each contain 300 images, 422 containing many incomplete ellipses and broken arcs respectively. The Concentric dataset and the 423 Concurrent dataset have 720 images and 1200 images respectively, whose contained concentric 424 arcs and concurrent arcs are generally difficult to handle. The tested four real-world datasets are 425 Prasad Dataset, Prasad+ Dataset, Random Dataset, and Smartphone Dataset. Prasad Dataset and 426 Prasad+ Dataset [5] totally contain 400 images from Caltech256 dataset [33] with low resolutions, 427 whose ellipses and occlusion cases are fewer than the other datasets. Random Dataset [6] has 400 428 images, whose quality is better than Prasad Dataset, containing overlapping ellipses and complicated 429 backgrounds. Smartphone Dataset has 629 images from 6 video shots [6], which are mainly from 430 traffic signs and bicycle wheels of various perspectives, generally used to test the performance of the 431 methods in practical application scenarios. 432

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Evaluation on variant axes ratio and orientation of ellipse. We generated two sets of ellipses 434 in various shapes, orientations, and sizes to investigate the potential of our method. In the first set, 435 10,000 ellipses are each generated in images respectively, whose centers and orientations are fixed, 436 but their semi-majors have lengths varied from 1 pixel to 100 pixels with an interval of 1 pixel, and 437 their semi-minors have the lengths by the ratios of the minor axis to the major axis that vary from 438 0.01 to 1.0 with an interval of 0.01. In the second set, 18,000 ellipses are each generated in images 439 respectively, whose orientations vary from -90° to 89° in a step of 1°. Here, with a direction, the 440 semi-majors for the ellipses are fixed in the length of 100 pixels, and their semi-minors have the 441 lengths varied by the ratios of the minor axis to the major axis varying from 0.01 to 1 in a step of 442 1. The results for the methods in comparison to detect the generated ellipses are shown in Fig. 8. 443 The effectiveness of these methods to detect various ellipses are measured by the recall rates. The 444 statistics in Table 4 show that our method can effectively detect a larger range of ellipses than the 445 compared methods in general, except that in handling the first set, where ours is a little inferior to 446 Meng et al. [8] in detecting the ellipses that are too small or too flat. 447

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Performance over different IoU In general, when a detected ellipse has its IoU bigger than a threshold, it is regarded as correctly detected. In the paper, we use the results by setting the threshold as 0.8 for real-world datasets and 0.9 for the synthetic datasets. To further demonstrate the performance of our method, we performed experiments with the threshold ranging from 0.5 to 0.99. The results for the four real-world datasets are shown in Fig. 9, showing that our method achieves the best performance. When the threshold is lower than 0.75, our F-measure values no longer change significantly, showing our potentials for high-quality ellipse detection.

Comparison on edge extraction. We compare our edge extraction results with that of the learning based method [25]. As shown in Fig. 10, we can obtain many more arcs for detecting ellipses as many as possible, especially those overlapped ones. The method of [25] mainly extracts the arcs on the outer contours of objects, missing many overlapped ellipses, as shown in the red boxes in Fig. 10.

More results on synthetic datasets. We provide some visual comparison between the results of 459 our method and that of [9] in Fig. 11 and Table 5. On the whole, we can always obtain many more 460 correct ellipses for some complicated cases. In this experiment, we have IoU = 0 . 9 for validating 461 ellipses because these images dose not contains noise or texture that may disturb arc extraction, as 462 suggested by [7, 8, 9]. We also list the statistics of comparison on precision, recall and F-measure in 463 Table 6. 464

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Notes: 1) [15] runs on GPU, and the other methods run on CPU. Time is in millisecond.

2) '*Ours' refers to using our method without filtering in edge detection and with constraints relaxed in arc determination.

More results on real-world datasets. In the main paper, we only provide the statistics of some 465 recent methods and limited visual results. Here, we provide more quantitative comparison in Table 7, 466 and more visualization of detected ellipses in Fig. 12. 467

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C Promotion to application of autonomous driving

Traffic sign detection is a crucial problem in autonomous driving, where it is very important to detect traffic signs as early and thoroughly as possible. Among all traffic signs, circular signs account for a large proportion, and provide key information about traffic rules and restrictions. Thus, ellipse detection in the captured images of the cameras for autonomous driving are much required.

We made a test by comparing our method and Jia et al. [12] on ellipses detection. Here, the used images are from the dataset collected from video frames captured by a mobile phone [12] and a set of complex real images containing circular traffic signs from the public Traffic Sign Detection Dataset (TSDD) 1 .

As illustrated by some results in Fig. 13, we can detect more traffic signs than the method of Jia et 477 al. [12]. Thus, we can promote the safety of autonomous driving, as discussed in the following. Firstly, 478 we can more effectively detect small-sized ellipses, as shown in Fig. 13(a)(f), which means that 479 traffic signs can be recognized from a greater distance, improving the timely response of autonomous 480 driving systems. Secondly, our method detects more traffic signs, as shown in Fig. 13(c)(e), thereby 481 avoiding the risk of missing critical information. Thirdly, we can effectively identify incomplete 482 signs, as shown in Fig. 13(b), which are quite common in real-world scenarios due to limitations 483 such as camera field of view or obstructions. Clearly, with our method, autonomous driving can be 484 promoted a lot. 485

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11. Safeguards

Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?

Answer: [No]

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Guidelines:

The answer NA means that the paper poses no such risks.

Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel edge-link method for ellipse detection with two core innovations:\n1. Adaptive arc generation: Adjusts search direction during edge pixel linking to produce smoother arcs.\n2. Grid-based arc grouping: Uses a grid to manage arcs and a center-outward traversal path to implicitly exclude non-elliptical arc groups, avoiding explicit checks for efficiency.\n3. Experiments on synthetic and real-world datasets show superior accuracy and speed vs. SOTA methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths​​\n1.Novel grid-based grouping: Implicit exclusion of useless arc groups via grid traversal is innovative and reduces computation significantly (Table 1: 74-88% reduction in checked groups).\n2.Effective arc generation: Adaptive search direction improves contour smoothness (Fig. 4), aiding consistent arc extraction for overlapped ellipses.\n3.Strong empirical results: Outperforms 10+ SOTA methods on F-measure/time across 8 datasets (Tables 2-3, Fig. 9), especially on high-resolution images.\nWeaknesses​​\n1.Limited validation scope: No tests on high-noise/low-contrast images. Missing comparison with deep learning methods. \n2.Incomplete complexity analysis: Lacks runtime breakdown (e.g., arc extraction vs. grouping).\n3.Unclear reproducibility without open-source code.\n\nQUESTIONS:\nWhy not compare with DL methods (e.g., [21, 22]) given their rising prominence?\nCan the grid resolution (Eq. 1) be optimized dynamically for uneven arc distributions？How might the current method perform on highly non-uniform inputs, and would adaptive grids mitigate potential biases?\nBeyond the tested datasets, how does performance degrade under higher noise levels or occlusion? Are there theoretical or empirical bounds for the method’s failure modes?\nCan the hyperparameter sensitivity be clarified via ablation studies？\n\nLIMITATIONS:\nArc extraction depends on edge detection quality (Sec. 6).\nGrid efficiency assumes moderate arc density; performance drops for highly cluttered scenes (e.g., Fig. 11 Occlusion#1).", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-20"}

comments: SUMMARY:
This paper presents two measures to improve edge-linking ellipse detection methods, which are 1) adaptively adjusting the search direction for arc-generation and 2) efficient paired arc grouping using grids. The experiments were performed in four synthetic datasets and four real-world datasets. The results show the effectiveness of the proposed method.

STRENGTHS AND WEAKNESSES:
Strengths:

1) Using grids to filter invalid arcs for arc grouping is simple yet effective.

2) The paper is easy to follow and well organized.

3) Overall, the experimental results are convincing and comprehensive.

Weaknesses:

1) Although the proposed methods could improve existing SOTA methods, it seems they are a bit straightforward. The proposed measures rely on many existing techniques as well, such as arc-search region. It would be great if the proposed method is unique compared to existing methods.

2) It would be more comprehensive if the deep-learning ellipse detection methods can be compared in experiments.

3) The topic of ellipse detection would be more welcomed in some image processing venues instead of NeurIPS.

QUESTIONS:
See strengths and weaknesses.

LIMITATIONS:
No negative societal impact.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-06-30

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper discusses the problem of robust and efficient ellipse detection in images. Starting from an existing arc extractor pipeline (Edge detection, contour extraction, contour segmentation and arc extraction), the authors first propose an improvement on contour extraction by changing the order the search order to extend smooth contours. The authors then propose an new arc group grouping method to extend arc pieces into ellipses. Redundant ellipses are then filtered to only keep a single representative.\n\nSTRENGTHS AND WEAKNESSES:\nThe two proposed improvements are interesting and efficient. They build upon previous work continue and extends previous work. Moreover, based on the reported results, it seems to work well both quantitatively and qualitatively.\n\nThe comparison with previous work is lacking. Methods looking at efficient arc completion, like {1}, are not discussed and the results are not compared. Most popular DL ellipse detection methods like {2} are not discussed and compared either. \n\nThe paper is lacking crucial ablations. The methods is a set of (clever) tricks but their independent impact is not measured. It's actually possible that some are hindering performance in some case (for example fusing close ellipses might remove true positives in the case of two real ellipses that overlap each other since only a single ellipse is allowed per arcs). While it doesn't seem to impact the performance given the results reported (it's probably a rare case if existing at all in the test data), it doesn't mean that the problem doesn't exists. Surprisingly this case is mentioned in the limitation part but the reason of failure given is the poor arc extraction.\n\n\n{1} Pătrăucean, Viorica, Pierre Gurdjos, and Rafael Grompone Von Gioi. \"A parameterless line segment and elliptical arc detector with enhanced ellipse fitting.\" In European Conference on Computer Vision, pp. 572-585. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.\n\n{2} Dong, Wenbo, Pravakar Roy, Cheng Peng, and Volkan Isler. \"Ellipse R-CNN: Learning to infer elliptical object from clustering and occlusion.\" IEEE Transactions on Image Processing 30 (2021): 2193-2206.\n\nQUESTIONS:\nHow does the methods perform against previous methods focusing on efficient selection of arcs for ellipse detection? (see {1} in the \"Strengths And Weaknesses\" section)\n\nLIMITATIONS:\nIn my opinion, the limitation listed is quite lacking. It focuses only on the arc extraction process (something that is barely addressed in the paper since it mostly uses previous work) and not the core part presented in the article.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces an efficient edge-link method for ellipse detection, underpinned by two key innovations. First, an adaptive contour extraction technique is proposed, which modifies the search direction strategy during edge pixel connection by prioritizing neighboring regions with minimal angle variation. This approach yields smoother and longer arc segments, thereby enhancing the stability of ellipse fitting. Second, the method employs an implicit exclusion mechanism for irrelevant arc groups. By managing arc segments with a grid-based framework and designing an outward traversal path from the center, arc groups unlikely to belong to the same ellipse are effectively discarded without explicit verification, substantially reducing computational load. Building on these components, the paper adopts a strategy of first generating a maximal set of candidate ellipses followed by the elimination of redundancies, ultimately achieving higher detection precision and reduced runtime compared to existing methods on both synthetic and real datasets.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Originality: This work introduces an innovative paradigm that implicitly eliminates redundant groups of arc segments through grid management and traversal path design. By complementing traditional explicit exclusion methods (e.g., feature mapping constraints), the proposed approach offers a novel direction for enhancing efficiency in edge-linking frameworks.\n\n2. Technical Quality: The method is meticulously detailed, featuring an adaptive contour extraction strategy based on angle-difference priority search and an improved arc search region design that dynamically excludes processed grids. The effectiveness of these components is rigorously validated through ablation experiments. Furthermore, comprehensive experimental comparisons across diverse synthetic and real-world scenarios demonstrate that the proposed approach significantly outperforms current state-of-the-art methods—achieving, for example, an F-measure of 0.7006 on the Smartphone dataset compared to Shen’s 0.6424.\n\n3. Significance: With its high efficiency—processing each image in less than 12 ms—the method is well-suited for real-time applications such as autonomous driving and industrial inspection. Although the code is not currently open-sourced, there is a commitment to releasing it upon acceptance. Reproducibility is ensured by using publicly available parameter settings and datasets (e.g., Caltech256 and TSDD).\n\n4. Clarity: The paper is well-structured, with a seamless integration of methodological descriptions and experimental analyses. Diagrams illustrating grid traversal paths and contour extraction comparisons provide intuitive support for the technical details, while supplementary materials further elaborate on the experimental procedures.\n\n\nWeakness:\n\n1. Insufficient theoretical analysis: There is a lack of theoretical justification for the “implicit exclusion rate” (e.g., the mathematical derivation of the expected exclusion ratio), with support provided solely through experimental statistics. This approach may be challenging to extend to scenarios with extreme data distributions.\n\n2. Parameter sensitivity: The grid resolution and arc extraction parameters (e.g., θarc, Larc) are set empirically, and their robustness across different datasets (such as low-contrast or high-noise images) has not been discussed.\n\n3. Shallow discussion of limitations: While the conclusion mentions the reliance on arc extraction, it does not delve into failure cases (e.g., severe occlusion or fragmented ellipses), nor does it analyze the method’s extendability to high-dimensional parameter spaces (such as three-dimensional ellipse detection).\n\nQUESTIONS:\nQ1. Theoretical Guarantee of the Implicit Exclusion Rate (Impacting Originality and Theoretical Depth)  \nCurrently, experimental results (see Table 1) indicate that the implicit exclusion rate can reach 74%–88%; however, a comprehensive theoretical analysis is absent. \nIt is recommended that the study derive a lower bound for the expected proportion of irrelevant arc groups implicitly excluded through the adopted grid partitioning and traversal strategies. This derivation might be based on a probabilistic model of search area coverage and could be detailed in an appendix or supplemented with references to the relevant geometric probability literature. Providing such a theoretical proof is likely to enhance the manuscript’s originality score, whereas reliance solely on experimental outcomes could lead to a slight deduction.\n\nQ2. Sensitivity Experiments for Key Parameters (Impacting Robustness)  \nThe manuscript does not discuss the sensitivity of key parameters, notably the grid resolution (as defined in Equation 1) and the thresholds for arc segments (θarc and Larc).\nTo address this, it is advisable to incorporate parameter perturbation experiments in an appendix. Specifically, by holding all other parameters constant, the grid resolution should be varied by ±20%, θarc by ±5°, and Larc by ±10 pixels, with corresponding impacts on the F-measure and running time reported. Furthermore, presenting the interaction of these parameter variations via heat maps (refer to appendix figures) would provide valuable insight. Demonstrating robustness to these parameter changes could improve the overall quality score; conversely, if the method exhibits high sensitivity, a discussion of adaptive selection strategies should be included to preclude potential score deductions.\n\nQ3. Analysis of Failure Cases (Impacting Discussion of Limitations)  \nAlthough the conclusion mentions that overlapping ellipse detection may fail, the manuscript does not provide specific examples or analyses of such failure cases. \nIt is suggested that the study include visualizations of these cases in an appendix—such as instances with false positives or false negatives where the Intersection over Union (IoU) falls below 0.5—and analyze the underlying causes, which might include issues like inadequate grid resolution or discontinuity in arc segments. Additionally, the authors are encouraged to discuss potential improvements, such as employing a multi-scale grid or incorporating dynamic thresholding. A thorough examination of these failure cases would strengthen the discussion of limitations and possibly enhance the clarity score; neglecting this analysis could result in a deduction.\n\nLIMITATIONS:\nIt is recommended to supplement the manuscript with the following additional analyses and discussions:\n\n1. Parameter Sensitivity: An evaluation of the robustness of the grid resolution and arc threshold parameters for low-contrast or high-noise images should be incorporated. For example, parameter perturbation experiments could be added in an appendix to quantitatively assess how variations in these parameters affect performance.\n\n2. Computational Complexity: The paper would benefit from a detailed discussion of the memory and time constraints associated with the grid traversal strategy, particularly when processing high-resolution images (e.g., 4K) or scenes containing densely packed ellipses. A Big-O complexity analysis or stress testing under extreme conditions is advised to thoroughly address these concerns.\n\n3. Negative Societal Impact: Although the manuscript states that there are no direct negative impacts, it does not consider the potential for misuse, such as forging traffic signs to mislead autonomous driving systems. A dedicated section discussing potential misuse scenarios and corresponding mitigation measures (for instance, the public disclosure of detection confidence thresholds) would strengthen the ethical considerations of the work.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-20"}