Ellipse center coordinate estimation system and estimation method thereof

Abstract

An ellipse center coordinate estimation system and a method for estimating the same are disclosed. The ellipse center coordinate estimation method comprises the steps of: an edge point detection unit detecting a set of edge points defined as an ellipse from an input image; a chord forming unit selecting two points from the set of edge points and forming a chord connecting the two points; a center point accumulation unit calculating the center of the chord and accumulating it in a two-dimensional accumulation space by applying a weight; and a center estimation unit detecting a maximum value among the density distributions in the two-dimensional accumulation space and estimating it as the center of the ellipse. By performing only a two-dimensional mode search instead of a five-dimensional parameter search, the amount of computation is significantly reduced, and the center error is small and stable even in partial contour or noisy environments.

Description

Technology Field

[0001] The present invention relates to an ellipse center coordinate estimation system and a method for estimating the same, and more specifically, to an ellipse center coordinate estimation system and a method for estimating the center of an ellipse from a part or the entire contour of an ellipse at high speed and high precision. Background Technology

[0003] Since ellipses are perspective projections of circular objects, they frequently appear in both natural and artificial environments. Consequently, robust ellipse detection and parameter estimation have long been unresolved problems in the field of computer vision. In particular, a critical parameter is the center of the ellipse, which is frequently used as a key feature in tasks such as camera calibration, visual tracking, and pose estimation. For example, in planar target calibration, the center of a projected circular marker provides observations for calibration algorithms. Similarly, in robotics and augmented reality, tracking the center of an elliptical reference marker is critical for determining the position of an object. Despite this importance, accurately locating the ellipse center in an image remains a challenging task, especially when noise, clutter, or incomplete contours are present.

[0004] Existing approaches to ellipse detection include Hough transform-based methods and algebraic fitting methods. Hough transform-based methods utilize searching for votes representing the ellipse in a high-dimensional parameter space (central coordinates, axes, and orientation), but they generally require significant computation and can be sensitive to parameter quantization. Direct cone fitting methods, such as the classical least-squares ellipse fitting proposed by Fitzgibbon et al., attempt to fit every edge point to the ellipse model.

[0005] While these methods are effective for clean and perfect ellipses, performance often degrades due to partial occlusion or outlier edges. If the data deviates from an ideal ellipse, it can generate deformed cones (e.g., hyperbolas). In practice, many vision systems that require the ellipse center utilize the principle of performing a full ellipse fit and then extracting the center from the fit. However, this indirect approach retains the aforementioned vulnerabilities and uses more information (and assumptions) than is necessary simply to find the center.

[0006] These methods require complete contour data or suffer from performance degradation in noisy and partially occluded environments. Additionally, the Hough transform requires the simultaneous exploration of multidimensional parameters, resulting in excessive computational and memory usage. Therefore, a method is required that can quickly and accurately estimate only the center of an ellipse even in partial contour or noisy environments. Prior art literature

[0008] Korean Registered Patent Publication No. 10-2176199 The problem to be solved

[0009] The present invention aims to provide an elliptical center coordinate estimation system and an estimation method that can significantly reduce computational load by performing only a 2D mode search instead of a 5D parameter search.

[0010] The present invention aims to provide an elliptical center coordinate estimation system and a method thereof that are stable and have small center error even in partial contour or noisy environments. means of solving the problem

[0012] A method for estimating the center coordinates of an ellipse according to one embodiment of the present invention may include: a step in which an edge point detection unit detects a set of edge points defined as an ellipse from an input image; a step in which a chord forming unit selects two points from the set of edge points and forms a chord connecting the two points; a step in which a center point accumulation unit calculates the coordinates of the center of the chord and then applies weights to accumulate them in a two-dimensional accumulation space; and a step in which a center estimation unit detects a maximum value among the density distributions of the two-dimensional accumulation space and estimates it as the coordinates of the center of the ellipse.

[0013] When accumulating the coordinates of the midpoint of the above chord in the accumulation space, a weight proportional to the length of each chord formed from the set of edge points can be assigned.

[0014] It may include a step of correcting the center coordinates of the subpixel precision by means of a mean-shift or a second-order approximation method near the maximum value of the above two-dimensional cumulative space.

[0015] When accumulating the coordinates of the midpoint of the above chord in the accumulation space, the coordinates of the midpoint of the above chord can be accumulated in the accumulation space when the midpoint of the above chord is located inside the convex hull.

[0016] An ellipse center coordinate estimation system according to one embodiment of the present invention may include: an edge detection unit that detects a set of edge points defined as an ellipse from an input image; a chord forming unit that selects two points from the set of edge points and forms a chord connecting the two points; a center accumulation unit that calculates the coordinates of the center of the chord and accumulates them in a two-dimensional accumulation space; and a center estimation unit that detects a maximum value among the density distributions of the two-dimensional accumulation space and estimates it as the coordinates of the center of the ellipse. Effects of the invention

[0018] According to the present invention, the amount of computation can be significantly reduced by performing only a 2-dimensional mode search instead of a 5-dimensional parameter search.

[0019] According to the present invention, the center error is small and stable even in partial contour or noisy environments. Brief explanation of the drawing

[0021] FIG. 1 is a block diagram of an ellipse center coordinate estimation system according to one embodiment of the present invention. FIG. 2 is a chord-central point density heatmap for an ellipse according to one embodiment of the present invention. FIG. 3 is a flowchart of an ellipse center coordinate estimation method according to one embodiment of the present invention. Specific details for implementing the invention

[0022] The advantages and features of the present invention and the methods for achieving them will become clear by referring to the following embodiments in conjunction with the accompanying drawings. However, the present invention is not limited to the following embodiments but may be implemented in various different forms. The embodiments are provided merely to ensure that the disclosure of the present invention is complete and to fully inform those skilled in the art of the scope of the invention, and the present invention is defined only by the scope of the claims.

[0024] FIG. 1 is a block diagram of an ellipse center coordinate estimation system according to one embodiment of the present invention, and FIG. 2 is a chord-central point density heatmap for an ellipse according to one embodiment of the present invention.

[0025] Referring to FIG. 1, the ellipse center coordinate estimation system (1000) may include an edge detection unit (100), a chord forming unit (200), a center accumulation unit (300), and a center estimation unit (400).

[0026] The edge detection unit (100) detects a set of edge points defined as an ellipse from an input image. Here, the ellipse is a shape centered at the origin, and the set of edge points can be extracted through an edge detector or a segmentation mask, etc.

[0027] The chord forming part (200) selects two points from a set of edge points and forms a chord connecting the two points.

[0028] The midpoint accumulation unit (300) calculates the coordinates of the midpoints of the chords, assigns weights, and accumulates them in a two-dimensional accumulation space. If we imagine all possible chords of an ellipse, the set of all midpoints constitutes a chord-midpoint set. Since the ellipse is centroidally symmetric (an ellipse is a convex even function curve with respect to the origin), every chord passing through the ellipse has a twin chord of equal length and parallel to the center on the opposite side. The midpoints of these twin chords coincide at the center. Generally, for every chord that does not pass through the center, there is another chord parallel to the first chord and whose midpoint is collinear with the first midpoint and the center. This means a line of midpoints passing through the center for each chord direction.

[0029] Precision can be improved by calculating the coordinates of the chord midpoints and assigning weights to them. Chords spanning a wider range of the ellipse (closer to the major axis) generate midpoints closer to the center, whereas very short chords confined to one end of the ellipse generate midpoints that are still peripheral. If edge points are sampled uniformly, backbias actually occurs (significantly more short chords than minor ones). To offset this, weights can be assigned by applying a length function to the voting of each chord.

[0030] Consequently, chord midpoints are more concentrated near the center than elsewhere on the image plane. This is because chords of any direction cause points to converge around the center. Conversely, points far from the actual center can occur only in chords of very specific directions and locations. This intuition is well illustrated in Figure 2, which shows a heatmap of chord-midpoint density for a representative ellipse. Midpoints are distributed across the entire elliptical area, but the density increases as they move toward the center. The point with the highest overall density is the actual center (indicated by the cyan cross).

[0031] In Figure 2, warmer colors result in more chord-midpoints distributed at specific locations. The actual center of the ellipse (cyan crosshairs) corresponds to the peak of this density. Although the chord-midpoints are spread out within the ellipse, they are strongly and sharply distributed at the center due to the symmetry of the ellipse.

[0032] The center point accumulation unit (300) assigns a weight proportional to the length of each chord formed from a set of edge points when accumulating the coordinates of the center point of the chord. Accordingly, the contribution of the long chord near the coordinates of the center point of the chord is increased, and noise suppression through the determination of the inside of the convex hull (a minimal convex outer perimeter that encloses all edge points) and mean-shift-based subpixel correction can be performed.

[0033] The center point accumulation unit (300) can accumulate the coordinates of the center point of the chord when the center point of the chord is located inside the convex hull. By doing so, accurate center estimation becomes possible by excluding centers that cannot be candidates for the ellipse center.

[0034] The center accumulation unit (300) can correct the center coordinates of the subpixel precision by means of a mean-shift method or a second-order approximation method near the maximum value of the 2D accumulation space.

[0035] Mean shift is a non-parametric (iterative) optimization algorithm used to find the mode of a data distribution, specifically the point of maximum density. It is a method that observes the surrounding data distribution from a specific initial point and moves the point in the direction of the weighted average of the surrounding points.

[0036] In the accumulator space, select an initial estimate near the maximum value and retrieve the accumulated values ​​included in its vicinity. Then, calculate the weighted average of the x, y plane coordinates using these accumulated values ​​as weights. The new coordinate moves in the direction where the accumulated value is higher than the previous coordinate. By repeating this process, it gradually converges to the mode (maximum value) position.

[0037] Since the mean shift method is nonparametric, it is less affected by the shape of the cumulative value distribution (e.g., asymmetry, multiple peaks), and servipixel precision can be achieved as long as the number of iterations is sufficient.

[0038] The second-order approximation method approximates the accumulated value near the maximum value with a two-dimensional quadratic function, and then calculates the servipixel coordinates of the maximum point by finding the vertex of that quadratic function. It uses the center cell with the maximum accumulated value and 8 surrounding cells (or a wider surrounding area), and views the accumulated value as in the form z = f(x, y). Then, it approximates (fits) the value with a quadratic function as shown in Equation 1.

[0039] [Mathematical Formula 1]

[0040]

[0041] Afterwards, the point where the gradient of the quadratic function becomes zero, that is, the vertex coordinates (x, y) are obtained by solving Equations 2 and 3. The derived (x, y) becomes the center correction value of the subpixel precision.

[0042] [Mathematical Formula 2]

[0043]

[0044] [Mathematical Formula 3]

[0045]

[0046] The second-order approximation method converges quickly and requires less computation, making it advantageous for real-time processing. It can also obtain very accurate approximations (sub-pixel level) when values ​​near the maximum point are smooth.

[0047] The center estimation unit (400) detects the maximum value among the density distributions of the two-dimensional accumulation space and estimates it as the coordinates of the center of the ellipse. A density function can be defined for the image plane of the ellipse edge points, and the density distribution can be efficiently approximated using random sampling or binned accumulation. All directions of the chords are the cause of the density that overlaps most at the center. If the center of the ellipse is not the origin, the maximum value is obtained at the actual center by shifting the coordinates. Therefore, the center of the ellipse can be found by finding the maximum value.

[0049] FIG. 3 is a flowchart of an ellipse center coordinate estimation method according to one embodiment of the present invention.

[0050] Referring to FIG. 3, the ellipse center coordinate estimation method may include S100 to S400, and details thereof will be referred to in FIG. 1 to FIG. 2.

[0051] The edge point detection unit (100) detects a set of edge points defined as an ellipse from the input image (S100).

[0052] After S100, the chord forming unit (200) selects two points from a set of edge points and forms a chord connecting the two points (S200).

[0053] After S200, the center point accumulation unit (300) calculates the coordinates of the center point of the chord, assigns weights, and accumulates them in a two-dimensional accumulation space (S300).

[0054] In S300, when accumulating the coordinates of the midpoint of the chord, by applying a weight proportional to the length of each chord formed from the set of edge points, the contribution of the long chord near the coordinates of the midpoint of the chord is increased, and noise suppression through convex hull internal discrimination and mean-shift-based subpixel correction can be performed.

[0055] In S300, when accumulating the coordinates of the center of the chord, the coordinates of the center of the chord can be accumulated when the center of the chord is located inside the convex hull.

[0056] After S300, the center estimation unit (400) detects the maximum value among the density distributions of the two-dimensional cumulative space and estimates it as the coordinates of the center of the ellipse (S400).

[0057] In S300, the center coordinates of the subpixel precision can be corrected by the mean-shift method or the second-order approximation method near the maximum value of the 2D cumulative space.

[0059] The embodiments of the present invention described above have been explained with reference to the embodiments illustrated in the drawings for the sake of understanding, but this is merely illustrative and those skilled in the art will understand that various modifications and equivalent alternative embodiments are possible therefrom. Accordingly, the true technical scope of protection of the present invention should be determined by the appended claims. Explanation of the symbols

[0061] 100: Edge detection unit 200: Current forming unit 300: Midpoint accumulation section 400: Center estimation section 1000: Ellipse Center Coordinate Estimation System

Claims

Claim 1 An ellipse center coordinate estimation method comprising: a step in which an edge point detection unit detects a set of edge points defined as an ellipse from an input image; a step in which a chord forming unit selects two points from the set of edge points and forms a chord connecting the two points; a step in which a center point accumulation unit calculates the coordinates of the center of the chord, assigns a weight, and accumulates them in a two-dimensional accumulation space; and a step in which a center estimation unit detects a maximum value among the density distributions in the two-dimensional accumulation space and estimates it as the coordinates of the center of the ellipse, wherein when accumulating the coordinates of the center of the chord, a weight proportional to the length of each chord formed from the set of edge points is assigned. Claim 2 delete Claim 3 An elliptical center coordinate estimation method according to claim 1, comprising the step of correcting the center coordinates of subpixel precision by a mean-shift method or a second-order approximation method near the maximum value of the two-dimensional cumulative space. Claim 4 A method for estimating the coordinates of an ellipse center, wherein, in claim 1, when accumulating the coordinates of the midpoint of the chord, the midpoint of the chord is located inside the convex hull. Claim 5 An ellipse center coordinate estimation system comprising: an edge detection unit that detects a set of edge points defined as an ellipse from an input image; a chord forming unit that selects two points from the set of edge points and forms a chord connecting the two points; a center point accumulation unit that calculates the center of the chord and accumulates it in a two-dimensional accumulation space; and a center estimation unit that detects a maximum value among the density distributions in the two-dimensional accumulation space to estimate the center of the ellipse and assigns a weight proportional to the length of each chord formed from the set of edge points when accumulating the coordinates of the center of the chord.

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