An ellipse detection method from the polar and pole definition of conics

Yoo, Jae Hung; Sethi, Ishwar K.

doi:10.1016/0031-3203(93)90039-y

Cited by 29 publications

(8 citation statements)

References 5 publications

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“…This result is clear since equation (10) implies that the angles 4~ and 0 are related by $ = 0 + n/2. Consequently, cos(0) = cos(4~ + n/2) = sin(q~) and sin 0 = sin(~b + n/2) = cos(q~).…”

Section: Two-plane Ht For Circlesmentioning

confidence: 57%

On using directional information for parameter space decomposition in ellipse detection

Aguado

Montiel

Nixon

1996

Pattern Recognition

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Abstract--In this paper we use the parameteric polar representation to extend the application of edge directional information from circle to ellipse extraction. As a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub-spaces and one final histogram accumulator. The mapping includes the tangent of the angle of the first and second directional derivatives. These tangents are computed by considering edge direction at two border points. We show that the use of gradient information for parameter space decomposition avoids the intensive point labelling imposed by geometric constraints used by other approaches. Computer vision Ellipse detection Image segmentationFeature extraction Parameter space decomposition Hough transform l. INTRODUCTIONThe detection of geometric primitives from an image is one of the basic tasks of computer vision. A geometric primitive is represented by a mathematical expression with a number of free parameters which define instances of a shape. Hence, the extraction problem centres on obtaining an estimate of the free parameters according to the information on an image. The Hough transform (HT) is a well-known method to detect shapes by independently considering geometric data composed of edge points. The independent evidence accumulation of the HT makes it robust, providing adequate results even for overlapping or partially occluded objects.In order to gather evidence, the HT defines a mapping from the image space into a parameter space. By considering each border point in an image, the mapping adds a vote to chosen cells in an accumulator which represents the parameter space. The cells increased are those whose associated parameters define the geometric primitive which passes through the image point. Therefore, local maxima in the accumulator array correspond to the parameters of detected shapes.The HT was originally proposed to fit straight lines and then extended to analytical curves31~ Although the technique can be used directly for any parameterized curve, the generalization implies an exponential increase in computational time and space requirements. for this reason, new methods based on the original HT have been proposed (a review of the methods can be seen in Illingworth & Kittler ~2~ and Leaversta~).* Author to whom correspondence should be addressed. © Crown copyright (1996). The aim of this paper is to show how directional information can be used to derive a mapping which decomposes the parameter space required for the implementation of the HT. In addition to image points, we consider edge direction as geometric data providing an important clue for evidence gathering in the parameter space.Edge direction information has been used successfully to reduce the computational requirements of the HT in circle extraction, ca'5) The general approach is to include gradient direction information in order to constrain the parameter space. Here we show how the parametric polar representation can be used to combine edge points an...

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“…This result is clear since equation (10) implies that the angles 4~ and 0 are related by $ = 0 + n/2. Consequently, cos(0) = cos(4~ + n/2) = sin(q~) and sin 0 = sin(~b + n/2) = cos(q~).…”

Section: Two-plane Ht For Circlesmentioning

confidence: 57%

On using directional information for parameter space decomposition in ellipse detection

Aguado

Montiel

Nixon

1996

Pattern Recognition

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“…Since we define d as the signed distance and orientation angle 0 any where in the interval of O-2ic, our Hough transform space is set accordingly. The peaks in the Hough space are detected by backmapping [15] to locate the lines. The result of backprojection of the Hough space is shown in Figure 3(d).…”

Section: Resultsmentioning

confidence: 99%

<title>Correspondence using property coherence</title>

Sethi

Chung

Yoo

1992

Applications of Artificial Intelligence X: Machine Vision and Robotics

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“…The resulting Hough space is thus three‐dimensional, and the classical circular HT algorithm has O ( N 3 ) space requirements and O ( N 4 ) time complexity for an image I ( x , y ) of size N × N pixels. The memory requirements and completion time can be reduced by completing the search in two consecutive steps (Illingworth & Kittler, 1987; Yoo & Sethi, 1993; Bennett et al , 1999; Kanatani & Ohta, 2004; Peng et al , 2007). First, the gradient of the image is determined by calculating the centred differences in intensity.…”

Section: Methodsmentioning

confidence: 99%

Evolute‐based Hough transform method for characterization of ellipsoids

Kaytanlı

Valentine

2013

Journal of Microscopy

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SummaryWe propose a novel and algorithmically simple Hough transform method that exploits the geometric properties of ellipses to enable the robust determination of the ellipse position and properties. We make use of the unique features of the evolute created by Hough voting along the gradient vectors of a two-dimensional image to determine the ellipse centre, orientation and aspect ratio. A second one-dimensional voting is performed on the minor axis to uniquely determine the ellipse size. This reduction of search space substantially simplifies the algorithmic complexity. To demonstrate the accuracy of our method, we present analysis of single and multiple ellipsoidal particles, including polydisperse and imperfect ellipsoids, in both simulated images and electron micrographs. Given its mathematical simplicity, ease of implementation and reasonable algorithmic completion time, we anticipate that the proposed method will be broadly useful for image processing of ellipsoidal particles, including their detection and tracking for studies of colloidal suspensions, and for applications to drug delivery and microrheology.

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An ellipse detection method from the polar and pole definition of conics

Cited by 29 publications

References 5 publications

On using directional information for parameter space decomposition in ellipse detection

On using directional information for parameter space decomposition in ellipse detection

<title>Correspondence using property coherence</title>

Evolute‐based Hough transform method for characterization of ellipsoids

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