Circularity Measuring in Linear Time

A Projection-Based Method for Shape Measurement

“…The methods in this research direction response to the problem: How much a given shape differs from a perfect circle. Several methods [18,19,20,21,22,23,24,25,26,27,28,29,30] have been proposed in the literature to deal with this problem. The classic measure based on non-compactness measure [18] using perimeter and area of the shape (4πA/P 2 ) is not satisfactory in reality because it is not really scale invariant and it can reach the perfect value for non circular shapes.…”

“…In general, there are two main following approaches for circularity measurement: contour-based and region-based approaches. The first direction contains the methods exploiting desirable properties of circular shapes [19,22,27,28,29] by taking into account their boundary properties: distances from centroid to boundary [19], Fourier transform (DFT) on boundary contour [22], separating circle problem [27,28], polygon similarity [29], linearity of boundary points in polar coordinate system [25], integer interval from boundary representation [46], etc. These methods can only deal with simple shapes and are generally sensible against non-linear deformations.…”

“…Thanks to the projection-based approach, our method can deal with complex shapes composed of several closed contours like moment-based methods [24]. This is an important advantage compared with contour-based methods [57,27,28,29] requiring shapes represented by a unique closed contour that is not always satisfied in real conditions (see Figure 6). Figure 7 presents the obtained results on compound shapes.…”

“…This approach producing high-dimensional feature vectors is suitable for generic applications such as shape retrieval [10,11,12], shape and curve matching [13,14,15]. The second one measures or estimates geometrical properties of shapes and thus the descriptors in this approach often have clear geometric interpretations such as measurements of ellipticity [16,17,1], circularity [18,19,20,21,22,23,24,25,26,27,28,29,30] , polygonality [31], triangularity [1], rectangularity [1,32], linearity [32], orientability [33,34].…”

Coronal loop detection from solar images and extraction of salient contour groups from cluttered images.

“…In this method, a set of points are transformed from Cartesian to polar coordinates as shown in Figure 2 Nguyen (Nguyen, et al, 2010) proposed a similar approach to Stojemenovic' s method ). Nguyen' s method transforms the points into tangent space which consists of the tangents between consecutive points on a polygonal curve.…”