Measure of circularity for parts of digital boundaries and its fast computation

Abstract

To cite this version:Tristan Roussillon, Isabelle Sivignon, Laure Tougne. Measure of circularity for parts of digital boundaries and its fast computation. Pattern Recognition, Elsevier, 2010, 43 (1) AbstractThis paper focuses on the design of an effective method that computes the measure of circularity of a part of a digital boundary. In spite of the specificity of the digital boundaries, an algorithm that only uses classical tools of computational geometry is derived. Even if a sophisticated machinery coming from linear programming can provide a linear time algorithm, its O(n log n) time complexity is better than many quadratic methods based on Voronoi diagrams. Moreover, this bound can be improve in the case of convex digital boundaries to reach linear time.

Autodetection of ancient Arabian tombs in high-resolution satellite imagery

“…There are a number of ways to do this, e.g. Haraliok (1974), Proffitt (1982), Giger, Doi, and MaoMahon (1988), Stojmenović, Nayak, and Zunic (2006), Stojmenović and Nayak (2007), Zunic and Hirota (2008), Roussillon, Sivignon, and Tougne (2010).…”

Topological relations between separating circles

“…2(b) shows the position of all circle centers. This area, which has also been called the arc center domain [8,18,20,19], is the projection of the domain onto the ab-plane. The 5 vertices correspond to the 5 circles shown in Fig.…”

“…Furthermore, O'Rourke et al proved that in the preimage there is a unique smallest separating circle, which can be found by convex programming, while the largest separating circle cannot be found by convex programming and is not always unique [16]. More recently, for the more difficult problem of circular arc segmentation, algorithms were introduced that incrementally construct the arc center domain, which is a 2D projection of the parameter domain [8,18,20,19]. Also here there is an obvious link between efficient arc segmentation and the incremental construction of a lower hull.…”

Faster circularity estimation by randomization

“…Identifying circular shapes or estimating circularity is a well-researched topic in discrete geometry [10], computer vision, and image processing [14]. It finds many applications in varied disciplines of science and engineering, such as, geology [15], biology [6,7], medical sciences [12], industrial processing [2,4], and computational metrology [1,13].…”

“…In our work, we have attempted to estimate the circularity of a digital object using certain efficient techniques of digital geometry. It may be noted that digital geometry is a study of the properties of sets of digital points [10,11], and forms the basis of shape recognition in image processing and pattern recognition [14]. Past few years have seen a considerable focus on object tracking which has applications in systems ranging from tracking of different objects in video sequences to tracking human bodies, human hands for sign language recognition, and faces for airport security, etc.…”