A novel scheme for progressive polygon approximation of shape contours

Hosur, P.I.; Ma, Kai-Kuang

doi:10.1109/mmsp.1999.793854

Cited by 15 publications

(6 citation statements)

References 2 publications

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“…Numerous algorithms have been proposed for the detection of dominant points in digital planar curves, falling broadly into two main categories. The first category includes algorithms that strive to minimize the number of edges or vertices required to approximate the curve, subject to defined error criteria [21][22][23]. The second category, by contrast, comprises algorithms that pinpoint specific points along the curve as dominant points [3, 5, 7, 10-12, 14, 16, 17, 24].…”

Section: Related Workmentioning

confidence: 99%

An Efficient Descriptor-Based Approach for Dominant Point Detection in Shape Contours

Parvez

2023

ATAIML

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Dominant points, or control points, represent areas of high curvature on shape contours and are extensively utilized in the representation of shape outlines. Herein, we introduce a novel, descriptor-based approach for the efficient detection of these pivotal points. Each point on a shape contour is evaluated and mapped to an invariant descriptor set, accomplished through the use of point-neighborhood. These descriptors are then harnessed to discern whether a point qualifies as a dominant one. Our proposed methodology eliminates the need for costly computations typically associated with evaluating candidate dominant points. Furthermore, our algorithm significantly outperforms its predecessors in terms of speed, relying solely on integer operations and obviating the necessity for an optimization phase. Experimental outcomes, derived from the widely used MPEG7 CE-Shape-1 Part B, denote a minimum enhancement of 2.3 times in terms of running time. This implies that the proposed methodology is particularly suitable for real-time applications or scenarios managing shapes comprising a substantial number of points.

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Section: Related Workmentioning

confidence: 99%

An Efficient Descriptor-Based Approach for Dominant Point Detection in Shape Contours

Parvez

2023

ATAIML

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“…A great number of algorithms for the generation of digital circles is known in the literature (for reviews, see [1,3]). In complexity, these algorithms range from the incremental discretization of the implicit or parametric representation of the Euclidean circle [7,9,22,23,19,24,6,25], the discretization of differential equations [28,15], sophisticted spline and polygonal approximations [26,13,17,4], to algorithms which utilize number-theoretical concepts [5]. Although all incremental algorithms utilize decision (or cost) functions, the concrete form of the latter, as well as their specific implementation, can lead to quite different representations of digital circles with the same radius (Fig.…”

Section: -Connected Signummentioning

confidence: 99%

“…where in the last step we used again (49) and the fact that s 2 n = 1 for all n. Finally, reordering terms in the last sum in (44) yields Here we made use of the explicit form of a n , which can easily be deduced from (17) as a n = a 0 + S n−1 with a 0 = r. Together with (53), we then have Finally, noting that π n = an 4r , and that the harmonic mean is the reciprocal dual of the arithmetic mean, we have proven Proposition 3.2.…”

Section: π On the Digital Circlementioning

confidence: 99%

On a recursive construction of circular paths and the search for $π$ on the integer lattice $\mathbb{Z}^2$

Rudolph-Lilith¹

2016

Preprint

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Digital circles not only play an important role in various technological settings, but also provide a lively playground for more fundamental numbertheoretical questions. In this paper, we present a new recursive algorithm for the construction of digital circles on the integer lattice Z 2 , which makes sole use of the signum function. By briefly elaborating on the nature of discretization of circular paths, we then find that this algorithm recovers, in a space endowed with 1 -norm, the defining constant π of a circle in R 2 .

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“…Depending on the related problem, a particular discretization technique is adopted in order to obtain the concerned type of digital disc/circle [32,56]. Some of these discretization techniques are presented in this section.…”

Section: Covering a Digital Disc By A Real Polygonmentioning

confidence: 99%

Real Polygonal Covers of Digital Discs – Some Theories and Experiments

Bhowmick

Bhattacharya

2009

Fundamenta Informaticae

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There are several algorithms for digitization of a real disc (circle) to derive a digital disc, and also for finding the real disc corresponding to a digital disc. However, the correspondence of a digital disc with a regular polygon in the real plane is not well studied. This paper presents some theories and related experiments on setting the correspondence from a digital disc to its polygonal cover in the real plane. For an ideal regular polygon covering a digital disc, all the grid points of the digital disc should lie on and inside the polygon, and vice versa. That an ideal regular polygon corresponding to a digital disc is possible for some of the digital discs, especially for the ones having smaller radii, is shown. Further, for a disc whose ideal regular polygon is not possible, an approximate polygon, tending to the ideal one, is possible, in which the error of approximation can be controlled by the number of vertices of the approximate polygon. These (ideal or approximate) polygonal covers of digital discs have several applications in many problems of point set pattern matching. We have reported the conditions under which an ideal regular polygon always exists corresponding to a digital disc, and the conditions under which the existence of an ideal regular polygon becomes uncertain. Experimental results have been given to demonstrate the possibilities of approximation and the trade-off in terms of error versus the number of vertices in the approximate polygon.

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A novel scheme for progressive polygon approximation of shape contours

Cited by 15 publications

References 2 publications

An Efficient Descriptor-Based Approach for Dominant Point Detection in Shape Contours

An Efficient Descriptor-Based Approach for Dominant Point Detection in Shape Contours

On a recursive construction of circular paths and the search for $π$ on the integer lattice $\mathbb{Z}^2$

Real Polygonal Covers of Digital Discs – Some Theories and Experiments

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