Testing for convexity with Fourier descriptors

Kakarala, Ramakrishna

doi:10.1049/el:19980943

Cited by 12 publications

(5 citation statements)

References 4 publications

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“…image retrieval, object classification, object recognition, and so forth). Different mathematical tools have been used to define the shape descriptors: algebraic invariants [10], Fourier analysis [13], statistics [17], morphological operations [24], curvature [25], integral transformations [21], fuzzy approaches [32], computational geometry [36], and so forth.…”

Section: Introductionmentioning

confidence: 99%

Measuring linearity of open planar curve segments

unić¹,

Rosin²

2011

Image and Vision Computing

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In this paper we define a new linearity measure for open planar curve segments. We start with the integral of the squared distances between all the pairs of points belonging to the measured curve segment, and show that, for curves of a fixed length, such an integral reaches its maximum for straight line segments. We exploit this nice property to define a new linearity measure for open curve segments. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured open line is a straight line segment. The new linearity measure is invariant with respect to translations, rotations and scaling transformations. Furthermore, it can be efficiently and simply computed using line moments. Several experimental results are provided in order to illustrate the behaviour of the new measure.

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Section: Introductionmentioning

confidence: 99%

Measuring linearity of open planar curve segments

unić¹,

Rosin²

2011

Image and Vision Computing

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“…Another reason is that a square has no straightforward geometric property which could lead to a simple definition of the shape squareness measure. In comparison, simple definitions of the convex shapes have led to several definitions for shape convexity measures [4,10,16,20,21,25,29].…”

Section: Resultsmentioning

confidence: 99%

“…Even for a single characteristic there often exist many alternative measures which are sensitive to different aspects of the shape, e.g. convexity [4,10,16,20,21,25,29]. Such a need for alternative measures is caused by the fact that there is no a single shape descriptor which is expected to perform efficiently in all possible applications -even the computation of perimeter is not a straightforward task [5,23].…”

Section: Introductionmentioning

confidence: 99%

Measuring Squareness and Orientation of Shapes

Rosin

Žunić

2010

J Math Imaging Vis

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In this paper we propose a measure which defines the degree to which a shape differs from a square. The new measure is easy to compute and being area based, is robust-e.g., with respect to noise or narrow intrusions. Also, it satisfies the following desirable properties:-it ranges over (0, 1] and gives the measured squareness equal to 1 if and only if the measured shape is a square;-it is invariant with respect to translations, rotations and scaling. In addition, we propose a generalisation of the new measure so that shape squareness can be computed while controlling the impact of the relative position of points inside the shape. Such a generalisation enables a tuning of the behaviour of the squareness measure and makes it applicable to a range of applications. A second generalisation produces a measure, parameterised by δ, that ranges in the interval (0, 1] and equals 1 if and only if the measured shape is a rhombus whose diagonals are in the proportion 1 : δ. The new measures (the initial measure and the generalised ones) are naturally defined and theoretically well founded-consequently, their behaviour can be well understood. As a by-product of the approach we obtain a new method for the orienting of shapes, which is demonstrated to be superior with respect to the standard method in several situations. The usefulness of the methods described in the manuscript is illustrated on three large shape databases: diatoms (ADIAC), MPEG-7 CE-1, and trademarks.

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“…Kakarala [25] uses the same boundary representation and derives the following expression for the Fourier expansion of the boundary curvature…”

Section: Fourier Descriptorsmentioning

confidence: 99%