Carlos Martinez-Ortiz

Linearity measure for curve segments

In this paper, we consider linearity measure for a bounded length curves. First, we define a new linearity measure for open curve segments, and then extend method to closed curves (contours). The derived measures (for both, open curve segments and closed curves) are invariant with respect to similarity transformations. The linearity measure for open curve segments picks the value 1 if and only if the measured open line segment is a perfect straight line segment while the established linearity measures for closed curves never reach 1, as preferred.

The distance between shape centroids is less than a quarter of the shape perimeter

In this paper we consider the distance between the shape centroid computed from the shape interior points and the shape centroid computed from the shape boundary points. We show that the distance between those centroids is upper bounded by the quarter of the perimeter of the shape considered. The obtained upper bound is sharp and cannot be improved. Next, we introduce the shape centredness as a new shape descriptor which, informally speaking, should indicate to which degree a shape has a uniquely defined centre. By exploiting the result mentioned above, we give a formula for the computation of the shape centredness. Such a computed centredness is invariant with respect to translation, rotation and scaling transformations.

Curvature weighted gradient based shape orientation

Determining the orientation of a shape is a common task in many image processing applications. It is usually part of the image preprocessing stages and further processing may rely on an adequate method to determine the orientation. There are several methods for computing the orientation of a shape, each of them with its own strengths and weaknesses; a method which performs outstandingly for one application may have a poor performance for a different application. In this paper we present a new method for computing shape orientation based on the projection of the tangent vectors of a shape onto a line and weighting them using a function of the curvature. Some of the results from Zunic (2008) [14] are particular cases of the results presented here.

Compactness measure for 3D shapes

In this paper we propose a new compactness measure which defines the degree to which a 3D shape differs from a perfect sphere. The new measure is easy to compute and satisfies the following desirable properties: - it ranges over (0, 1] and gives the measured compactness equal to 1 if and only if the measured shape is a sphere; - it is invariant with respect to translations, rotations and scaling. Compared with a naive 3D compactness measure, which consider the relation between the shape volume and surface area, the new measure performs better in the case of shapes with deep intrusions and in case of compound shapes. In contrast to such a compactness measure, the new measure depends on the mutual position of the components inside a compound shape. Several experimental results are provided in order to illustrate the behaviour of the new measure.

Measuring Cubeness of 3D Shapes

In this paper we introduce a new measure for 3D shapes: cubeness. The new measure ranges over [0,1] and reaches 1 only when the given shapes is a cube. The new measure is invariant with respect to rotation, translation and scaling, and is also robust with respect to noise.

SHAPE RECTANGULARITY MEASURES

This paper introduces a family of rectangularity measures. The measures depend on two parameters which enable their flexibility, i.e. the possibility to adapt with respect to a concrete application. Several rectangularity measures exist in the literature, and they are designed to evaluate numerically how much the shape considered differs from a perfect rectangle. None of these measures distinguishes rectangles whose edge ratios differ, i.e. they assume that all rectangles (including squares) have the same shape. Such property can be a disadvantage in applications. In this paper, we consider differently elongated rectangles to have different shapes, and propose a family of new rectangularity measures which assigns different values to rectangles whose edge ratios differ. The new rectangularity measures are invariant with respect to translation, rotation and scaling transformations. They range over the interval ]0, 1] and attain the value 1 only for perfect rectangles with a desired edge ratio.

Measuring shape rectangularities

This paper introduces a family of rectangularity measures. Several rectangularity measures already exist in literature, and all of them evaluate how much the shape considered differs from a perfect rectangle. But all existing measures assume that all rectangles have the same shape, and a consequence is that these measures do not distinguish among the rectangles whose edge-ration differs. In this paper we consider that differently elongated rectangles have different shape and propose a family of new rectangularity measures which distinguish among such rectangles. New rectangularity measures are invariant with respect to translation, rotation and scaling transformations. In addition, we introduce a tuning parameter which enables an additional flexibility of the new measures with respect to performing applications.

Measuring cubeness in the limit cases

Abstract In this paper we show that the recently introduced family of the cubeness measures C β ( S ) ( β > 0 ) satisfy the following desirable property: lim β → ∞ C β ( S ) = 0 , for any given 3D shape S different from a cube. The result implies that the behaviour of cubeness measures changes depending on the selected value of β and the cubeness measure can be arbitrarily close to zero for a suitably large value of β. This also implies that for a suitable value of β, the measure C β ( S ) can be used for detecting small deviations of a shape from a perfect cube. Some examples are given to illustrate these properties.

A family of cubeness measures

AbstractIn this paper we introduce a family of cubeness measures,