Shape measurement using LIP-signature

Highlights

• An invariant shape signature to non-linear deformations and similarity transforms.

• A unifying approach for measurement of orientation, orientability and linearity.

• Ability to deal with compound shapes containing different connected components.

• Orientability can be used as a good shape feature for shape description.

• An effective shape descriptor.

Abstract

A novel approach is proposed for orientation measurement and shape representation by exploiting some beneficial invariant geometric properties in the projection space. It is based on the introduction of a new shape signature (LIP-signature) which is invariant to additive noise, non-linear deformations, and geometric transformations such as rotation, scaling and translation (RST transformations). The proposed shape signature contains meaningful geometric information that can be easily exploited for a unifying approach of orientation/linearity measurement by detecting the possible orientation and the orientation merit of a given shape. In addition, a simple yet effective shape descriptor is also introduced by taking into account the beneficial properties of LIP-signature. Our methods can be directly applied to complex shapes composed of several closed contours or to degraded shapes being affected by additive noise, occlusion or other non-linear deformations. Different experiments validate the interest of the proposed approach.

Introduction

Shape description is an important topic which has been exploited in many applications such as object recognition, shape retrieval thanks to the high discriminant power of shapes. Although numerous methods have been introduced, conception of a good shape descriptor remains a challenging problem. Two main challenges make the recognition of shape instances from a same category difficult: similarity transformations (RST) such as rotation, scaling, translation and nonlinear deformations such as noise, occlusion. Thus, a good shape description should be invariant to similarity transformations and insensible against nonlinear deformations. In addition, it should be discriminative and informative that tolerates the differences of shapes from the same class and but it also allows to distinguish shapes from different categories (Rosin, 2003).

Generally, there are two main directions for recognition tasks using shape information. The first one describes shapes based on different types of transforms. It is suitable for generic applications such as shape retrieval (Zhang and Lu, 2003), shape matching (Jia, Fan, Liu, Li, Luo, Guo, 2016, Jia, Fan, Luo, Liu, Guo, 2014, Li, Tan, 2010, Wang, Bai, You, Liu, Latecki, 2012) because it can provide high dimensional feature vectors. In order to work in the context of visual search, the methods in this direction should also be robust against projective/perspective deformations. Popular methods are based on Radon-based transform (Hasegawa, Tabbone, 2014, Hoang, Tabbone, 2012, Tabbone, Wendling, Salmon, 2006), Fourier-based transform (Bowman, Soga, Drummond, 2001, Chen, Defrise, Deconinck, 1994, Hoang, Tabbone, 2012, Zhang, Lu, 2002), Hough transforms (Ballard, 1981), image moments (Hoang, Tabbone, 2014, Miao, 2000), projective invariant (Jia, Fan, Liu, Li, Luo, Guo, 2016, Li, Tan, 2010), characteristic ratio (Jia et al., 2014), height function (Wang et al., 2012), geometrical approaches (Latecki, Lakämper, 2000, Mokhtarian, 1995). The second one aims at measuring geometric properties of shapes. Therefore, the methods in this direction usually have clear geometric interpretation and can solve some specific problems such as circular separability (Fisk, 1986), ellipse detection (Nguyen and Kerautret, 2011), polygon approximation (Nguyen and Debled-Rennesson, 2009), circularity measurement (Nguyen and Debled-Rennesson, 2010), sigmoidality measurement Rosin (2004), polygonality measurement (Nguyen and Hoang, 2015), or arc segmentation (Nguyen and Debled-Rennesson, 2011). For simplicity, from now on, this direction is called shape measurement.

In this paper, we are interested in shape measurement by introducing a novel method for orientation detection and measurement of orientability and linearity of a given shape. We then review hereafter existing methods in the literature concerning these topics. Measuring shape’s orientation, which is an interesting topic in shape measurement, has been considered in numerous works (Ha, Moura, 2003, Ha, Moura, 2005, Lin, 1993, Lin, 1996, Tsai, Chou, 1991, Zunic, Rosin, Kopanja, 2006). The classical approach (Jain et al., 1995) defined orientation as the axis of the least second moment of inertia. Tsai and Chou (1991) proposed to detect principal axes of shapes having symmetry properties. Lin, 1993, Lin, 1996 defined shape orientation using universal principal axes, formed of half lines starting from the shape centroid. Ha and Moura (2003) detected orientation of shape by removing orientational ambiguity from an arbitrary shape. Zunic et al. (2006a) presented a measure based on the degree that a shape has a dominant orientation. Zunic and Rosin (2009) determined orientation by maximizing the total length of all line segments inside shape that have the same direction. The orientation of multi-component shapes can also be determined by using boundary information (Rosin, Zunic, 2011, Zunic, Stojmenovic, 2008). In Shen and Ip (1997), the orientation of a shape is defined by at most three non-zero generalized complex moments. Martinez-Ortiz and Zunic (2010) computed shape orientation utilizing the projection of the tangent vectors of a shape onto a line and weighting them using a function of the curvature. Tzimiropoulos et al. (2009) used image moments to propose a unifying framework for shape orientation/symmetry detection. Beside the detection of orientation of shapes, deciding how clearly an arbitrary shape has an orientation, called orientability or orientation merit, was also considered. In Zunic et al. (2006b), the orientability is defined by considering the bounding box including a given shape.

On the other hand, linearity measurement is to define how an open curve, a set of planar points or a shape is similar to a line segment. It is a classical topic in many domains such as pattern recognition, visualization and particularly discrete geometry. Existing methods in discrete geometry (Jean Pierre Reveillès, 1991, Melter, Rosenfeld, 1989) established different criteria for recognition of line segment. Different works (Rosin, Pantovic, Zunic, 2016, Stojmenovic, Nayak, Zunic, 2008, Zunic, Rosin, 2011) estimate how an open curve is similar to a line segment.

Our contributions for shape measurement, presented in this paper, is five-fold. First, we present a novel shape signature, called LIP-signature, that is invariant to RST transformations and robust against non linear deformations. Second, we introduce a novel approach for orientation measurement of shapes based on the rich geometric information of LIP-signature. Third, we also propose to measure orientability of the considered shape that is still rarely introduced, except Zunic et al. (2006b). It could be also considered as a linearity measure. Based on LIP-signature, our proposed measures are robust against RST transformations, additional noise and non linear deformations. Moreover, they can be applied for compound shapes containing different connected components. It is well-known that contour-based methods can not be used for these cases. Fourth, we propose to use the normalized LIP-signature to introduce an effective descriptor for shape classification thanks to its beneficial properties. Finally, we introduce two available datasets for evaluation of shape measurement methods.

The rest of this paper is organized as follows. Section 2 proposes a new shape signature, called LIP-signature, shows its important geometric properties and proposes an efficient implementation of LIP-signature based on Radon transform. The next section addresses the problem of orientation measurement using LIP-signature, and introduces a shape descriptor based on the normalization of LIP-signature. The experiments in Section 4 validate the interest of our proposed approach. The last section presents the conclusions and perspectives of our work.