2D shape representation and similarity measurement for 3D recognition problems: An experimental analysis

Abstract

One of the most usual strategies for tackling the 3D object recognition problem consists of representing the objects by their appearance. 3D recognition can therefore be converted into a 2D shape recognition matter. This paper is focused on carrying out an in depth qualitative and quantitative analysis with regard to the performance of 2D shape recognition methods when they are used to solve 3D object recognition problems. Well known shape descriptors (contour and regions) and 2D similarities measurements (deterministic and stochastic) are thus combined to evaluate a wide range of solutions. In order to quantify the efficiency of each approach we propose three parameters: Hard Recognition Rate (Hr), Weak Recognition Rate (Wr) and Ambiguous Recognition Rate (Ar). These parameters therefore open the evaluation to active recognition methods which deal with uncertainty. Up to 42 combined methods have been tested on two different experimental platforms using public database models. A detailed report of the results and a discussion, including detailed remarks and recommendations, are presented at the end of the paper.

Introduction

Three-dimensional object recognition is the process of finding an object in a scene. This task implies determining the object’s identity and/or its pose (position and orientation) with regard to a particular reference frame. For instance, in object manipulation with robots, the pose of the object must be extracted through an accurate estimation of the translation and rotation parameters with regard to the robot coordinate system.

In the field of three-dimensional object recognition using a monocular sensor, two main streams appear: view-based (or appearance-based) approaches and structural (or primitive-based) approaches. Since primitive-based approaches yield a low performance when unexpected changes occur in the scene, view-based methods have become a popular representation scheme owing to their robustness to noise, photometric effects, blurred vision and changing illumination. The main advantage of this approach (view-based methods) is that the image of the query object can be directly compared with a set of stored images in a database which are efficient and robust to variations in the scene. Indeed, the 3D problem has led to a 2D shape recognition question in which multiple views associated with the object from different points of views have to be handled. Each view in the database is thus associated with a particular viewpoint that corresponds with the current camera position (position and orientation). From here on, we shall use the term ‘shape’ to refer to the appearance of the object from a specific viewpoint – in a 2D context and ‘object’ as a general word to describe something in a 3D dimension environment. The 3D object pose estimation will signify geometric transformations between the camera position in the scene and the viewpoint from which the object is viewed in the database, whereas shape pose estimation will concern rotation, translation and scale in a 2D context.

Meanwhile, when a single view is taken to recognize an object, the principal problem is that one 2D image frequently provides insufficient information with which to identify the object and correctly estimate its pose. Uncertainty and ambiguity problems frequently arise in such cases owing to the fact that no depth information is available. Different objects might therefore seem to be quite similar from different viewpoints, which affect the robustness of the 3D recognition system. In active recognition systems this handicap is addressed by moving the camera to different positions and processing several captures of the object until the uncertainty is resolved. Classical active recognition systems are made up of three main stages: the shape recognition algorithm – which concerns shape identification and shape pose estimation in a 2D context, the fusion stage – in which the combination of the hypotheses obtained from each sensor position is carried out, and the next-best-view planning stage – in which the optimal next sensor positions are computed (González et al., 2008). The two last stages are used to improve the active recognition efficiency, thus reducing hypothesis uncertainty.

Since the view-based strategy converts 3D object recognition into a 2D shape recognition problem, an enormous amount of approaches concerning how to represent 2D shapes and how to measure similarities between shapes can be found in literature (Bustos et al., 2005). However, to the best of our knowledge, no comparative study of different 2D shape recognition algorithms adapted to view-based 3D recognition systems has yet been reported. In order to provide a solution to this issue, the goal of this paper is simply to carry out an in depth qualitative and quantitative analysis with regard to the performance of 2D shape recognition methods when they are used to solve 3D object recognition problems.

The paper is structured as follows. In Section 2 we tackle the requirements of 2D shape representation models, and compare different representation, identification and shape pose estimation methods to be implemented in 3D applications. Several unclear questions concerning the performance of shape recognition systems in 3D recognition environments are also discussed. Section 3 presents the statement of the experimental tests developed in Sections 4 Recognition using Platform 1, 5 Recognition tests using Platform 2. Sections 4 Recognition using Platform 1, 5 Recognition tests using Platform 2 are focused on evaluating the recognition performance in systems using two platforms. Finally, in Section 6 we present a discussion of the experimental results along with our conclusions.