Coarse-to-fine planar object identification using invariant curve features and B-spline modeling

Abstract

This paper presents a hybrid algorithm for coarse-to-fine matching of affine-invariant object features and B-spline object curves, and simultaneous estimation of transformation parameters. For coarse-matching, two dissimilar measures are exploited by using the significant corners of object boundaries to remove candidate objects with large dissimilarity to a target object. For fine-matching, a robust point interpolation approach and a simple gradient-based algorithm are applied to B-spline object curves under MMSE criterion. The combination of coarse and fine-matching steps reduces the computational cost without degrading the matching accuracy. The proposed algorithm is evaluated using affine transformed objects.

Introduction

The identification, matching and analysis of objects of interest are of prime importance in application domains including target tracking in traffic [1], [2], robot autonomous navigation [3], reconstruction of body structures in medicine [4], the use of eyes as an interface for controlling computer graphics [5], gesture analysis and recognition [6], image browsing and retrieval [7], and object-oriented video coding [8]. Object-matching means establishing correspondences between object boundaries, shapes, texture and various other features in a set of images. Since an object may undergo various affine transformations including rotations, scalings and translations, object-matching also means computing any transformation parameters based on 2D or 3D object representations [9]. These methods can be further classified as boundary, region and model-based methods [10]. If an object is simple, the matching and analysis of affine objects could be successfully performed using boundary-based approaches.

A direct approach is to match object boundary curves extracted from images, where the objects may undergo various affine transformations (e.g. rotations, scalings and translations) and small deformations. One method to compare two object curves is to match the corresponding points on two curves assuming affine rigid objects [11]. However, the method is both sensitive to noise because of imperfect data, and to imprecise correspondences. Instead of point matching, a variety of less noise-sensitive approaches have been proposed based on comparing corresponding line segments and polygonal arcs [12], [13]. Many techniques have also been proposed for representing a curve by a set of features or by models. These include Fourier descriptors [14], B-splines [15], [16], autoregressive model [17], moments [18], curvatures [19], HMM models [20] and wavelets [21]. Among these methods, B-splines are often used in computer graphics because of their properties of continuity, local shape controllability, and affine invariance [22]. In [15] a scheme for matching and classification of B-spline curves is presented. However, it requires two separate stages for classifying objects and estimating the corresponding affine parameters. Furthermore, the method uses the point where a curve crosses the positive horizontal x-axis, which is arbitrary for affine curves, as the starting point. This will result in a lack of good correspondences between curve segments and hence increase the error in curve matching.

Motivated by the above problems, we present a hybrid two-step matching scheme which explores both dissimilarities of object features and of B-spline approximated curves. In the feature-based coarse-matching step, a small number of significant corners is extracted from each discrete object curve to form affine-invariant object features. Since objects may undergo various affine transformations, features which are affine invariant are more attractive for object-matching. Many curve features, e.g., arc length and the area within an object boundary, are affine invariant [23], [24]. We introduce two dissimilar measures on affine-invariant features based on significant corners. These enable a fast identification between affine and non-affine objects based on a small set of features. To maintain high reliability in object identification, only candidate objects with large affine dissimilarities to a target object are rejected in the coarse-matching step. The non-rejected objects are then passed to the fine-matching process, which not only enables matching based on the entire curve-shape information, but also enables the estimation of parameters associated with affine objects. We also introduce a gradient-based algorithm which simultaneously matches B-spline modeled object curves and estimates transformation parameters. This algorithm incorporates a robust method of assigning corresponding curve points via interpolation.

The remaining of the paper is organized as follows. Section 2 describes the coarse-matching algorithm including the method for estimating significant corners and the two dissimilar measures. Section 3 describes the fine-matching algorithm, including the selection of corresponding curve points and the gradient-based MMSE matching algorithm. Section 4 presents the experimental results and evaluations. Finally Section 5 concludes the paper.