Feature vector field and feature matching

Abstract

In this paper, we propose a feature vector field for images, which is built by the inner products and exterior products of image gradients. The feature vector field effectively represents image edges and feature points including corners and edge points with big curvature. Using the feature vector field, some novel descriptors are constructed for point matching and curve matching. The descriptors are all invariant to image Euclidean transformations and linear intensity changes. The experiments show that the descriptors also have a good adaptability to small image affine transformation, JPEG compression and nonlinear changes of intensity.

Introduction

Feature matching including point matching and curve matching plays an important role in many tasks of computer vision, such as image registration, 3D reconstruction, object recognition and video understanding. In recent years, a significant progress has been made in the field of feature matching, and quite a number of algorithms have been proposed. Next, we briefly review some related methods in literature.

Point matching: The point matching methods can be mainly divided into two groups: intensity distribution based methods and gradient distribution based methods. Both of them use a descriptor to represent intensity distribution or gradient distribution in local image regions. Cross-correlation [1], [2], [3] is a classical descriptor based on the intensity distribution, and spin image [4] is a more distinctive descriptor of this kind. Among the gradient distribution based descriptors, Scale Invariant Feature Transform (SIFT) proposed by Lowe [5] is the most famous one. Following [5], many similar variants are reported, such as shape context [6], GLOH [7] and SURF [8], etc. Besides the above two main types, some other kinds of techniques are also reported in literature, such as local jet [9], steerable filters [10], moment invariants [11] and complex filters [12], [13]. Mikolajczy and Schmid [7] evaluated these popular descriptors on real images, and the following conclusions are drawn: Firstly, the performance of descriptors is independent of feature detectors; Secondly, SIFT based descriptors perform best among descriptors with high dimensionality. Thirdly, the best low dimensional descriptors are gradient moments and steerable filters.

Curve matching: Compared to point matching, little progress has been made in curve matching (including line matching) in recent years. Only a few methods for curve matching are reported in literature until now. For images of planar surfaces, Lourakis et al. [14] reported an approach using “2 lines+2 points” projective invariants for line matching. Herbert et al. [15] presented a method for automatic matching in color images. The main drawback of this method is its heavy reliance on color information. While color provides a very strong cue for discrimination, it may fail in the case where color feature is not distinctive, such as on gray images or remote sensing images. Schmid and Zisserman [16] applied geometrical constraints (epipolar geometry, one parameter family of homographies and curvature of curves) and cross correlation to line matching and curve matching. Grouping matching strategy proposed by Deng and Lin [17] has the advantage that more geometric information is available for removing ambiguities, and can cope with more significant camera motion. However, it often has high complexity and is sensitive to line topological connections or inaccuracy of endpoints. Mikolajczyk et al. [18] also proposed a curve descriptor by generalizing SIFT point descriptor, and Orrite and Herrero [19] developed the continuity Hausdorff distance for matching partially occluded curve invariant under projective transformation. Most of the existing methods for curve matching either require prior knowledge or are limited to specific scenes, such as geometries between images or planar scenes.

In this paper, a feature vector field for images, which represents image edges and feature points including corners and edge points with high curvature, is introduced using inner product and exterior product of image gradients. Then, several novel descriptors, with invariance to image Euclidean transformation and linear change of intensity for point matching and curve matching, are constructed based on the proposed feature vector field. These descriptors are very simple to construct, they only need to compute the mean and standard deviation of feature vectors defined in sub-regions of the support region. Experiments show that the descriptors are robust and have good adaptability to image affine distortion, JPEG compression and nonlinear changes of intensity.

This paper is organized as follows. Section 2 introduces the inner and exterior correlation and defines the feature vector field for images. Section 3 elaborates how to construct the descriptors for feature matching in detail. The experimental results are reported in Section 4. Section 5 is some discussions on the feature vector field and the descriptors, and Section 6 concludes the paper.