Affine invariant functions are constructed in spatial domain. Unlike the previous affine representation functions in transform domain, these functions are constructed directly on the object contour without any transformation. To eliminate the effect of the choice of points on the contour, an affine invariant function using seven points on the contour is constructed. For objects with several separable components, a closed curve is derived to construct the affine invariant functions. Several experiments have been conducted to evaluate the performance of the proposed method. Experimental results show that the constructed affine invariant functions can be used for object classification.
Recognizing objects that are subjected to certain viewing transformation is important in the field of computer vision [
The extraction of affine invariant features plays a very important role in object recognition and has been found application in many fields such as shape recognition and retrieval [
Many algorithms have been developed for affine invariant features extraction. Based on whether the features are extracted from the contour only or from the whole-shape region, the approaches can be classified into two main categories: region-based methods and contour-based methods [
Due to the spatial and frequency localization property of wavelets, many wavelet-based algorithms have been developed for the extraction of affine invariant features. It is reported that these wavelet-based methods outperform Fourier descriptors [
However, in all these methods, AIFs are constructed in transform domain. That is to say, the shape contour is firstly transformed by a linear operator (e.g., wavelet transform, Fourier transform, etc.). Then AIFs are constructed from the transformed contour. In this paper, we construct AIF directly by the shape contour without any transformation. Equidistant Points on the object contour are used to construct AIFs. To eliminate the effect of the choice of points on the contour, an AIF using seven points on the contour is constructed. In addition, the shape contour is not available [
The rest of the paper is organized as follows: in Section
Consider a parametric point
If
To establish one-to-one relation between two contour, the object contour should be parameterized. The arc length parameter transforms linearly under any liner transformation up to the similarity transform including translation, rotation, and scaling. But, it is not a suitable parameter for the constructing affine invariant function.
There are two parameters which are liner under an affine transformation: the affine arc length [ For the discrete object contour Select the starting point on object contour as the starting point Using the same method, from point
In the experiments of this paper, the object contour or GC is normalized and resampled such that
In this part, we will derive invariant function from the normalized object contours. Correlation coefficient is used to measure the similarity of two AIFs. To construct AIFs from objects with several separable components, we convert the object into a closed curve by performing projections along lines with different polar angles.
Let
Let
Figure
(a) A plane object. (b) The boundary of plane in (a). (c) The invariant function for the boundary in (b).
(a) An affine transformation version of Figure
(a) The Chinese character “Yang’’. (b) GC of Chinese in (a). (c) The AIF for GC in (b).
Experimental results show that the choice of
We have seen from Figures
In this paper, we construct AIFs in spatial domain. Therefore, to eliminate the effect of starting point, we use correlation coefficient as in [
AIFs given in (
In this section, we evaluate the discriminate ability of the proposed method. In the first experiment, we examine the proposed method by using some airplane images. Object contours can be derived from these images. In the second experiment, we evaluate the discriminate ability of the proposed method by using some Chinese characters. These characters have several separable components, and contours are not available for these objects.
In the following experiments, the classification accuracy is defined as
The first experiment is conducted to classify the airplane images. Seven airplane images shown in Figure
Classification accuracies for different
32 | 64 | 96 | 128 | |
Accuracy rates | 90.05% | 96.51% | 93.03% | 87.59% |
160 | 192 | 224 | AIF in ( | |
Accuracy rates | 93.03% | 96.51% | 88.61% | 92.52% |
The airplane models.
In this experiments, we extract affine invariant features from objects with several separable components. 10 Chinese characters shown in Figure
Test characters used in the second experiment.
In this paper, we construct AIFs in spatial domain. Unlike the previous affine representation functions in transform domain, these AIFs are constructed directly on the object contour without any transformation. This technique is based upon object contours, parameterized by an affine invariant parameter, and shifting of the contour. To eliminate the effect of the choice of points on the contour, an AIF using seven points on the contour is constructed. For objects with several separable components, a closed curve is derived to construct the AIFs. Several experiments have been conducted to evaluate the performance of the proposed method.
This work was supported in part by the National Science Foundation under Grant 60973157, 61003209, in part by the Natural Science Foundation of Jiangsu Province Education Department under Grant 08KJB520004.