doi:10.1016/j.patrec.2004.11.006 
Copyright © 2004 Elsevier B.V. All rights reserved.
A new scheme for extraction of affine invariant descriptor and affine motion estimation based on independent component analysis
Department of Electronics Engineering, Fudan University, No. 220, Handan Road, Shanghai 200433, China
Received 18 September 2004.
Available online 10 December 2004.
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Abstract
This paper proposes a new scheme based on independent component analysis (ICA) for object recognition with affine transformation and for affine motion estimation between video frames. For different affine shapes of a recognized object, an invariant descriptor can be extracted by ICA, and it can solve some object recognition problems. This method also can be used to estimate the affine motion between two frames, which is important in high compression rate coding such as MPEG4 or MPEG7 standard. Simulation results show that the proposed method has a better performance than other traditional methods in pattern recognition and affine motion estimation.
Keywords: Independent component analysis (ICA); Affine invariant descriptor; Negentropy; Kurtosis; Affine motion estimation
Fig. 1. (a) Object “a”; (b) affine transformed shape of object “a”.
Fig. 2. (a) Two sampled random variables of Xa; (b) Two sampled random variables of Xa′.
Fig. 3. The results, Ya and 
by using the proposed method for Xa and Xa′. (a) Two random variables of Ya; (b) Two random variables of MYa′.
Fig. 4. The invariant descriptor of Fig. 1.
Fig. 5. Test shape: (a) original shape, (b) its affine transformed result.
Fig. 6. The comparative result of proposed method, Fourier method and BSM method.
Fig. 7. (a) Ten known airplane models. (b) The affine transformed images correspond to the model images in (a) respectively.
Fig. 8. Affine parameters estimation. (a–c) Real key images taken from different angles. (d) The affine parameters estimation result between (b) and (a) by our method. (e) The affine parameters estimation result between (c) and (a) by our method. (f) The affine parameters estimation result between (b) and (a) by Fourier method. (g) The affine parameters estimation result between (c) and (a) by Fourier method.
Table 1.
Kurtosis of Xa, Xa′, Ya and MYa′
Table 2.
Actual motion and estimated parameters
Table 3.
The recognition results for test images in different deflections using proposed method
Table 4.
The recognized results for each test image using our method and the Fourier method (the viewpoint angle degree is 40-Horizontal and 10-Vertical)
Table 5.
The average time of affine motion estimation for different number of contour points
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