Compactification of Affine Transformation Filter Using Tensor Decomposition

Keypoint matching is used in a variety of tasks such as specific object recognition and panoramic image generation. Affine-SIFT (ASIFT) enables affine invariant matching by generating many affine transformation images of an input image. It describes the scale-invariant feature transform (SIFT) features of the generated image. However, ASIFT must perform multiple costly online computations for affine transformation. We represent an oriented FAST and rotated BRIEF (ORB) descriptor in a linear filter subjected to many affine transformations. We calculate the affine features by convolving the generated filter with the patch image. However, convolving the 19,200 filters generated by the affine transformation is inefficient. In order to reduce the convolution processing, the affine transformation filter is made compact by a factorization method. We built a 4-order tensor using the affine transformation filter. The 4-order tensor decomposes into the Tucker model. We reduce dimensions appropriately for each mode. In this way, we propose a compact and accurate feature description. Our evaluation experiments confirmed that the proposed method reduces the processing time to 19% while maintaining the same precision as singular value decomposition, which is the conventional method.

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