Image smoothing using a metric tensor for an affine invariant scale space

Abstract

This paper proposes a new image smoothing method using a metric tensor for affine invariant scale space. In the field of image processing and recognition, Gaussian filtering is a common procedure for image smoothing. For example, scale space construction based on Gaussian filtering is sometimes used as a preprocessing of various image processing tasks. However Gaussian filtering is not affine invariant. This paper proposes a new method for image smoothing that is invariant under such affine transformation that does not change the area of any region in the image. It is shown that a scale space representation can be constructed collaterally with the image smoothing. Experimental results show that the proposed method is almost never affected by affine transformation different from usual Gaussian filtering. In the proposed method, processing results are expected to be not affected much by variation of the viewpoint.