Geometrical image filtering with connected operators and image inpainting This paper deals with the joint use of connected operators and image inpainting for image filtering. Connected operators filter the image by merging its flat zones while preserving contour information. Image inpainting restores the values of an image for a destroyed or consciously masked subregion of the image domain. In the present paper, it will be shown that image inpainting can be combined with connected operators to perform an efficient geometrical filtering technique. First, connected operators are presented and their drawbacks for certain applications are highlighted. Second, image inpainting methodology is introduced and a structural image inpainting algorithm is described. Finally, a general filtering scheme is proposed to show how the drawbacks of connected operators can be efficiently solved by structural image inpainting.

Efficient and consistent recursive filtering of images with reflective extension Recursive filters are commonly used in scale space construction for their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of reflectively extended images for filters with symmetric denominator. We begin with an analysis of reflective extensions and their effect on nonrecursive filtering operators. Based on the nonrecursive case, we derive a formulation of recursive filtering on reflective domains as a linear but timevarying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring the same order of computation as the standard recursive filtering. We give experimental evidence to verify these claims.