Fast Algorithms for Low-Level Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matrix computations (3rd ed.)
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Recursive filtering of images with symmetric extension
Signal Processing
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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 non-recursive case, we derive a formulation of recursive filtering on reflective domains as a linear but time-varying 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.