Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
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.)
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
Efficient and consistent recursive filtering of images with reflective extension
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Perfect reconstruction IIR digital filter banks supporting nonexpansive linear signal extensions
IEEE Transactions on Signal Processing
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Recursive filters are widely used in image analysis due to 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 symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists.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 less computation than the standard recursive filtering. We give experimental evidence to verify these claims.