Fast algorithms for computing image local statistics in windows of arbitrary shape and weights Computing image local statistics is required in many image processing applications such as local adaptive image restoration, enhancement, segmentation, target location and tracking, to name a few. These computations must be carried out in sliding window of a certain shape and weights. Generally, it is a time consuming operation with perpixel computational complexity of the order of the window size, which hampers realtime applications. For acceleration of computations, recursive computational algorithms are used. However, such algorithms are available only for windows of certain specific forms, such as rectangle and octagon, with uniform weights. We present a general framework of fast parallel and recursive computation of image local statistics in sliding window of almost arbitrary shape and weights with perpixel computational complexity that is substantially of lower order than the window size. As an illustration of this framework, we describe methods for computing image local moments such as local mean and variance, image local histograms and local order statistics (in particular, minimum, maximum, median), image local ranks, image local DFT, DCT, DcST spectra in polygonshaped windows as well as in windows with nonuniform weights, such as Sine lobe, Hann, Hamming and Blackman windows.

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.