  Computational complexity of the brute-force implementation of the bilateral
filter (BF) depends on its filter kernel size. To achieve the constant-time BF
whose complexity is irrelevant to the kernel size, many techniques have been
proposed, such as 2D box filtering, dimension promotion, and shiftability
property. Although each of the above techniques suffers from accuracy and
efficiency problems, previous algorithm designers were used to take only one of
them to assemble fast implementations due to the hardness of combining them
together. Hence, no joint exploitation of these techniques has been proposed to
construct a new cutting edge implementation that solves these problems. Jointly
employing five techniques: kernel truncation, best N -term approximation as
well as previous 2D box filtering, dimension promotion, and shiftability
property, we propose a unified framework to transform BF with arbitrary spatial
and range kernels into a set of 3D box filters that can be computed in linear
time. To the best of our knowledge, our algorithm is the first method that can
integrate all these acceleration techniques and, therefore, can draw upon one
another's strong point to overcome deficiencies. The strength of our method has
been corroborated by several carefully designed experiments. In particular, the
filtering accuracy is significantly improved without sacrificing the efficiency
at running time.
