This paper presents an efficient constant-time bilateral filter that produces a near-optimal performance tradeoff between approximate accuracy and computational complexity without any complicated parameter adjustment, called a compressive bilateral filter (CBLF). The constant-time means that the computational complexity is independent of its filter window size. Although many existing constant-time bilateral filters have been proposed step-by-step to pursue a more efficient performance tradeoff, they have less focused on the optimal tradeoff for their own frameworks. It is important to discuss this question, because it can reveal whether or not a constant-time algorithm still has plenty room for improvements of performance tradeoff. This paper tackles the question from a viewpoint of compressibility and highlights the fact that state-of-the-art algorithms have not yet touched the optimal tradeoff. The CBLF achieves a near-optimal performance tradeoff by two key ideas: 1) an approximate Gaussian range kernel through Fourier analysis and 2) a period length optimization. Experiments demonstrate that the CBLF significantly outperforms state-of-the-art algorithms in terms of approximate accuracy, computational complexity, and usability.

There have been many applications of the Hilbert curve, such as image processing, image compression, computer hologram, etc. The Hilbert curve is a one-to-one mapping between N-dimensional space and one-dimensional (l-D) space which preserves point neighborhoods as much as possible. There are several algorithms for N-dimensional Hilbert scanning, such as the Butz algorithm and the Quinqueton algorithm. The Butz algorithm is a mapping function using several bit operations such as shifting, exclusive OR, etc. On the other hand, the Quinqueton algorithm computes all addresses of this curve using recursive functions, but takes time to compute a one to-one mapping correspondence. Both algorithms are complex to compute and both are difficult to implement in hardware. In this paper, we propose a new, simple, nonrecursive algorithm for N-dimensional Hilbert scanning using look-up tables. The merit of our algorithm is that the computation is fast and the implementation is much easier than previous ones.

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There has been significant recent interest in stereo correspondence algorithms for use in the urban automotive environment [1,2,3]. In this paper we evaluate a range of dense stereo algorithms, using a unique evaluation criterion which provides quantitative analysis of accuracy against range, based on ground truth 3D annotated object information. The results show that while some algorithms provide greater scene coverage, we see little differentiation in accuracy over short ranges, while the converse is shown over longer ranges. Within our long range accuracy analysis we see a distinct separation of relative algorithm performance. This study extends prior work on dense stereo evaluation of Block Matching (

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