Cosine integral images for fast spatial and range filtering

Elboher, Elhanan; Werman, Michael

doi:10.1109/icip.2011.6116704

Cited by 28 publications

(13 citation statements)

References 10 publications

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“…Due to caching considerations, our implementation is about twice as fast. For the integral image based methods there is no public implementation except CII [22] which was proposed by the authors of the current paper. tions for kernel approximation, we tested our proposed method with two sets of parameters.…”

Section: Resultsmentioning

confidence: 99%

“…Additions [20] 53 18 CII [22] 12k − 8 8k − 8 SII [24] 4k + 1 k Deriche [7] 8k − 2 8k Young and 4k 4k + 4 van Vliet [8] Proposed method 4k 2k Each constant c i can be used both in the negative interval [−p i , −p i−1 ] and in the positive one [p i−1 , p i ], however, this requires 2k constant function. Actually, the same approximation can be computed using 'weighted slices':…”

Section: Methodsmentioning

confidence: 99%

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Efficient and accurate Gaussian image filtering using running sums

Elboher

Werman

2012

2012 12th International Conference on Intelligent Systems Design and Applications (ISDA)

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This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the error function used for kernel approximation and its relation to the properties of the input signal. Based on natural image statistics we propose a quadratic form kernel error function so that the SSD error of the output image is minimized. We apply the proposed approach to approximate the Gaussian kernel by linear combination of constant functions. This results in a very efficient Gaussian filtering method. Our experiments show that the proposed technique is faster than state of the art methods while preserving similar accuracy.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Efficient and accurate Gaussian image filtering using running sums

Elboher

Werman

2012

2012 12th International Conference on Intelligent Systems Design and Applications (ISDA)

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“…Most of them share a general framework that they approximate a BLF by a bunch of spatial linear filters, i.e., convolutions. In dealing with a large filter window, each spatial filter is generally operated by the Fast Fourier Transform (FFT), the extended integral images [24]- [27], or the recursive filters [28]- [31]. For instance, Weiss [16] designed a BLF specialized in the box spatial kernel that can be convolved fast by a histogram technique.…”

Section: Introductionmentioning

confidence: 99%

Compressive Bilateral Filtering

Sugimoto

Kamata

2015

IEEE Trans. on Image Process.

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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.

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“…Equation 10 is computed as follows: for each k = 1...K the entire image is mapped by U k (denote I When w depends only on the value difference (x−y), a 1D frequency decomposition is also possible. This approach was suggested in [5] for fast image filtering. The function w(x−y) is expressed as a linear combination of cosine frequencies cos(k(x−y)), the discrete cosine transform (DCT) of w. Following the identity cos(k(x−y)) = cos(kx) cos(ky) + sin(kx) sin(ky), w can be approximated in the same form as Equation 8 by a linear combination of cosine and sine functions (vectors) weighted by the DCT coefficients.…”

Section: Based On Equationmentioning

confidence: 99%

The Generalized Laplacian Distance and Its Applications for Visual Matching

Elboer

Werman

Hel-Or

2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

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The graph Laplacian operator, which originated in spectral graph theory, is commonly used for learning applications such as spectral clustering and embedding. In this paper we explore the Laplacian distance, a distance function related to the graph Laplacian, and use it for visual search. We show that previous techniques such as Matching by Tone Mapping (MTM) are particular cases of the Laplacian distance. Generalizing the Laplacian distance results in distance measures which are tolerant to various visual distortions. A novel algorithm based on linear decomposition makes it possible to compute these generalized distances efficiently. The proposed approach is demonstrated for tone mapping invariant, outlier robust and multimodal template matching.

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Cosine integral images for fast spatial and range filtering

Cited by 28 publications

References 10 publications

Efficient and accurate Gaussian image filtering using running sums

Efficient and accurate Gaussian image filtering using running sums

Compressive Bilateral Filtering

The Generalized Laplacian Distance and Its Applications for Visual Matching

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