Summed-area tables for texture mapping

Crow, Franklin C.

doi:10.1145/800031.808600

Cited by 667 publications

(266 citation statements)

References 8 publications

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“…

Binarize all images and detect the edges, with M athematica's built-in functions Binarize and EdgeDetect .

Calculate the integral image of each image. The process is detailed in [19]. The calculation of the integral image is not necessary, but vastly speeds up the algorithm by allowing quick calculation of the number of pixels in a given box.

We take ϵ from three pixels to four pixels, with a step size of only 1.

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Automatic prediction of tumour malignancy in breast cancer with fractal dimension

2016

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Breast cancer is one of the most prevalent types of cancer today in women. The main avenue of diagnosis is through manual examination of histopathology tissue slides. Such a process is often subjective and error-ridden, suffering from both inter- and intraobserver variability. Our objective is to develop an automatic algorithm for analysing histopathology slides free of human subjectivity. Here, we calculate the fractal dimension of images of numerous breast cancer slides, at magnifications of 40×, 100×, 200× and 400×. Using machine learning, specifically, the support vector machine (SVM) method, the F1 score for classification accuracy of the 40× slides was found to be 0.979. Multiclass classification on the 40× slides yielded an accuracy of 0.556. A reduction of the size and scope of the SVM training set gave an average F1 score of 0.964. Taken together, these results show great promise in the use of fractal dimension to predict tumour malignancy.

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“…

Binarize all images and detect the edges, with M athematica's built-in functions Binarize and EdgeDetect .

We take ϵ from three pixels to four pixels, with a step size of only 1.

…”

Section: Methodsmentioning

confidence: 99%

“…The process is detailed in [19]. The calculation of the integral image is not necessary, but vastly speeds up the algorithm by allowing quick calculation of the number of pixels in a given box.…”

Section: Methodsmentioning

confidence: 99%

Automatic prediction of tumour malignancy in breast cancer with fractal dimension

2016

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“…The method is known as integral images [24] (or summed area tables [6] in the context of texture mapping) and it allows to efficiently compute the sum of values of any image in a rectangular subset of a grid. A recent review of the integral image algorithm and its application is proposed in [10].…”

Section: Fast Nlm-p Using Integral Imagesmentioning

confidence: 99%

“…The source code associated to this publication is available at the IPOL webpage 6 . It corresponds to an ANSI C (C89) implementation of Algorithm 1 and Algorithm 5.…”

Section: Source Codementioning

confidence: 99%

Parameter-Free Fast Pixelwise Non-Local Means Denoising

Froment¹

2014

Image Processing on Line

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This article proposes a fast and open-source implementation of the well-known Non-Local Means (NLM) denoising algorithm, in its original pixelwise formulation. The fast implementation is based on the computation of patch distances using sums of lines that are invariant under a patch shift. The optimal parameters of NLM (in the average peak signal to noise ratio -PSNR -sense) are computed from an image database, thereby leading to a parameter-free NLM implementation. Comparison is performed with the parameter-free blockwise NLM implementation already proposed in IPOL journal by Buades, Coll and Morel. As expected the blockwise implementation offers better PSNR, at least when the noise standard deviation is large enough, but there is no significant difference in quality when performing visual inspection. The highlight is that the proposed parameter-free pixelwise NLM implementation is faster than the patchwise one by a factor of 6 to 49. Source CodeThe reviewed source code and documentation for the parameter-free fast pixelwise NLM algorithm are available from the web page of this article 1 . Compilation and usage instructions are included in the README.txt file of the archive.

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“…In addition, we describe a novel fractal analysis algorithm based on integral images [21] which speeds up the computation of these generalized dimensions by orders of magnitude, and we validate our algorithm and approach by applying it to increasingly complex data, producing meaningful results throughout. We also illustrate our method with the analysis of a set of histology images acquired from tissue samples of breast tumours with modified Bloom-Richardson grades of 1, 2, and 3, in which we determine the spatial scale intervals that exhibit statistically significant differences in fractal dimensions between the different tumour grades.…”

Section: Introductionmentioning

confidence: 99%

Scale-Specific Multifractal Medical Image Analysis

Braverman

Tambasco

2013

Computational and Mathematical Methods in Medicine

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Fractal geometry has been applied widely in the analysis of medical images to characterize the irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter rather than a single number. We describe this approach in the context of the more generalized Rényi entropy, in which we can also compute the information and correlation dimensions of images. In addition, we describe and validate a computational improvement to box-counting fractal analysis. This improvement is based on integral images, which allows the speedup of any box-counting or similar fractal analysis algorithm, including estimation of scale-dependent dimensions. Finally, we applied our technique to images of invasive breast cancer tissue from 157 patients to show a relationship between the fractal analysis of these images over certain scale ranges and pathologic tumour grade (a standard prognosticator for breast cancer). Our approach is general and can be applied to any medical imaging application in which the complexity of pathological image structures may have clinical value.

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Summed-area tables for texture mapping

Cited by 667 publications

References 8 publications

Automatic prediction of tumour malignancy in breast cancer with fractal dimension

Automatic prediction of tumour malignancy in breast cancer with fractal dimension

Parameter-Free Fast Pixelwise Non-Local Means Denoising

Scale-Specific Multifractal Medical Image Analysis

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