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Let (mathbb {I}) and (mathbb {I}^{2}) be the integral image of the input image I and the squared intensity image, i.e., an image whose value at pixel (x,y) is I 2 x,y), we have: mu x,y,d) = frac{1}{D}f(mathbb{I},x,y,d) (14).
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where is the integral image, and is the original image pixel's value.
where (mathbb {P}_{k}) is the integral image of the posterior probability image.
where (mathbb {I}^{l}) is the integral image of I l, and Z the normalizing constant such that (sum _{l} h_{l} = 1).
It is worthy to be noted that the integral image can be used to speed-up the calculation of histogram in local window around each pixel that is needed for AHE as well.
Once the K means, μ 1,…,μ K, are updated, the standard deviations are recomputed via the integral image (mathbb {D}_{k}) of the following squared difference image D k : D_{k} x,y)=P_{k} x,y),left(I x,y -mu^{(t+1)}_{k}right)^{2}.
Each feature component i is used to generate the integral image A uv (i) (bottom left) and the crossed product between features i and j is used to calculate the second order integral images B uv (i,j).
To speed-up the mixture parameter estimation, we propose an EM algorithm that is also based on the integral image data structure.
A stored address should hold the position of a particular sub-window and its scale; there is no need for two-dimensional positioning, since the Integral Image is created as a monodimensional table for a better RAM storage.
And Radon transformation is the integral of the image pixels on each straight line, then each straight line in the image will become a bright spot in the ρ – θ space, which turn the line detection into detecting highlights in Radon domain.
A copy of the integral image is available to each block as well as three pairs of logical memory are working in ping pong to accelerate the processing.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com