Method and system for fast normalized cross-correlation between an image and a Gaussian for detecting spherical structures

A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform a method of identifying spherical objects in a digital image, wherein said image comprises a plurality of intensities corresponding to a domain of points in a D-dimensional space, said method comprising the steps of:

• calculating a local cross-correlation between a point in the domain of the image and a Gaussian spatial filter GK of standard deviation σK about a Gaussian neighborhood GN of standard deviation σN about the point, wherein the local cross-correlation correlation is calculated by convolving over a difference of the Gaussians GN and GK according to the formula
• <I,GK>P=K·(GN,K−GN)*I(p)
• wherein I(p) is the image at the point p, GN GK=K.GN,K with
• K
• =
• 1
• (
• 2
• ⁢
• π
• ⁡
• (
• σ
• N
• 2
• +
• σ
• K
• 2
• )
• )
• D
• being constant,
• σ
• N
• ,
• K
• =
• σ
• N
• ⁢
• σ
• K
• (
• σ
• N
• 2
• +
• σ
• K
• 2
• )
• ,
• and * is a convolution operator;
• calculating a local standard deviation of the point in the image;
• calculating a local standard deviation of the spatial filter;
• calculating a cross-correlation ratio by dividing the local cross-correlation by the product of the local standard deviation of the image and the local standard deviation of the spatial filter;
• and
• analyzing the cross-correlation ratio to determine whether an object about said point is spherically symmetric.

A method of identifying spherical objects in a digital image, wherein said image comprises a plurality of intensities corresponding to a domain of points in a D-dimensional space, said method comprising the steps of:

• providing a Gaussian neighborhood GN of standard deviation σN about a point p in the domain of the image I;
• providing a Gaussian kernel GK of standard deviation σK;
• calculating a local cross-correlation of the Gaussian kernel about the point p in the neighborhood GN
• calculating a local variance of the Gaussian kernel according to the formula
• σ
• 2
• ⁡
• (
• G
• K
• )
• =
• 1
• (
• 2
• ⁢
• π
• ⁢
• ⁢
• σ
• K
• ⁢
• (
• σ
• K
• 2
• +
• 2
• ⁢
• σ
• N
• 2
• )
• )
• D
• -
• 1
• (
• 2
• ⁢
• π
• ⁡
• (
• σ
• K
• 2
• +
• σ
• N
• 2
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• D
• calculating a square root of the local variance of the Gaussian kernel in order to determine its local standard deviation;
• and
• calculating a cross-correlation ratio by dividing the local cross-correlation by the product of the local standard deviation of the image and the local standard deviation of the Gaussian kernel,
• wherein the cross-correlation ratio can take continuous values from −1, and wherein a spherically symmetric Gaussian shaped object has a value of 1.