Volterra filters for enhancement of contours in images
First Claim
Patent Images
1. A method of enhancing contours in a noisy image, said method comprising the steps of:
- a) capturing said noisy image as a first distribution m of spatially distributed intensity values b) transforming said intensity values of said first distribution m into a second distribution U of spatially distributed intensity values representing an enhanced image having enhanced contours therein, by using a transformation model, which defines a cubic filter, as follows;
U=a0+a3[Gm+G*m]+a2[G(diag m)Gm+Gm·
G*m+G*(diag m)G*m]+a1[G(diag m)G(diag m)Gm+G(diag m)Gm·
G*m+Gm·
G*(diag m)G*m+G*(diag m)G*(diag m)G*m],where;
diag m is a diagonal operator comprising a matrix with said first distribution m along the diagonal of said matrix and zeroes elsewhere;
the operation “
·
”
indicates the taking of a componentwise product of two vectors, wherein in s·
v evaluated at location r is the product of the two numbers s(r) and v(r), where s and v are each functions of r, a0, a1, a2, and a3 are real-valued parameters controlling the relative importance of constant, linear, quadratic, and cubic terms, respectively, in said transformation model;
G=G(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a forward direction along said contour; and
G*=G*(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a backward direction along said contour.
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Abstract
Enhancement of contours in images that are noisy or otherwise corrupted is important in medical imaging, scanning for weapons detection, and many other fields. Here, the Curve Indicator Random Field (CIRF) is used as a model of uncorrupted images of contours for constructing linear, quadratic and cubic Volterra filters involving a number of adjustable parameters.
36 Citations
20 Claims
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1. A method of enhancing contours in a noisy image, said method comprising the steps of:
-
a) capturing said noisy image as a first distribution m of spatially distributed intensity values b) transforming said intensity values of said first distribution m into a second distribution U of spatially distributed intensity values representing an enhanced image having enhanced contours therein, by using a transformation model, which defines a cubic filter, as follows; U=a0+a3[Gm+G*m]+a2[G(diag m)Gm+Gm·
G*m+G*(diag m)G*m]+a1[G(diag m)G(diag m)Gm+G(diag m)Gm·
G*m+Gm·
G*(diag m)G*m+G*(diag m)G*(diag m)G*m],where;
diag m is a diagonal operator comprising a matrix with said first distribution m along the diagonal of said matrix and zeroes elsewhere;
the operation “
·
”
indicates the taking of a componentwise product of two vectors, wherein in s·
v evaluated at location r is the product of the two numbers s(r) and v(r), where s and v are each functions of r, a0, a1, a2, and a3 are real-valued parameters controlling the relative importance of constant, linear, quadratic, and cubic terms, respectively, in said transformation model;
G=G(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a forward direction along said contour; and
G*=G*(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a backward direction along said contour. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A computer readable medium including computer instructions for carrying out a method of enhancing contours in a noisy image, said method comprising the steps of:
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a) capturing said noisy image as a first distribution m of spatially distributed intensity values b) transforming said intensity values of said first distribution m into a second distribution U of spatially distributed intensity values representing an enhanced image having enhanced contours therein, by using a transformation model, which defines a cubic filter, as follows; U=a0+a1[Gm+G*m]+a2[G(diag m)Gm+Gm·
G*m+G*(diag m)G*m]+a3[G(diag m)G(diag m)Gm+G(diag m)Gm·
G*m+Gm·
G*(diag m)G*m+G*(diag m)G*(diag m)G*m],where;
diag m is a diagonal operator comprising a matrix with said first distribution m along the diagonal of said matrix and zeroes elsewhere;
the operation “
·
”
indicates the taking of a componentwise product of two vectors, wherein in s·
v evaluated at location r is the product of the two numbers s(r) and v(r), where s and v are each functions of r, a0, a1, a2, and a3 are real-valued parameters controlling the relative importance of constant, linear, quadratic, and cubic terms, respectively, in said transformation model;
G=G(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a forward direction along said contour; and
G*=G*(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a backward direction along said contour. - View Dependent Claims (9, 10, 11, 12)
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13. A system for enhancing contours in a noisy image, said system comprising:
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a) a camera for capturing said noisy image as a first distribution m of spatially distributed intensity values b) a computer for transforming said intensity values of said first distribution m into a second distribution U of spatially distributed intensity values representing an enhanced image having enhanced contours therein, by using a transformation model, which defines a cubic filter, as follows; U=a0+a1[Gm+G*m]+a2[G(diag m)Gm+Gm·
G*m+G*(diag m)G*m]+a3[G(diag m)G(diag m)Gm+G(diag m)Gm·
G*m+Gm·
G*(diag m)G*m+G*(diag m)G*(diag m)G*m,where;
diag m is a diagonal operator comprising a matrix with said first distribution m along the diagonal of said matrix and zeroes elsewhere;
the operation “
·
”
indicates the taking of a componentwise product of two vectors, wherein in s·
v evaluated at location r is the product of the two numbers s(r) and v(r), where s and v are each functions of r, a0, a1, a2, and a3 are real-valued parameters controlling the relative importance of constant, linear, quadratic, and cubic terms, respectively, in said transformation model;
G=G(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a forward direction along said contour; and
G*=G*(r1, r2) comprises a matrix of probabilities, each entry of which represents the probability that a contour passing through location r1 passes through location r2 in a backward direction along said contour. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20)
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Specification