Patent EP0391587A2 successfully refreshed from Google Patents.
EP0391587A2
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Method and apparatus for fast generation of warping coefficients
Assignee: 3M Co
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Filing: 1990-03-27
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Granted: —
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Expires: 2010-03-27
Abstract
Abstract A polynomial warp of a first image for comparison with a second image is performed by precalculating and storing a matrix for use in determining the warping coefficients. A group of control points is preselected in the second image and located in the first image. The matrix products of the precalculated matrix and each of two column vectors containing the coordinates of the control points in the first image are calculated. The results of this matrix multiplication are two column vectors containing the warping coefficients. Those coefficients are then used to perform the image warping.
Inventors
- 👤 Frederick M. C/O Minnesota Mining Waltz
- 👤 John C. C/O Minnesota Mining Schultz
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-11-08 13:24
CPC Classifications
G; G06; G06T; G06T7/00
Claims Analysis
Total Claims: 11
Claim 1
Independent Claim
238 words
A method of performing a polynomial warp of a first digitized image in a u-v plane for comparison with a second digitized image in an x-y plane each image comprising a plurality of pixels and each pixel having a gray scale value associated therewith, said method being according to the warping equations and where n and m are positive integers equal to the order of the warping and [A] and [B] are (n + 1) by (m + 1) matrices of warping coefficients, said method comprising the steps of: preselecting a set of control points in said second image, said set including at least (n + 1) x (m + 1) points; precalculating a matrix [M] such that and where [u] and [v] are column vectors of (n + 1) x (m + 1) arbitrary (u,v) pairs and [a] and [b] are column vectors containing the warping coefficients of [A] and [B] respectively; precalculating the inverse, [M]-', of [M] and storing the values of [M]-'; locating (n + 1) x (m + 1) of said control points in said first image; computing the values of said warping matrices by calculating and where u and v are column vectors containing the u and v values of said control points; calculating the (u,v) value of each pixel of the x-y plane by using said warping equations; and determining the gray scale value in the vicinity of each calculated (u,v) point.
Claim 2
Independent Claim
238 words
A method of performing a polynomial warp of a first digitized image in a u-v plane for comparison with a second digitized image in an x-y plane each image comprising a plurality of pixels and each pixel having a gray scale value associated therewith, said method being according to the warping equations and where n and m are positive integers equal to the order of the warping and [A] and [B] are (n + 1) by (m + 1) matrices of warping coefficients, said method comprising the steps of: preselecting a set of control points in said second image, said set including at least (n + 1) x (m + 1) points; precalculating a matrix [M] such that and where [u] and [v] are column vectors of (n + 1) x (m + 1) arbitrary (u,v) pairs and [a] and [b] are column vectors containing the warping coefficients of [A] and [B] respectively; precalculating the inverse, [M]-', of [M] and storing the values of [M]-'; locating (n + 1) x (m + 1) of said control points in said first image; computing the values of said warping matrices by calculating and where u and v are column vectors containing the u and v values of said control points; calculating the (u,v) value of each pixel of the x-y plane by using said warping equations; and determining the gray scale value in the vicinity of each calculated (u,v) point.
Claim 3
Dependent Claim
49 words
The method of Claim 1 wherein said step of locating said control points in said first image includes the step of correlating the image of each control point in said second image with a region of said first image in which the control point is expected to be found.
Claim 4
Dependent Claim
18 words
The method of Claim 2 wherein said control points are located in said first image to subpixel accuracy.
Claim 5
Dependent Claim
46 words
The method of Claim 3 wherein said subpixel accuracy is achieved by utilizing pseudo-pixels, each pseudo-pixel having assigned thereto a gray scale value, said gray scale values assigned to said pseudo-pixels being determined by taking weighted averages of said gray scale values associated with actual pixels.
Claim 6
Dependent Claim
32 words
The method of Claim 1 wherein said gray scale value in the vicinity of each calculated (u,v) point is equal to the gray scale value of the pixel containing said (u,v) point.
Claim 7
Dependent Claim
51 words
The method of Claim 1 wherein said gray scale value in the vicinity of each calculated (u,v) point is equal to a weighted average of the gray scale value of the pixel containing said (u,v) point and the gray scale values of the pixels surrounding said pixel containing said (u,v) point.
Claim 8
Dependent Claim
30 words
The method of Claim 1 wherein more than (n + 1) x (m + 1 ) control points are preselected in said second image and located in said first image.
Claim 9
Dependent Claim
210 words
Apparatus for performing a polynomial warp of a first digitized image in a u-v plane for comparison with a second digitized image in an x-y plane, a plurality of control points having been preselected in said second image, each image comprising a plurality of pixels and each pixel having a gray scale value associated therewith, said apparatus performing the warp according to the equations and where n and m are positive integers equal to the order of the warping and [A] and [B] are (n + 1) by (m + 1) matrices of warping coefficients, said apparatus comprising: means for storing said first digitized image; means for locating said control points in said first image and storing the calculated u and v values; means for storing a matrix [M] -1 such that and where [a] and [b] are column vectors containing the warping coefficients of [A] and [B] respectively and [u ] and [v are column vectors containing the u and v values of the control points; means for multiplying [Mr1 times [u'] to obtain the warping coefficients; and means for utilizing said warping coefficients to calculate (u,v) values for each pixel in said second image and determine the gray scale values in the vicinity of said calculated (u,v) points.
Claim 10
Dependent Claim
210 words
Apparatus for performing a polynomial warp of a first digitized image in a u-v plane for comparison with a second digitized image in an x-y plane, a plurality of control points having been preselected in said second image, each image comprising a plurality of pixels and each pixel having a gray scale value associated therewith, said apparatus performing the warp according to the equations and where n and m are positive integers equal to the order of the warping and [A] and [B] are (n + 1) by (m + 1) matrices of warping coefficients, said apparatus comprising: means for storing said first digitized image; means for locating said control points in said first image and storing the calculated u and v values; means for storing a matrix [M] -1 such that and where [a] and [b] are column vectors containing the warping coefficients of [A] and [B] respectively and [u ] and [v are column vectors containing the u and v values of the control points; means for multiplying [Mr1 times [u'] to obtain the warping coefficients; and means for utilizing said warping coefficients to calculate (u,v) values for each pixel in said second image and determine the gray scale values in the vicinity of said calculated (u,v) points.
Claim 11
Dependent Claim
20 words
The apparatus of Claim 8 wherein said means for locating said control points in said first image includes a convolver.
References Cited (Backward Citations)
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