Method and apparatus for zooming digital images

Claim 3

The method of claim 1 wherein the initial pixel array is arranged in y columns and x rows and wherein the step of selecting includes the step of, for each interpixel interval between pixels in adjacent columns, selecting a row convolution window for each adjacent pixel consisting of pixels which are in the same row as the interpixel interval of interest and wherein, after step (B)(ii) is completed, the method further includes the steps of: for each interpixel interval between pixels in adjacent rows on the interpolated image, selecting a separate column convolution window for each adjacent pixel on the interpolated image, each column window including image pixels within the same column as, and proximate the interpixel interval of interest; for each column window: (i) determining a convolution filter coefficient for each window pixel; (ii) convoluting the pixel intensities in each window as a function of the coefficients to generate an intermediate value; and (iii) interpolating the intermediate values to generate a final pixel intensity, the final pixel intensities together forming the final image.

Claim 4

The method of claim 2 wherein n is a magnification factor, the step of interpolating to generate interpolated pixel intensities includes interpolating to generate n interpolated pixel intensities and the step of interpolating to generate final pixel intensities includes interpolating to generate n final intensities.

Claim 5

The method of claim 2 wherein the window is an m×1 array and wherein an expanded region of interest includes m/2 rows of pixels above and below the region of interest and the step of selecting row convolution windows for each interval of interest includes selecting row convolution windows for each interval in the expanded region of interest.

Claim 6

The method of claim 1 wherein each of the windows includes the same number of pixels.

Claim 7

The method of claim 1 wherein the image is to be magnified by a factor n and the step of determining convolution filter coefficients includes the steps of: calculating linear interpolation coefficients; calculating cubic interpolation coefficients; and mathematically combining the cubic interpolation coefficients and linear interpolation coefficients to determine the filter coefficients.

Claim 8

The method of claim 6 wherein the step of mathematically combining includes the step of solving the following equation: A= (Λ T Λ) −1 Λ T C where A is a filter coefficient matrix, Λ is a linear interpolation matrix and C is a vector corresponding to the cubic interpolation coefficients.

Claim 9

The method of claim 6 wherein the image is to be magnified by a factor n and the step of interpolating includes the step of mathematically combining each of the intermediate values as a function of factor n.

Claim 12

The method of claim 1 wherein the convolution window is one dimensional and includes m pixels and the step of convoluting includes solving the following equations: b 1 = ∑ i = 1 m  a i  I i and b 2 = ∑ i = 1 m  a i  I i + 1 where b 1 and b 2 are the intermediate values, a i are the linear interpolation coefficients and I i are the initial pixel intensities of pixels in the convolution window.

Claim 13

The method of claim 1 wherein the hardware is capable of performing high speed two dimensional convolution and bilinear interpolation, the step of selecting convolution windows including the step of selecting four m×m windows, each window including the interval of interest.

Claim 16

The method of claim 12 wherein the step of interpolating includes the steps of, where n is odd, solving the following equation: O ij =  ( n - i + 1 )  ( n - j + 1 ) n 2  b 11 + ( n - i + 1 )  ( j - 1 ) n 2  b 12 +  ( i - 1 )  ( n - j + 1 ) n 2  b 21 + ( i - 1 )  ( j - 1 ) n 2  b 22 and where n is even, solving the following equation: O ij =  ( n - i + 0.5 )  ( n - j + 0.5 ) n 2  b 11 + ( n - i + 0.5 )  ( j - 0.5 ) n 2  b 12 +  ( i - 0.5 )  ( n - j + 0.5 ) n 2  b 21 + ( i - 0.5 )  ( j - 0.5 ) n 2  b 22

Claim 17

A pulse sequencing program to be used with a digital imaging system to facilitate magnification of a region of interest on an initial digital image wherein the region of interest includes a plurality of pixels of interest, adjacent portions of adjacent pixels of interest forming interpixel intervals of interest, each pixel of interest characterized by a pixel intensity, the sequencing program performing the steps of: (A) for each interpixel interval of interest, identifying adjacent pixels; (B) for each adjacent pixel: (i) selecting a convolution window and for each window: (a) determining a convolution filter coefficient for each window pixel; (b) convoluting the intensities of the pixels in the window using the coefficients to generate an intermediate value; and (ii) interpolating the intermediate values to generate at least two interpolated pixel intensities, the interpolated pixel intensities together forming an interpolated image.

Claim 18

A pulse sequencing program to be used with a digital imaging system to facilitate magnification of a region of interest on an initial digital image wherein the region of interest includes a plurality of pixels of interest, adjacent portions of adjacent pixels of interest forming interpixel intervals of interest, each pixel of interest characterized by a pixel intensity, the sequencing program performing the steps of: (A) for each interpixel interval of interest, identifying adjacent pixels; (B) for each adjacent pixel: (i) selecting a convolution window and for each window: (a) determining a convolution filter coefficient for each window pixel; (b) convoluting the intensities of the pixels in the window using the coefficients to generate an intermediate value; and (ii) interpolating the intermediate values to generate at least two interpolated pixel intensities, the interpolated pixel intensities together forming an interpolated image.

Claim 19

The program of claim 14 wherein the initial pixel array is arranged in y columns and x rows and wherein the step of selecting includes the step of, for each interval of interest between pixels in adjacent columns, selecting a row convolution window for each adjacent pixel consisting of pixels which are in the same row as the interval of interest and wherein, after step (B)(ii) is completed, the program further includes the steps of: for each interval between pixels in adjacent rows on the interpolated image, selecting a separate column convolution window for each adjacent pixel on the interpolated image, each column window including image pixels within the same column as, and proximate the interval; for each column window: (i) determining a convolution filter coefficient for each window pixel; (ii) convoluting the pixel intensities in each window using the coefficients to generate an intermediate value; and (iii) interpolating the intermediate values to generate a final pixel intensity, the final pixel intensities together forming the final image.

Claim 20

The program of claim 15 wherein n is a magnification factor, the step of interpolating to generate interpolated pixel intensities includes interpolating to generate n interpolated pixel intensities and the step of interpolating to generate final pixel intensities includes interpolating to generate n final intensities.

Claim 21

The program of claim 15 wherein each window is an m×1 array and wherein an expanded region of interest includes m/2 rows of pixels above and below the region of interest and the step of selecting first and second convolution windows for each interval of interest includes selecting first and second row convolution windows for each interval in the expanded region of interest.

Claim 22

The program of claim 14 wherein each of windows includes the same number of pixels.

Claim 23

The program of claim 14 wherein the image is to be magnified by a factor n and the step of determining convolution filter coefficients includes the steps of: calculating linear interpolation coefficients; calculating cubic interpolation coefficients; and mathematically combining the cubic interpolation coefficients and linear interpolation coefficients to determine the filter coefficients.

Claim 24

The program of claim 19 wherein the step of mathematically combining includes the step of solving the following equation: A= (Λ T Λ) −1 Λ T C where A is a filter coefficient matrix, Λ is a linear interpolation matrix and C is a vector corresponding to the cubic interpolation coefficients.

Claim 25

The program of claim 19 wherein the image is to be magnified by a factor n and the step of interpolating includes the step of mathematically combining each of the intermediate values as a function of factor n.

Claim 26

A pulse sequence program to be used with a digital imaging system to facilitate magnification of a region of interest on an initial digital image wherein the region of interest includes a plurality of pixels of interest, adjacent portions of adjacent pixels of interest forming interpixel intervals of interest, each pixel of interest characterized by a pixel intensity, the sequencing program performing the steps of: (A) for each interpixel interval of interest, identifying adjacent pixels; (B) for each adjacent pixel: (i) selecting a convolution window and for each window: (a) determining a convolution filter coefficient for each window pixel; (b) convoluting the intensities of the pixels in the window using the coefficients to generate an intermediate value; and (ii) interpolating the intermediate values to generate at least two interpolated pixel intensities, the interpolated pixel intensities together forming an interpolated image; wherein the image is to be magnified by a factor n and the step of determining convolution filter coefficients includes the steps of: calculating linear interpolation coefficients; calculating cubic interpolation coefficients; and mathematically combining the cubic interpolation coefficients and linear interpolation coefficients to determine the filter coefficients; wherein the image is to be magnified by a factor n and the step of interpolating includes the step of mathematically combining each of the intermediate values as a function of factor n; wherein the step of mathematically combining includes the step, where n is odd, of solving the following equation: O k = ( n - k + 1 ) n  ∑ i = 1 m  a i  I i + ( k - 1 ) n  ∑ i = 1 m  a i  I i + 1 and where n is even, solving the following equation: O k = ( n - k + 1 ) n  ∑ i = 1 m  a i  I i + ( k - 1 ) n  ∑ i = 1 m  a i  I i + 1 where O k is output pixel intensity, n is the factor by which the image is to be magnified, k is 1 through n, a i are coefficients of the convolution filter, m is the number of pixels in each window and I i and I i+1 are the initial pixel intensities of pixels in the convolution window.

Claim 27

A pulse sequence program to be used with a digital imaging system to facilitate magnification of a region of interest on an initial digital image wherein the region of interest includes a plurality of pixels of interest, adjacent portions of adjacent pixels of interest forming interpixel intervals of interest, each pixel of interest characterized by a pixel intensity, the sequencing program performing the steps of: (A) for each interpixel interval of interest, identifying adjacent pixels; (B) for each adjacent pixel: (i) selecting a convolution window and for each window: (a) determining a convolution filter coefficient for each window pixel; (b) convoluting the intensities of the pixels in the window using the coefficients to generate an intermediate value; and (ii) interpolating the intermediate values to generate at least two interpolated pixel intensities, the interpolated pixel intensities together forming an interpolated image; wherein the image is to be magnified by a factor n and the step of determining convolution filter coefficients includes the steps of: calculating linear interpolation coefficients; calculating cubic interpolation coefficients; and mathematically combining the cubic interpolation coefficients and linear interpolation coefficients to determine the filter coefficients; wherein the image is to be magnified by a factor n and the step of interpolating includes the step of mathematically combining each of the intermediate values as a function of factor n; wherein the step of mathematically combining includes the step, where n is odd, of solving the following equation: O k = ( n - k + 1 ) n  ∑ i = 1 m  a i  I i + ( k - 1 ) n  ∑ i = 1 m  a i  I i + 1 and where n is even, solving the following equation: O k = ( n - k + 1 ) n  ∑ i = 1 m  a i  I i + ( k - 1 ) n  ∑ i = 1 m  a i  I i + 1 where O k is output pixel intensity, n is the factor by which the image is to be magnified, k is 1 through n, a i are coefficients of the convolution filter, m is the number of pixels in each window and I i and I i+1 are the initial pixel intensities of pixels in the convolution window.

Claim 28

A pulse sequence program to be used with a digital imaging system to facilitate magnification of a region of interest on an initial digital image wherein the region of interest includes a plurality of pixels of interest, adjacent portions of adjacent pixels of interest forming interpixel intervals of interest, each pixel of interest characterized by a pixel intensity, the sequencing program performing the steps of: (A) for each interpixel interval of interest, identifying adjacent pixels; (C) for each adjacent pixel: (i) selecting a convolution window and for each window: (a) determining a convolution filter coefficient for each window pixel; (b) convoluting the intensities of the pixels in the window using the coefficients to generate an intermediate value; and (ii) interpolating the intermediate values to generate at least two interpolated pixel intensities, the interpolated pixel intensities together forming an interpolated image; wherein the convolution window is one dimensional and includes m pixels and the step of convoluting includes solving the following equations: b 1 = ∑ i = 1 m  a i  I i and b 2 = ∑ i = 1 m  a i  I i + 1 where b 1 and b 2 are the intermediate values, ai are the linear interpolation coefficients and I i are the initial pixel intensities of pixels in the convolution window.

Claim 29

A pulse sequence program to be used with a digital imaging system to facilitate magnification of a region of interest on an initial digital image wherein the region of interest includes a plurality of pixels of interest, adjacent portions of adjacent pixels of interest forming interpixel intervals of interest, each pixel of interest characterized by a pixel intensity, the sequencing program performing the steps of: (A) for each interpixel interval of interest, identifying adjacent pixels; (C) for each adjacent pixel: (i) selecting a convolution window and for each window: (a) determining a convolution filter coefficient for each window pixel; (b) convoluting the intensities of the pixels in the window using the coefficients to generate an intermediate value; and (ii) interpolating the intermediate values to generate at least two interpolated pixel intensities, the interpolated pixel intensities together forming an interpolated image; wherein the convolution window is one dimensional and includes m pixels and the step of convoluting includes solving the following equations: b 1 = ∑ i = 1 m  a i  I i and b 2 = ∑ i = 1 m  a i  I i + 1 where b 1 and b 2 are the intermediate values, ai are the linear interpolation coefficients and I i are the initial pixel intensities of pixels in the convolution window.

Claim 30

The program of claim 14 wherein the hardware is capable of performing high speed two dimensional convolution and bilinear interpolation, the step of selecting convolution windows includes the step of selecting four m×m window including the pixel of interest.

Claim 31

The program of claim 23 wherein the step of convoluting includes solving the following equations: b 11 = ∑ i = 1 m  ∑ j = 1 m  a ij  I ij b 12 = ∑ i = 1 m  ∑ j = 1 m  a ij  I ij + 1 b 21 = ∑ i = 1 m  ∑ j = 1 m  a ij  I i + 1  j b 22 = ∑ i = 1 m  ∑ j = 1 m  a ij  I i + ij + 1 where b 11 , b 12 , b 21 , and b 22 are intermediate values, a ij are the linear interpolation coefficients and I ij , I ij+1 , I I+1j and I I+ij+1 are the initial pixel intensities of pixels in the convolution window.

Claim 34

The apparatus of claim 26 wherein the initial pixel array is arranged in y columns and x rows and wherein when selecting, the convolver, for each interval of interest between pixels in adjacent columns, selects a row convolution window for each adjacent pixel consisting of pixels which are in the same row as the interval of interest and wherein, after the interpolated image has been generated, the interpolated image is provided to the convolver which, for each interval between pixels in adjacent rows on the interpolated image, selects a separate column convolution window for each adjacent pixel on the interpolated image, each column window including adjacent image pixels within the same column as, and proximate the interval, for each column window, convolutes the pixel intensities in each window using the coefficients to generate an intermediate value, the intermediate values provided to the interpolator which again interpolates the intermediate values to generate a final pixel intensity, the final pixel intensities together forming the final image.

Claim 35

The apparatus of claim 27 wherein each window includes an m×1 array and wherein an expanded region of interest includes m/2 rows of pixels above and below the region of interest and the convolver selects first and second row convolution windows for each interval in the expanded region of interest.

Claim 36

The apparatus of claim 26 wherein each of the first and second sub-windows include m pixels.

Claim 37

The apparatus of claim 26 wherein the determiner mathematically combines by solving the following equation: A= (Λ T Λ) −1 Λ T C where A is a filter coefficient matrix, Λ is a linear interpolation matrix and C is a vector corresponding to the cubic interpolation coefficients.

Claim 40

The apparatus of claim 31 wherein the interpolator interpolates by, where n is odd, solving the following equation: O k = ( n = k + 1 ) n  ∑ i = 1 m  a i  I i + ( k - 1 ) n  ∑ i = 1 m  a i  I i + 1 and where n is even, solving the following equation: O k = ( n = k + 0.5 ) n  ∑ i = 1 m  a i  I i + ( k - 0.5 ) n  ∑ i = 1 m  a i  I i + 1 where O k is output pixel intensity, n is the factor by which the image is to be magnified, k is 1 through n, a i are coefficients of the convolution filter, m is the number of pixels in each window and I i and I i+1 are the initial pixel intensities of pixels in the convolution window.

Claim 43

The apparatus of claim 33 wherein the convolver convolves by solving the following equations: b 11 = ∑ i = 1 m  ∑ j = 1 m  a ij  I ij b 12 = ∑ i = 1 m  ∑ j = 1 m  a ij  I ij + 1 b 21 = ∑ i = 1 m  ∑ j = 1 m  a ij  I i + 1  j b 22 = ∑ i = 1 m  ∑ j = 1 m  a ij  I i + ij + 1 where b 11 , b 12 , b 21 , and b 22 are intermediate values, a ij are the linear interpolation coefficients and I ij , I ij+1 , I I+1j and I I+ij+1 are the initial pixel intensities of pixels in the convolution window.

Claim 44

The apparatus of claim 34 wherein the interpolator interpolates by, where n is odd, solving the following equation: Q ij =  ( n - i + 1 )  ( n - j + 1 ) n 2  b 11 + ( n - i + 1 )  ( j - 1 ) n 2  b 12 +  ( i - 1 )  ( n - j + 1 ) n 2  b 21 + ( i - 1 )  ( j - 1 ) n 2  b 22 and, where n is even, solving: O ij =  ( n - i + 0.5 )  ( n - j + 0.5 ) n 2  b 11 + ( n - i + 0.5 )  ( j - 0.5 ) n 2  b 12 +  ( i - 0.5 )  ( n - j + 0.5 ) n 2  b 21 + ( i - 0.5 )  ( j - 0.5 ) n 2  b 22 where   O ij   is   output   pixel   intensity  .380 where O ij is output pixel intensity.