UP-SCALING IMAGES USING INTERPOLATING FUNCTION
An embodiment is a method and apparatus to provide a technique to scale up an image. A first image at a first size is expanded to a second size in first and second dimensions. The second size is larger than the first size and includes the first size and interpolating positions. The expanded image is convolved with a two-dimensional finite-impulse response (FIR) filter having coefficients determined by a two-dimensional interpolating function to generate interpolated pixels at the interpolating positions. The interpolated pixels are part of an up-scaled image at the second size.
1 . A method comprising:
expanding a first image at a first size to a second size in first and second dimensions, the second size being larger than the first size and including the first size and interpolating positions; and
convolving the expanded image with a two-dimensional finite-impulse response (FIR) filter having coefficients determined by a two-dimensional interpolating function to generate interpolated pixels at the interpolating positions, the interpolated pixels being part of an up-scaled image at the second size.
2 . The method of claim 1 wherein expanding the first image comprises:
creating an image array having the second size k times the first size in the first and second dimensions; and
copying the first image to the image array such that pixels of the first image occupy every k positions in the image array.
3 . The method of claim 1 wherein the two-dimensional interpolating function is separable into a first one-dimensional interpolating function in the first dimension and a second one-dimensional interpolating function in the second dimension.
4 . The method of claim 3 wherein convolving comprises:
convolving the expanded image with the first one-dimensional interpolating function in the first dimension to produce a first convolved image; and
convolving the first convolved image with the second one-dimensional interpolating function in the second dimension to produce the interpolated pixels.
5 . The method of claim 1 wherein convolving comprises convolving in spatial-domain or performing an equivalent of convolution by a pointwise multiplication in frequency domain.
6 . The method of claim 1 further comprising:
transferring the up-scaled image to a film recorder to record the up-scaled image on a film.
7 . The method of claim 1 further comprising:
re-sampling a second image from a third size to the first image at the first size prior to expanding the first image to the second size, the third size being larger than the first size; and
performing digital image processing on the first image prior to expanding the first image to the second size.
8 . The method of claim 7 wherein the third size is equal to the second size.
9 . An article of manufacture comprising:
a machine-accessible storage medium including information that, when accessed by a machine, causes the machine to perform operations comprising:
expanding a first image at a first size to a second size in first and second dimensions, the second size being larger than the first size and including the first size and interpolating positions; and
convolving the expanded image with a two-dimensional finite-impulse response (FIR) filter having coefficients determined by a two-dimensional interpolating function to generate interpolated pixels at the interpolating positions, the interpolated pixels being part of an up-scaled image at the second size.
10 . The article of manufacture of claim 9 wherein the information causing the machine to perform expanding the first image comprises information that, when accessed by the machine, causes the machine to perform operations comprising:
creating an image array having the second size N times the first size in the first and second dimensions; and
copying the first image to the image array such that pixels of the first image occupy every N positions in the image array.
11 . The article of manufacture of claim 9 wherein the two-dimensional interpolating function is separable into a first one-dimensional interpolating function in the first dimension and a second one-dimensional interpolating function in the second dimension.
12 . The article of manufacture of claim 11 wherein the information causing the machine to perform convolving comprises information that, when accessed by the machine, causes the machine to perform operations comprising:
convolving the expanded image with the first one-dimensional interpolating function in the first dimension to produce a first convolved image; and
convolving the first convolved image with the second one-dimensional interpolating function in the second dimension to produce the interpolated pixels.
13 . The article of manufacture of claim 9 wherein the information causing the machine to perform convolving comprises information that, when accessed by the machine, causes the machine to perform operations comprising convolving in spatial-domain or performing an equivalent of convolution by a pointwise multiplication in frequency domain.
14 . The article of manufacture of claim 9 wherein the information further comprising information that, when accessed by the machine, causes the machine to perform operations:
transferring the up-scaled image to a film recorder to record the up-scaled image on a film.
15 . The article of manufacture of claim 9 wherein the information further comprising information that, when accessed by the machine, causes the machine to perform operations:
re-sampling a second image from a third size to the first image at the first size prior to expanding the first image to the second size, the third size being larger than the first size; and
performing digital image processing on the first image prior to expanding the first image to the second size.
16 . The article of manufacture of claim 15 wherein the third size is equal to the second size.
17 . An apparatus comprising:
an image expander to expand a first image at a first size to a second size in first and second dimensions, the second size being larger than the first size and including the first size and interpolating positions, and
a convolver coupled to image expander to convolve the expanded image with a two-dimensional finite-impulse response (FIR) filter having coefficients determined by a two-dimensional interpolating function to generate interpolated pixels at the interpolating positions, the interpolated pixels being part of an up-scaled image at the second size.
18 . The apparatus of claim 17 wherein image expander creates an image array having the second size k times the first size in the first and second dimensions; and copies the first image to the image array such that pixels of the first image occupy every k positions in the image array.
19 . The apparatus of claim 17 wherein the two-dimensional interpolating function is separable into a first one-dimensional interpolating function in the first dimension and a second one-dimensional interpolating function in the second dimension.
20 . The apparatus of claim 19 wherein the convolver comprises:
a first one-dimensional convolver to convolve the expanded image with the first one-dimensional interpolating function in the first dimension to produce a first convolved image; and
a second one-dimensional convolver to convolve the first convolved image with the second one-dimensional interpolating function in the second dimension to produce the interpolated pixels.
21 . The apparatus of claim 17 wherein the convolver convolves in spatial-domain or performs an equivalent of convolution by a pointwise multiplication in frequency domain.
22 . The apparatus of claim 17 wherein the image scale processor transfers the up-scaled image to the film recorder to record the up-scaled image on a film.
23 . The apparatus of claim 17 further comprising:
a re-sampler to re-sample a second image from a third size to the first image at the first size, the third size being larger than the first size.
24 . The apparatus of claim 23 wherein the third size is equal to the second size.