Digital scaling
First Claim
1. A method to process digital data, the method comprising:
- receiving digital data comprising values, the values assigned to regions and representing quantities of a wave form over the regions;
selecting a region of the regions, wherein the region is assigned a value of the digital data;
dividing the region into a plurality of subregions; and
assigning a value to each of the plurality of subregions, wherein the average of the values of the subregions, weighted by measures of the subregions, is approximately equal to the value of the region, thereby increasing the number of data points of the digital data, wherein assigning a value to a subregion comprises assigning a value based upon the value of the region and the value of neighboring regions, wherein;
the region comprises an interval;
the plurality of subregions comprise a first and a second subinterval of the interval;
the neighboring regions comprise a first and a second neighboring region, wherein the first neighboring region neighbors the first subinterval and the second neighboring region neighbors the second subinterval; and
assigning a value to each subregion comprises assigning a value to each subregion based upon the value of the region and values of the neighboring regions, andwherein assigning a value to each subregion based upon the value of the region and values of the neighboring regions comprises;
selecting a function f piecewise linear over the subregions; and
assigning to each subregion an integral of f over the subregion divided by a measure of the subregion, wherein a value of an integral of f over the region divided by a measure of the region is approximately equal to the value of the region.
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Abstract
Computer program products and arrangements to process digital data are contemplated. The digital data may contain values, representing quantities of a wave form over regions. Embodiments include transformations, code, state machines or other logic to process digital data by dividing one of the regions, where one of the values represents a quantity of a wave form over the region. The embodiments may include assigning a value to each of the subregions. The average of the values of the subregions, weighted by the measures of the subregions, may approximately equal the value of the region. The regions may comprise pixels and the values of the pixels may represent the intensity of light waves over the pixels. The embodiments may include the processing of digital data in cameras, televisions, audio players, seismic devices, and medical imaging devices. The subdivision of regions and the assignment of value to the subregions may utilize derivative migration.
60 Citations
32 Claims
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1. A method to process digital data, the method comprising:
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receiving digital data comprising values, the values assigned to regions and representing quantities of a wave form over the regions; selecting a region of the regions, wherein the region is assigned a value of the digital data; dividing the region into a plurality of subregions; and assigning a value to each of the plurality of subregions, wherein the average of the values of the subregions, weighted by measures of the subregions, is approximately equal to the value of the region, thereby increasing the number of data points of the digital data, wherein assigning a value to a subregion comprises assigning a value based upon the value of the region and the value of neighboring regions, wherein; the region comprises an interval; the plurality of subregions comprise a first and a second subinterval of the interval; the neighboring regions comprise a first and a second neighboring region, wherein the first neighboring region neighbors the first subinterval and the second neighboring region neighbors the second subinterval; and assigning a value to each subregion comprises assigning a value to each subregion based upon the value of the region and values of the neighboring regions, and wherein assigning a value to each subregion based upon the value of the region and values of the neighboring regions comprises; selecting a function f piecewise linear over the subregions; and assigning to each subregion an integral of f over the subregion divided by a measure of the subregion, wherein a value of an integral of f over the region divided by a measure of the region is approximately equal to the value of the region. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 27, 28, 30, 31)
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17. A computer program product comprising a tangible computer-readable storage medium, wherein the storage medium does not comprise a transitory signal, the storage medium having a computer readable program, wherein the computer readable program when executed on a computer causes the computer to:
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receive digital data comprising values, the values assigned to regions and representing quantities of a wave form over the regions; select a region of the regions, wherein the region is assigned a value of the digital data; divide the region into a plurality of subregions; and assign a value to each of the plurality of subregions, wherein the average of the values of the subregions, weighted by measures of the subregions, is approximately equal to the value of the region, thereby increasing the number of data points of the digital data, wherein assigning a value to a subregion comprises assigning a value based upon the value of the region and the value of neighboring regions, wherein; the region comprises an interval; the plurality of subregions comprise a first and a second subinterval of the interval; the neighboring regions comprise a first and a second neighboring region, wherein the first neighboring region neighbors the first subinterval and the second neighboring region neighbors the second subinterval; and assign a value to each subregion comprises assigning a value to each subregion based upon the value of the region and values of the neighboring regions, and wherein assigning a value to each subregion based upon the value of the region and values of the neighboring regions comprises; selecting a function f piecewise linear over the subregions; and assigning to each subregion an integral of f over the subregion divided by a measure of the subregion, wherein a value of an integral of f over the region divided by a measure of the region is approximately equal to the value of the region. - View Dependent Claims (18, 19, 20, 21, 29)
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32. A method to process digital data, the method comprising:
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receiving digital data comprising values, the values assigned to regions and representing quantities of a wave form over the regions; selecting a region of the regions, wherein the region is assigned a value of the digital data; dividing the region into a plurality of subregions; and assigning a value to each of the plurality of subregions, the assigning comprising; selecting a function f integrable over the subregions and the region, wherein a value of an integral of f over the region divided by a measure of the region is approximately equal to the value of the region ; and assigning to each subregion a value of an integral of f over the subregion divided by a measure of the subregion, wherein the average of the values of the subregions, weighted by measures of the subregions, is approximately equal to the value of the region, thereby increasing the number of data points of the digital data, wherein; the region comprises an interval; the plurality of subregions comprise a first and a second subinterval of the interval; the neighboring regions comprise a first and a second neighboring region, wherein the first neighboring region neighbors the first subinterval and the second neighboring region neighbors the second subinterval; assigning a value to a subregion comprises assigning a value based upon the value of the region and the value of neighboring regions; and the selecting comprises selecting the function f, wherein f is piecewise linear over the interval.
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Specification