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US6172773B1 Expired / Lapsed US ⏱️ 0.0 years remaining

Void and cluster apparatus and method for generating dither templates

Assignee: Hewlett Packard Development Co LP
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Filing: 1999-05-10
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Granted: 2001-01-09
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Expires: 2019-05-10
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Abstract

Abstract An apparatus for dithering an input image to produce an output array for representation on an output device is described. The apparatus includes an input device to store input image pixels having a first plurality of chrominance or luminance levels; a dithering system including a dither template including an M by N matrix of integer threshold values, the uniform distribution of threshold values throughout the dither template possessing homogeneous attributes. The apparatus further includes a normalizer unit for normalizing the threshold values of the dither template for storage in a dither matrix according to the first plurality of chrominance or luminance levels of the input image pixels and a second plurality of chrominance or luminance levels of the output array and a summation unit to add the input image pixel chrominance or luminance values to the normalized threshold values of the dither matrix. A quantizer unit is provided to adjust summation unit output to a closest output array chrominance or luminance levels of an output device.

Inventors

  • 👤 Robert Alan Ulichney

Bibliographic Details

Application Number —
Jurisdiction US
Data Source google_patents
Last Synchronized 2026-11-09 19:25
CPC Classifications
H; H04; H04N; H04N19/00; H04N19/90; H04N1/00; H04N1/40; H04N1/405; H04N1/4051

Claims Analysis

Total Claims: 52
Claim 1
Independent Claim 239 words
An apparatus comprising: a memory device having locations corresponding to M rows and N columns of elements, said elements having a binary bit pattern of M rows and N columns comprising, said binary bit pattern first type bit elements and second type bit elements, with the type bit element with the greatest number of elements in said pattern array being a majority type element, and the type bit element of least number of elements in said pattern being a minority type element; means for iteratively selecting and moving said minority type elements and said majority type elements between element locations within said pattern memory device, said minority type elements selected in relation to neighboring minority type elements according to a first spatial characteristic, and said majority type elements selected in relation to neighboring minority type elements according to a second, different spatial characteristic, until said minority type elements and said majority type elements have been uniformly distributed to locations within said pattern memory device to provide a modified pattern of first and second type bit elements having homogeneous attributes; and means for providing a modified convolution result for each element of said pattern, including: multiplication means for multiplying the binary element value of said neighboring elements by a spatial domain function to generate a filter result; and summing means for adding said filter result of each of said neighboring elements to produce said modified convolution result for said element.
Claim 2
Independent Claim 239 words
An apparatus comprising: a memory device having locations corresponding to M rows and N columns of elements, said elements having a binary bit pattern of M rows and N columns comprising, said binary bit pattern first type bit elements and second type bit elements, with the type bit element with the greatest number of elements in said pattern array being a majority type element, and the type bit element of least number of elements in said pattern being a minority type element; means for iteratively selecting and moving said minority type elements and said majority type elements between element locations within said pattern memory device, said minority type elements selected in relation to neighboring minority type elements according to a first spatial characteristic, and said majority type elements selected in relation to neighboring minority type elements according to a second, different spatial characteristic, until said minority type elements and said majority type elements have been uniformly distributed to locations within said pattern memory device to provide a modified pattern of first and second type bit elements having homogeneous attributes; and means for providing a modified convolution result for each element of said pattern, including: multiplication means for multiplying the binary element value of said neighboring elements by a spatial domain function to generate a filter result; and summing means for adding said filter result of each of said neighboring elements to produce said modified convolution result for said element.
Claim 3
Dependent Claim 36 words
The apparatus of claim 1 , wherein said spatial domain function comprises an M×N distribution of weighted values used to determine a relative contribution of a neighboring element to the modified convolution result for each element.
Claim 4
Dependent Claim 63 words
The apparatus of claim 1 , wherein said means for calculating said modified convolution result further comprises: means for calculating the indices of said pattern element for which said modified convolution result is provided in a weighted distribution of values having corresponding indices, and for adjusting selected indices of said weighted distribution for portions of said weighted distribution falling outside of said pattern.
Claim 5
Dependent Claim 35 words
The apparatus of claim 3 , wherein said means for adjusting further comprises: means for wrapping around said portions of said weighted distribution falling outside of said pattern into corresponding opposite portions of said pattern.
Claim 6
Independent Claim 203 words
An apparatus comprising: a memory device having locations corresponding to M rows and N columns of elements, said elements having a binary bit pattern of M rows and N columns comprising, said binary bit pattern first type bit elements and second type bit elements, with the type bit element with the greatest number of elements in said pattern array being a majority type element, and the type bit element of least number of elements in said pattern being a minority type element; means for iteratively selecting and moving said minority type elements and said majority type elements between element locations within said pattern memory device, said minority type elements selected in relation to neighboring minority type elements according to a first spatial characteristic, and said majority type elements selected in relation to neighboring minority type elements according to a second, different spatial characteristic, until said minority type elements and said majority type elements have been uniformly distributed to locations within said pattern memory device to provide a modified pattern of first and second type bit elements having homooenous attributes; and wherein said first spatial characteristic and said different spatial characteristic are respective modified convolution results for each element in said pattern memory device.
Claim 7
Independent Claim 203 words
An apparatus comprising: a memory device having locations corresponding to M rows and N columns of elements, said elements having a binary bit pattern of M rows and N columns comprising, said binary bit pattern first type bit elements and second type bit elements, with the type bit element with the greatest number of elements in said pattern array being a majority type element, and the type bit element of least number of elements in said pattern being a minority type element; means for iteratively selecting and moving said minority type elements and said majority type elements between element locations within said pattern memory device, said minority type elements selected in relation to neighboring minority type elements according to a first spatial characteristic, and said majority type elements selected in relation to neighboring minority type elements according to a second, different spatial characteristic, until said minority type elements and said majority type elements have been uniformly distributed to locations within said pattern memory device to provide a modified pattern of first and second type bit elements having homooenous attributes; and wherein said first spatial characteristic and said different spatial characteristic are respective modified convolution results for each element in said pattern memory device.
Claim 8
Dependent Claim 39 words
The apparatus of claim 5 , wherein said first spatial characteristic is a highest modified convolution result of said minority type elements with relation to said modified convolution results of other minority type elements within said pattern memory device.
Claim 9
Dependent Claim 42 words
The apparatus of claim 5 , wherein said second, different spatial characteristic is a lowest modified convolution value of a majority type element with relation to said modified convolution results of each of other majority type elements within said pattern memory device.
Claim 10
Independent Claim 316 words
An apparatus comprising: means for storing a binary bit pattern having M rows and N columns comprising first type bit elements and second type bit elements, wherein the type bit element of greatest number in said pattern is a majority type element, and the type bit element of at least number in said pattern array is a minority type element; means for storing a dither template having M rows and N columns of integer threshold values in a template memory device having corresponding M rows and N columns of element locations; means for iteratively selecting a minority type element from said corresponding location from said pattern, said minority type element at said corresponding location selected in relation to neighboring minority type elements according to a first spatial characteristic, said means for iteratively selecting a minority type element further comprising: means for replacing said minority type element at said corresponding memory location with a majority type element to provide a second pattern array, and concurrently assigning a threshold value to a corresponding element location of said template memory; means for iteratively selecting a majority type element from said pattern, said majority type element selected in relation to neighboring minority type elements according to a second, different spatial characteristic, said means for iteratively selecting a majority type element further comprising: means for replacing said majority type element at said corresponding pattern location with a minority type element to provide a third modified pattern, and concurrently assigning a threshold value to a corresponding element location of said template memory; and means for providing a modified convolution result for each element of said pattern including: multiplication means for multiplying the binarv element value of said neighboring elements by a spatial domain function to generate a filter result; and summing means for adding said filter result of each of said neighboring elements to produce said modified convolution result for said element.
Claim 11
Independent Claim 316 words
An apparatus comprising: means for storing a binary bit pattern having M rows and N columns comprising first type bit elements and second type bit elements, wherein the type bit element of greatest number in said pattern is a majority type element, and the type bit element of at least number in said pattern array is a minority type element; means for storing a dither template having M rows and N columns of integer threshold values in a template memory device having corresponding M rows and N columns of element locations; means for iteratively selecting a minority type element from said corresponding location from said pattern, said minority type element at said corresponding location selected in relation to neighboring minority type elements according to a first spatial characteristic, said means for iteratively selecting a minority type element further comprising: means for replacing said minority type element at said corresponding memory location with a majority type element to provide a second pattern array, and concurrently assigning a threshold value to a corresponding element location of said template memory; means for iteratively selecting a majority type element from said pattern, said majority type element selected in relation to neighboring minority type elements according to a second, different spatial characteristic, said means for iteratively selecting a majority type element further comprising: means for replacing said majority type element at said corresponding pattern location with a minority type element to provide a third modified pattern, and concurrently assigning a threshold value to a corresponding element location of said template memory; and means for providing a modified convolution result for each element of said pattern including: multiplication means for multiplying the binarv element value of said neighboring elements by a spatial domain function to generate a filter result; and summing means for adding said filter result of each of said neighboring elements to produce said modified convolution result for said element.
Claim 12
Dependent Claim 29 words
The apparatus of claim 8 , wherein said first spatial characteristic and said different spatial characteristic are respective modified convolution results for each element in said pattern memory device.
Claim 13
Dependent Claim 37 words
The apparatus of claim 8 , wherein said first spatial characteristic is a highest modified convolution result of said minority type elements with relation to said modified convolution results of other minority type elements within said pattern.
Claim 14
Dependent Claim 40 words
The apparatus of claim 8 , wherein said second, different spatial characteristic is a lowest modified convolution value of a majority type element with relation to said modified convolution results of each of other majority type elements within said pattern.
Claim 15
Dependent Claim 36 words
The apparatus of claim 8 , wherein said spatial domain function comprises an M×N distribution of weighted values used to determine a relative contribution of a neighboring element to the modified convolution result for each element.
Claim 16
Dependent Claim 54 words
The apparatus of claim 8 , further comprising: means for calculating the indices of said pattern element for which said modified convolution result is provided in a weighted distribution of values having corresponding indices, and for adjusting selected indices of said weighted distribution for portions of said weighted distribution falling outside of said pattern.
Claim 17
Dependent Claim 35 words
The apparatus of claim 13 , wherein said means for adjusting further comprises: means for wrapping around said portions of said weighted distribution falling outside of said pattern into corresponding opposite portions of said pattern.
Claim 18
Independent Claim 131 words
An apparatus comprising: a dithering system responsive to input image pixels from an input device having a first plurality of representation levels, including a memory for storing a dither template comprising an M by N array of elements representing a uniform distribution of integer threshold values having homogeneous attributes; means, responsive to said first plurality of representation levels, a second plurality of representation levels of an output device, and to said threshold values of said dither template, for providing a normalized dither matrix comprising normalized threshold values; adding means for adding said input image pixel representation levels to said normalized threshold values to provide summation signals; quantizer means for mapping said summation signals to said second plurality of representation levels to provide output pixels; and means for storing said output pixels.
Claim 19
Independent Claim 131 words
An apparatus comprising: a dithering system responsive to input image pixels from an input device having a first plurality of representation levels, including a memory for storing a dither template comprising an M by N array of elements representing a uniform distribution of integer threshold values having homogeneous attributes; means, responsive to said first plurality of representation levels, a second plurality of representation levels of an output device, and to said threshold values of said dither template, for providing a normalized dither matrix comprising normalized threshold values; adding means for adding said input image pixel representation levels to said normalized threshold values to provide summation signals; quantizer means for mapping said summation signals to said second plurality of representation levels to provide output pixels; and means for storing said output pixels.
Claim 20
Dependent Claim 30 words
The apparatus of claim 15 , further comprising an input device to store an input image comprising a plurality of input image pixels having said first plurality of representation levels.
Claim 21
Dependent Claim 26 words
The apparatus of claim 15 , further comprising means for converting said output pixels to provide a representation of said input image on an output device.
Claim 22
Dependent Claim 85 words
The apparatus of claim 15 , wherein said dithering system further comprises: means for storing a pattern having M by N element locations, said elements of said pattern comprising an initial binary pattern of first type bit elements and second type bit elements, wherein said type bit element of greatest number are majority type elements and said type bit elements of least number are minority type elements, wherein said majority type elements and said minority type elements are related by first and second spatial characteristics.
Claim 23
Dependent Claim 86 words
The apparatus of claim 18 , further comprising: means for iteratively selecting and moving said minority types and majority types between element locations within said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, and said majority type element location selected in relation to neighboring minority type elements according to said second, different spatial characteristic, until said first and majority types have been moved to element locations to form a modified pattern with homogeneous attributes.
Claim 24
Dependent Claim 124 words
The apparatus of claim 18 further comprises: means for selecting a minority type element location of said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including means for replacing said minority type element with said majority type element and concurrently defining a threshold value for a corresponding integer location of said dither template; and means for selecting a majority type element location of said pattern, said majority type element location selected in relation to neighboring minority type elements according to said second, different spatial characteristic, including means for replacing said majority type element with said minority type element and concurrently defining a threshold value for a corresponding location of said dither template.
Claim 25
Dependent Claim 67 words
The apparatus of claim 18 , further comprising means for providing a modified convolution result for each element of said pattern, including: multiplication means for multiplying the binary element value of said neighboring elements by a spatial domain function to generate a filter result; and summing means for adding said filter result of each of said neighboring elements to produce said modified convolution result for said element.
Claim 26
Dependent Claim 28 words
The apparatus of claim 18 , wherein said first spatial characteristic and said second, different spatial characteristic are respective modified convolution results for each element in said pattern.
Claim 27
Dependent Claim 38 words
The apparatus of claim 18 , wherein said first spatial characteristic is a highest modified convolution value of a minority type element relative to said modified convolution values of each of said minority type elements of said pattern.
Claim 28
Dependent Claim 39 words
The apparatus of claim 18 , wherein said different spatial characteristic is a lowest modified convolution value of a majority type element relative to said modified convolution values of each of said elements majority type elements of said pattern.
Claim 29
Dependent Claim 36 words
The apparatus of claim 18 , wherein said spatial domain function comprises an M×N distribution of weighted values used to determine a relative contribution of a neighboring element to the modified convolution result for each element.
Claim 30
Dependent Claim 54 words
The apparatus of claim 18 , further comprising: means for calculating the indices of said pattern element for which said modified convolution result is provided in a weighted distribution of values having corresponding indices, and for adjusting selected indices of said weighted distribution for portions of said weighted distribution falling outside of said pattern.
Claim 31
Dependent Claim 35 words
The apparatus of claim 26 , wherein said means for adjusting further comprises: means for wrapping around said portions of said weighted distribution falling outside of said pattern into corresponding opposite portions of said pattern.
Claim 32
Independent Claim 236 words
A method comprising the steps of: a. storing in a memory device a pattern having M rows and N columns of locations, said pattern comprising a binary pattern of fist type bit elements and second type bit elements, wherein said type bit element of greatest number in said pattern is a majority type element, and said type bit element of least number in said pattern is a minority-type element; b. iteratively selecting and moving said minority type elements and said majority type elements in said memory device between memory locations, wherein said minority type element location in memory is selected in relation to neighboring minority type elements according to a first spatial characteristic and said majority type element location in memory is selected in relation to neighboring minority type elements according to a second, different spatial characteristic; repeating said step of iteratively selecting and moving until said minority type elements and majority type elements are uniformly distributed at pattern locations in said memory device to provide a modified pattern having homogeneous attributes; and c. calculating a modified convolution result for each element of said pattern, comprising the steps of: c1. multiplying the binary element value of each of said neighboring elements by a spatial domain function to generate a filter result for each of said neighboring elements; and c2. summing said filter result of said neighboring elements to produce said modified convolution result of said element.
Claim 33
Independent Claim 236 words
A method comprising the steps of: a. storing in a memory device a pattern having M rows and N columns of locations, said pattern comprising a binary pattern of fist type bit elements and second type bit elements, wherein said type bit element of greatest number in said pattern is a majority type element, and said type bit element of least number in said pattern is a minority-type element; b. iteratively selecting and moving said minority type elements and said majority type elements in said memory device between memory locations, wherein said minority type element location in memory is selected in relation to neighboring minority type elements according to a first spatial characteristic and said majority type element location in memory is selected in relation to neighboring minority type elements according to a second, different spatial characteristic; repeating said step of iteratively selecting and moving until said minority type elements and majority type elements are uniformly distributed at pattern locations in said memory device to provide a modified pattern having homogeneous attributes; and c. calculating a modified convolution result for each element of said pattern, comprising the steps of: c1. multiplying the binary element value of each of said neighboring elements by a spatial domain function to generate a filter result for each of said neighboring elements; and c2. summing said filter result of said neighboring elements to produce said modified convolution result of said element.
Claim 34
Dependent Claim 31 words
The method of claim 28 , wherein said first spatial characteristic and said second, different spatial characteristic are determined by calculating a modified convolution result for each element in said pattern.
Claim 35
Dependent Claim 36 words
The method of claim 28 , wherein said first spatial characteristic is a highest convolution result of said minority type elements with relation to said convolution results of the other minority type elements of said pattern.
Claim 36
Dependent Claim 37 words
The method of claim 28 , wherein said second, different spatial characteristic is a lowest convolution result of said majority type elements in relation to said convolution results of the other majority type elements of said pattern.
Claim 37
Dependent Claim 36 words
The method of claim 28 , wherein said spatial domain function comprises an M×N distribution of weighted values used to determine a relative contribution of a neighboring element to the modified convolution result for each element.
Claim 38
Dependent Claim 54 words
The method of claim 28 , further comprising the step of: calculating the indices of said pattern element for which said modified convolution result is provided in a weighted distribution of values having corresponding indices, and adjusting selected indices of said weighted distribution for portions of said weighted distribution falling outside of said pattern.
Claim 39
Dependent Claim 36 words
The method of claim 33 , wherein said step of adjusting further comprises the step of: wrapping around said portions of said weighted distribution falling outside of said pattern into corresponding opposite portions of said pattern.
Claim 40
Dependent Claim 114 words
The method of claim 28 , wherein said step of providing a modified convolution result for each element of said pattern includes the step of calculating: F  ( x , y ) = ∑ p = - M / 2 M / 2   ∑ q = - N / 2 N / 2   Pattern   ( p ′ , q ′ ) * f  ( p , q ) wherein F(x,y) provides said modified convolution result of said element at location x,y of said pattern, and p and q are indices to a spatial domain function, and adjusting p and q to provide p′ and q′ respectively.
Claim 41
Independent Claim 321 words
A method comprising the steps of: a. storing in a memory device a pattern having M rows and N columns of locations, said pattern comprising a binary pattern first type bit elements and second type bit elements, wherein said type bit element of greatest number in said pattern is a majority type element, and said type bit element of least number in said pattern is a minority type element; b. selecting a minority type element location from said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including replacing said minority type element with a majority type element and concurrently assigning a threshold value to a corresponding location of said dither template until no minority type elements remain in said pattern; c. selecting a majority type element location from said pattern, said majority type element location selected in relation to neighboring minority type elements according to said second, different spatial characteristic, including replacing said majority type element with said minority type element and concurrently assigning a threshold value to a corresponding location of said dither template until the number of minority type elements in said pattern exceeds the number of majority type elements in said pattern; d. evaluating the bit type of the majority type element and the minority type element, wherein the type bit element of greatest number in said pattern is a majority type element, and the type bit element of least number in said pattern is a minority type element; and e. selecting a minority type element location from said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including replacing said minority type element with said majority type element and concurrently assigning a threshold value to a corresponding location of said dither template until a threshold value has been assigned to all dither template elements.
Claim 42
Independent Claim 321 words
A method comprising the steps of: a. storing in a memory device a pattern having M rows and N columns of locations, said pattern comprising a binary pattern first type bit elements and second type bit elements, wherein said type bit element of greatest number in said pattern is a majority type element, and said type bit element of least number in said pattern is a minority type element; b. selecting a minority type element location from said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including replacing said minority type element with a majority type element and concurrently assigning a threshold value to a corresponding location of said dither template until no minority type elements remain in said pattern; c. selecting a majority type element location from said pattern, said majority type element location selected in relation to neighboring minority type elements according to said second, different spatial characteristic, including replacing said majority type element with said minority type element and concurrently assigning a threshold value to a corresponding location of said dither template until the number of minority type elements in said pattern exceeds the number of majority type elements in said pattern; d. evaluating the bit type of the majority type element and the minority type element, wherein the type bit element of greatest number in said pattern is a majority type element, and the type bit element of least number in said pattern is a minority type element; and e. selecting a minority type element location from said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including replacing said minority type element with said majority type element and concurrently assigning a threshold value to a corresponding location of said dither template until a threshold value has been assigned to all dither template elements.
Claim 43
Independent Claim 271 words
A method comprising the steps of: a. storing in a memory device a pattern having M rows and N columns of locations, said pattern comprising a binary pattern first type bit elements and second type bit elements, wherein said type bit element of greatest number in said pattern is a majority type element, and said type bit element of least number in said pattern is a minority type element; b. selecting a minority type element location from said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including replacing said minority type element with a majority type element and concurrently assigning a threshold value to a corresponding location of said dither template until no minority type elements remain in said pattern c. selecting a majority type element location from said pattern, said majority type element location selected in relation to neighboring minority type elements according to said second, different spatial characteristic, including replacing said majority type element with said minority type element and concurrently assigning a threshold value to a corresponding location of said dither template until the number of minority type elements in said pattern exceeds the number of majority type elements in said pattern; and d. calculating a modified convolution result for each element of said pattern, comprising the steps of: d1. multiplying the binary element value of each of said neighboring elements by a spatial domain function to generate a filter result for each of said neighboring elements; and d2. summing said filter result of said neighboring elements to produce said modified convolution result of said element.
Claim 44
Independent Claim 271 words
A method comprising the steps of: a. storing in a memory device a pattern having M rows and N columns of locations, said pattern comprising a binary pattern first type bit elements and second type bit elements, wherein said type bit element of greatest number in said pattern is a majority type element, and said type bit element of least number in said pattern is a minority type element; b. selecting a minority type element location from said pattern, said minority type element location selected in relation to neighboring minority type elements according to said first spatial characteristic, including replacing said minority type element with a majority type element and concurrently assigning a threshold value to a corresponding location of said dither template until no minority type elements remain in said pattern c. selecting a majority type element location from said pattern, said majority type element location selected in relation to neighboring minority type elements according to said second, different spatial characteristic, including replacing said majority type element with said minority type element and concurrently assigning a threshold value to a corresponding location of said dither template until the number of minority type elements in said pattern exceeds the number of majority type elements in said pattern; and d. calculating a modified convolution result for each element of said pattern, comprising the steps of: d1. multiplying the binary element value of each of said neighboring elements by a spatial domain function to generate a filter result for each of said neighboring elements; and d2. summing said filter result of said neighboring elements to produce said modified convolution result of said element.
Claim 45
Dependent Claim 31 words
The method of claim 37 , wherein said first spatial characteristic and said second, different spatial characteristic are determined by calculating a modified convolution result for each element in said pattern.
Claim 46
Dependent Claim 36 words
The method of claim 37 , wherein said first spatial characteristic is a highest convolution result of said minority type elements with relation to said convolution results of the other minority type elements of said pattern.
Claim 47
Dependent Claim 37 words
The method of claim 37 , wherein said second, different spatial characteristic is a lowest convolution result of said majority type elements in relation to said convolution results of the other majority type elements of said pattern.
Claim 48
Dependent Claim 36 words
The method of claim 37 , wherein said spatial domain function comprises an M×N distribution of weighted values used to determine a relative contribution of a neighboring element to the modified convolution result for each element.
Claim 49
Dependent Claim 54 words
The method of claim 37 , further comprising the step of: calculating the indices of said pattern element for which said modified convolution result is provided in a weighted distribution of values having corresponding indices, and adjusting selected indices of said weighted distribution for portions of said weighted distribution falling outside of said pattern.
Claim 50
Dependent Claim 36 words
The method of claim 42 , wherein said step of adjusting further comprises the step of: wrapping around said portions of said weighted distribution falling outside of said pattern into corresponding opposite portions of said pattern.
Claim 51
Dependent Claim 30 words
The method of claim 43 wherein the step of adjusting p and q to provide p′ and q′ is calculated by the respective equations: p′=(M+x−p) modulo M q′=(N+y−q) modulo N.
Claim 52
Dependent Claim 84 words
The method of claim 43 , wherein said spatial domain function is a symmetric Gaussian function, given by the equation: f  ( p , q ) = A    - ( p 2 / 2  σ p 2 + q 2 / 2  σ q 2 ) wherein that p 2 +q 2 is the distance from said element for which F (x,y) is provided to a neighboring element, σ p =σ q =σ, and A is a constant.

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