Coding method and apparatus for resampling and filtering images using discrete cosine transforms

Claim 3

The method of claim 1, wherein said hybrid IDECT is mathematically defined as: ##EQU16## for 0≦x≦(N-1), where: said predetermined range is defined from 0 to (N-1); S(u) represents said at least one DECT matrix of DECT coefficients; s'(x) represents said hybrid IDECT matrix which represents said output image; u is an integer variable: x is a real number indexed according to Δx within said predetermined range; N is an upper integer limit of said predetermined range; ##EQU17## for u=0; and C u =1 for u≠0, and said hybrid inverse basis matrix is generated from ##EQU18##

Claim 4

The method of claim 1, further comprising a process of generated a filtered said output image filtering the input image in a manner similar to a mathematical convolution, said process comprising the steps of: selecting a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which will facilitate one of smearing and sharpening the spatial image; generating a padded kernel matrix having a second number of kernel coefficients in the spatial domain by padding said kernel matrix with zeros; producing a discrete odd cosine transform (DOCT) basis matrix of DOCT basis coefficients.; generating a DOCT matrix of DOCT coefficients by matrix product multiplication of said DOCT basis matrix times said padded kernel matrix; generating a filtered matrix by mask multiplication of said at least one DECT matrix with said DOCT matrix; and generating said filtered output image of pixels, represented by a filtered said hybrid IDECT matrix, by performing said inverse discrete cosine transformation of said filtered matrix in accordance with said hybrid IDECT basis matrix.

Claim 5

The method of claim 3, wherein said at least one DECT matrix overlaps an adjacent said at least one DECT matrix.

Claim 6

The method of claim 4, wherein said kernel matrix comprises k elements in one dimension, and said overlapping DECT matrix overlaps by k elements, k being a preselected integer.

Claim 7

The method of claim 3, wherein said DOCT matrix is generated from the DOCT equation: ##EQU19## for 0≦u≦(N-1); where said predetermined range is defined from 0 to (N-1); N is an upper integer limit of said predetermined range; i is an integer variable representing an index of said image data points; H(u) represents said DOCT matrix of DOCT coefficients; h P (i) represents said padded kernel matrix; h P (i)=0 for |i|>(k-1)/2; d i =1/2 for i=0; and d i =1 for i=1, 2 . . . (N-1).

Claim 8

The method of claim 3, wherein said predetermined criterion comprises one of smearing and sharpening the image.

Claim 11

The apparatus of claim 8, wherein said means for generating the resampled matrix comprises means for solving the inverse DECT equation: ##EQU20## for 0≦x≦(N-1), where: S(u) represents said at least one DECT matrix of DECT coefficients; s'(i) represents said resampled matrix of resampled image data points for the given range; x is a real number indexed by Δx within said given range where Δx=(N-1)/(N'-1); ##EQU21## for u=0; and C u =1 for u≠0, and said means for generating the hybrid inverse DECT basis matrix comprises means for generating the inverse DECT basis matrix from ##EQU22##

Claim 12

The apparatus of claim 8, further comprising means for filtering the spatial image in a manner similar to a mathematical convolution, said filtering means comprising: means for selecting a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which facilitates one of smearing and sharpening of the spatial image; means for generating a padded kernel matrix of N coefficients in the spatial domain by padding said kernel matrix with zeros; means for producing an N element discrete odd cosine transform (DOCT) basis matrix; means for generating a DOCT matrix of N DOCT coefficients by matrix product multiplication of said DOCT basis matrix times said padded kernel matrix; means for generating a filtered matrix by mask multiplication of said at least one DECT matrix with said DOCT matrix; and means for generating a filtered said resampled image represented by a matrix of N' filtered and resampled image data points in the spatial domain by performing a hybrid inverse DECT of said filtered matrix in accordance with said hybrid inverse DECT basis matrix.

Claim 13

The apparatus of claim 10, further comprising means for overlapping said at least one DECT matrix with an adjacent said at least one DECT matrix.

Claim 14

The apparatus of claim 11, wherein said means for overlapping comprises means for overlapping by k elements, wherein k is a preselected integer.

Claim 15

The apparatus of claim 10, wherein said means for generating the DOCT matrix comprises means for solving the equation: ##EQU23## for 0≦u≦(N-1); where H(u) represents said DOCT matrix of DOCT coefficients; h P (i) represents said coefficients of the padded kernel matrix; h P (i)=0 for |i|>(k-1)/2; i is an integer index: d i =1/2 for i=0; and d i =1 for i=1, 2 . . . (N-1).

Claim 16

The apparatus of claim 10, wherein said predetermined criterion comprises one of smearing and sharpening the image.

Claim 19

The method of claim 15; wherein said inverse DECT of step (d) is represented as: ##EQU24## for 0≦x≦(N-1), where: said predetermined range is 0 to (N-1); S(u) represents said at least one DECT matrix of DECT coefficients; s'(x) represents said at least one second matrix; u is an integer; x is a real number: ##EQU25## for u=0; and C u =1 for u≠0, and said hybrid inverse DECT basis matrix is generated from ##EQU26##

Claim 20

The method of claim 15, further comprising a step for generating the resampled image in the spatial domain from said second matrix.

Claim 21

The method of claim 15, further comprising a process of filtering the image represented in the spatial domain in a manner similar to a mathematical convolution, said filtering process comprising the steps of: selecting a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which facilitates one of smearing and sharpening of the spatial image; generating a padded kernel matrix of N coefficients in the spatial domain by padding said kernel matrix with zeros; producing an N element discrete odd cosine transform (DOCT) basis matrix; generating a DOCT matrix of N DOCT coefficients by matrix product multiplication of said DOCT basis matrix times said padded kernel matrix; generating a filtered matrix by mask multiplication of said at least one DECT matrix with said DOCT matrix; and generating a filtered said at least one second matrix of N' filtered and resampled image data points in the spatial domain by performing a hybrid inverse DECT of said filtered matrix in accordance with said hybrid inverse DECT basis matrix.

Claim 22

The method of claim 18, wherein said at least one first matrix overlaps an adjacent said at least one first matrix.

Claim 23

The method of claim 19, wherein said kernel matrix comprises k elements in one dimension, and said overlapping matrices overlap by k elements, k being a predefined integer.

Claim 24

The method of claim 18, wherein said DOCT matrix is generated from the DOCT equation: ##EQU27## for 0≦u≦(N-1); where H(u) represents said DOCT matrix; h P (i) represents said padded kernel matrix; h P (i)=0 for |i|>(k-1)/2; i and u are integers; d i =1/2 for i=0; and d i =1 for i=1, 2 . . . (N-1).

Claim 25

The method of claim 18, wherein said predetermined criterion comprises one of smearing and sharpening the image.

Claim 26

A process of generating a filtered image, said process comprising the steps of: providing an input signal of an input image represented in a spatial domain as at least one spatial matrix of N image data points for a predetermined range, N being a predetermined integer; producing a discrete even cosine transform (DECT) basis matrix corresponding to said at least one spatial domain matrix; generating a DECT signal comprising at least one DECT matrix of N DECT coefficients in response to both said DECT basis matrix and said input signal; selecting a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which facilitates one of smearing and sharpening of the input image; generating a padded kernel signal comprising a padded kernel matrix of N coefficients in the spatial domain; producing an N element discrete odd cosine transform (DOCT) basis matrix corresponding to said at least one spatial domain matrix; generating a DOCT signal in response to said DOCT basis matrix and said padded kernel signal; generating a mask signal in response to said DECT signal and said padded kernel signal; generating a hybrid inverse discrete cosine transform (IDECT) basis matrix of N' elements where N'≠N corresponding to said at least one DECT matrix: generating an IDECT signal comprising IDECT coefficients of at least one IDECT matrix in response to both said mask signal and said IDECT basis matrix, and generating said filtered image from an image generator in response to said IDECT signal.

Claim 27

A process of generating a filtered image, said process comprising the steps of: providing an input signal of an input image represented in a spatial domain as at least one spatial matrix of N image data points for a predetermined range, N being a predetermined integer; producing a discrete even cosine transform (DECT) basis matrix corresponding to said at least one spatial domain matrix; generating a DECT signal comprising at least one DECT matrix of N DECT coefficients in response to both said DECT basis matrix and said input signal; selecting a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which facilitates one of smearing and sharpening of the input image; generating a padded kernel signal comprising a padded kernel matrix of N coefficients in the spatial domain; producing an N element discrete odd cosine transform (DOCT) basis matrix corresponding to said at least one spatial domain matrix; generating a DOCT signal in response to said DOCT basis matrix and said padded kernel signal; generating a mask signal in response to said DECT signal and said padded kernel signal; generating a hybrid inverse discrete cosine transform (IDECT) basis matrix of N' elements where N'≠N corresponding to said at least one DECT matrix: generating an IDECT signal comprising IDECT coefficients of at least one IDECT matrix in response to both said mask signal and said IDECT basis matrix, and generating said filtered image from an image generator in response to said IDECT signal.

Claim 28

The process of claim 23, wherein said at least one spatial matrix overlaps an adjacent said at least one spatial matrix.

Claim 29

The process of claim 24, wherein said kernel matrix comprises k elements in one dimension, and said overlapping matrices overlap by k elements, k being a preselected integer.

Claim 30

The process of claim 23, wherein said DOCT matrix is generated from the DOCT equation: ##EQU28## for 0≦u≦(N-1); where H(u) represents said DOCT matrix of DOCT coefficients; h P (i) represents said padded kernel matrix; h P (i)=0 for |i|>(N-1)/2; i and u are integers; d i =1/2 for i=0; and d i =1 for i=1, 2 . . . (N-1).

Claim 31

The process of claim 23, wherein said predetermined criterion comprises one of smearing and sharpening the image.

Claim 32

The process of claim 23, wherein said filtered image is reproduced from said filtered reconstructed matrices.

Claim 37

A process of generating a filtered image, said process comprising the steps of: providing an input signal from an image acquisition device of an input image represented in a spatial domain as at least one spatial matrix of N image data points over a predetermined range, N being a predetermined integer; producing a discrete even cosine transform (DECT) basis matrix corresponding to said at least one spatial domain matrix in a processor; generating a DECT signal in said processor, said DECT signal comprising at least one DECT matrix of N DECT coefficients, in response to both said DECT basis matrix and said input signal; selecting, from a selection device, a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which facilitates one of smearing and sharpening of the input image; generating a padded kernel signal in said processor, said padded kernel signal comprising a padded kernel matrix of N coefficients in the spatial domain; producing, in said processor, an N element discrete odd cosine transform (DOCT) basis matrix corresponding to said at least one spatial domain matrix; generating, in said processor, a DOCT signal in response to said DOCT basis matrix and said padded kernel signal; generating a mask signal in said processor in response to said DECT signal and said padded kernel signal; generating, in said processor, a hybrid inverse discrete cosine transform (IDECT) basis matrix of N' elements, where N'≠N, corresponding to said at least one DECT matrix; generating an IDECT signal in said processor, said IDECT signal comprising IDECT coefficients of at least one IDECT matrix in response to both said mask signal and said IDECT basis matrix; and generating said filtered image from an image generator in response to said IDECT signal.

Claim 38

A process of generating a filtered image, said process comprising the steps of: providing an input signal from an image acquisition device of an input image represented in a spatial domain as at least one spatial matrix of N image data points over a predetermined range, N being a predetermined integer; producing a discrete even cosine transform (DECT) basis matrix corresponding to said at least one spatial domain matrix in a processor; generating a DECT signal in said processor, said DECT signal comprising at least one DECT matrix of N DECT coefficients, in response to both said DECT basis matrix and said input signal; selecting, from a selection device, a kernel in the spatial domain, represented as a kernel matrix, according to a predetermined criterion which facilitates one of smearing and sharpening of the input image; generating a padded kernel signal in said processor, said padded kernel signal comprising a padded kernel matrix of N coefficients in the spatial domain; producing, in said processor, an N element discrete odd cosine transform (DOCT) basis matrix corresponding to said at least one spatial domain matrix; generating, in said processor, a DOCT signal in response to said DOCT basis matrix and said padded kernel signal; generating a mask signal in said processor in response to said DECT signal and said padded kernel signal; generating, in said processor, a hybrid inverse discrete cosine transform (IDECT) basis matrix of N' elements, where N'≠N, corresponding to said at least one DECT matrix; generating an IDECT signal in said processor, said IDECT signal comprising IDECT coefficients of at least one IDECT matrix in response to both said mask signal and said IDECT basis matrix; and generating said filtered image from an image generator in response to said IDECT signal.