# US 8,855,195 B1 · Image processing system and method

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- Number: US 8,855,195 B1
- Document ID: US8855195B1
- Status: Granted
- Kind: B1
- Application number: 14/343,844
- Filed: 2012-09-10
- Published: 2014-09-25
- Granted: 2014-10-07
- Earliest claimed: 2011-09-09
- Assignees: Panamorph, Inc.
- Applicants: Shawn L. Kelly
- Inventors: Shawn L. Kelly
- Web page: https://patentgrep.com/patent/US8855195B1

## CPC

- G06T 9/00: Image coding (bandwidth or redundancy reduction for static pictures H04N1/41; coding or decoding of static colour picture signals H04N1/64; methods or arrangements for coding, decoding, compressing or decompressing digital video signals H04N19/00)
- G06T 1/00: General purpose image data processing
- G06T 3/4092: Image resolution transcoding, e.g. by using client-server architectures
- H04N 19/85: using pre-processing or post-processing specially adapted for video compression
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- H04N: PICTORIAL COMMUNICATION, e.g. TELEVISION

## Abstract

A relatively higher resolution digitized image organized as a plurality of first kernel arrays, each with a plurality of pixels, is transformed into a corresponding relatively-smaller second kernel array of a relatively-lower-resolution image and an associated set of remaining pixels. Down-sampled pixels of the second kernel array are generated from linear interpolation of original pixels of the first kernel array. Associated interpolation coefficients incorporate perturbations to locations of the down-sampled pixels that are symmetric with respect to centers of the first and second kernel arrays. Down-sampled pixels of the second kernel array can be recombined with the associated set of remaining pixels to reconstruct the relatively higher resolution digitized image substantially without loss of associated information, or used directly to reconstruct an approximation thereof, with associated encoding and decoding processes adapted to reduce the susceptibility of image reconstruction errors caused by subsequent image compression.

## Claims

### Claim 1

A method of processing an image representation, comprising:
a. either receiving a first group of a second plurality of pixels, or extracting said first group of said second plurality of pixels from a first image representation, wherein said first group of said second plurality of pixels comprises a fourth two-dimensional array of pixels representative of a digitized image at a first resolution thereof, a width of said digitized image is along a first dimension of said fourth two-dimensional array of pixels, a height of said digitized image is along a second dimension of said fourth two-dimensional array of pixels, and
b. displaying a first two-dimensional array of pixels, wherein said first two-dimensional array of pixels is representative of said digitized image at a second resolution thereof, said second resolution is relatively higher than said first resolution, and the operation of displaying said first two-dimensional array of pixels comprises determining at least one pixel of said first two-dimensional array of pixels responsive to an algebraic combination of at least one corresponding pixel of said first group of said second plurality of pixels and at least one pixel selected from the group consisting of a corresponding pixel of a second group of a third plurality of pixels, and an estimate of a corresponding at least one pixel of said first two-dimensional array of pixels, wherein, if used, said corresponding pixel of said second group of said third plurality of pixels is either received or extracted from either said first image representation or a second image representation, and if used, said estimate of said corresponding at least one pixel of said first two-dimensional array of pixels is responsive to a corresponding pixel of said first group of said second plurality of pixels and responsive to a difference between different corresponding pixels of said first group of said second plurality of pixels.

### Claim 2 (depends on 1)

A method of processing an image representation as recited in claim 1, further comprising reconstructing said first two-dimensional array of pixels from said first and second groups of said second and third pluralities of pixels prior to the operation of displaying said first two-dimensional array of pixels, wherein the operation of reconstructing said first two-dimensional array of pixels comprises inserting therein either rows or columns of pixels from said second group of said third plurality of pixels between pixels of said first two-dimensional array of pixels determined responsive to pixels of corresponding rows or columns of said first group of said second plurality of pixels and responsive to said rows or columns of pixels from said second group of said third plurality of pixels.

### Claim 3 (depends on 1)

A method of processing an image representation as recited in claim 1, wherein the operation of reconstructing said first two-dimensional array of pixels comprises determining at least one row or column of pixels in said first two-dimensional array of pixels is responsive to an algebraic combination of a corresponding row or column of pixels of said first group of said second plurality of pixels and a corresponding row or column of pixels of said second group of said third plurality of pixels.

### Claim 4 (depends on 1)

A method of processing an image representation as recited in claim 1, further comprising electronically stretching said first two-dimensional array of pixels along either said height or said width prior to the operation of displaying said first two-dimensional array of pixels.

### Claim 5 (depends on 1)

A method of processing an image representation as recited in claim 1, further comprising decoding said first image representation so as to generate a third two-dimensional array of pixels, wherein said third two-dimensional array of pixels comprises said first group of said second plurality of pixels and said second group of said third plurality of pixels, and said first group of said second plurality of pixels is contiguous within said third two-dimensional array of pixels.

### Claim 6 (depends on 1)

A method of processing an image representation as recited in claim 1, further comprising:
a. decoding said first image representation so as to generate said first group of said second plurality of pixels;
b. decoding said second image representation so as to generate said second group of said third plurality of pixels; and
c. synchronously combining said first and second groups of said second and third pluralities of pixels so as to provide for displaying said first two-dimensional array of pixels.

### Claim 7 (depends on 1)

A method of processing an image representation as recited in claim 1, wherein a first plurality of pixels of said first two-dimensional array of pixels is organized as a corresponding second two-dimensional array of a plurality of first kernel arrays, said first group of said second plurality of pixels of said fourth two-dimensional array of pixels is organized as a fifth two-dimensional array of a plurality of second kernel arrays, said plurality of first kernel arrays are in one-to-one correspondence with said plurality of second kernel arrays, each first kernel array of said plurality of first kernel arrays is equal in size and dimensionality, each second kernel array of said plurality of second kernel arrays is equal in size and dimensionality and equal in dimensionality of each said first kernel array, a size of each said first kernel array is greater than a size of each corresponding said second kernel array, and each said first kernel array is formed from said corresponding second kernel array and one or more corresponding values of said second group of said third plurality of pixels responsive to a similar set of algebraic operations relative to elements of said first and second kernel arrays for different said first and second kernel arrays.

### Claim 8 (depends on 7)

A method of processing an image representation as recited in claim 7, wherein said algebraic operations are selected from the group consisting of left binary shift, right binary shift, addition and subtraction.

### Claim 9 (depends on 7)

A method of processing an image representation as recited in claim 7, wherein said dimensionality is linear in one of row or column space of each of said first and fourth two-dimensional arrays of pixels.

### Claim 10 (depends on 9)

A method of processing an image representation as recited in claim 9, wherein each said first kernel array comprises a linear array of three pixels in row or column space and each second kernel array comprises a corresponding linear array of two pixels in the same said row or column space.

### Claim 11 (depends on 10)

A method of processing an image representation as recited in claim 10, wherein each element AEDGE of said first kernel array is given by the quantity: ((α+β)·B−β·ACENTER)/α, wherein AEDGE is a corresponding edge pixel of said first kernel array corresponding to said element B of said second kernel array, ACENTER is the relatively central pixel of said first kernel array, and said relatively central pixel, if stored, is stored in said second group of said third plurality of pixels.

### Claim 12 (depends on 11)

A method of processing an image representation as recited in claim 11, wherein the values of α and θ are given by the combination (α, β) of (2, 1).

### Claim 13 (depends on 9)

A method of processing an image representation as recited in claim 9, wherein each first kernel array comprises a linear array of four pixels in row or column space and each second kernel array comprises a corresponding linear array of three pixels in the same said row or column space.

### Claim 14 (depends on 13)

A method of processing an image representation as recited in claim 13, wherein for said four pixels of said first kernel array consecutively designated as A1, A2, A3 and A4, for said corresponding three pixels of said second kernel array consecutively designated as B1, B2 and B3, and for one of said A1 or said A2 storable in said second group of said third plurality of pixels and designated as AX, the other of A2 or said A1 is given by the quantity ((α+β)·B1−α·AX)/β, said A3 is given by the quantity 2·B2−A2, and said A4 is given by the quantity ((α+β)·B3−β·A3)/α.

### Claim 15 (depends on 14)

A method of processing an image representation as recited in claim 14, wherein the values of alpha and beta are selected from the group of combinations (α, β) consisting of (1,0), (3,1), (4,1), (5,3) and (7,1).

### Claim 16 (depends on 13)

A method of processing an image representation as recited in claim 13, wherein for said four pixels of said first kernel array consecutively designated as A1, A2, A3 and A4, for said corresponding three pixels of said second kernel array consecutively designated as B1, B2 and B3, and for the quantity (A3−A2+μ)/2 storable in said second group of said third plurality of pixels and designates as γ, wherein mu is a constant, said A2 is given by the quantity B2−γ+μ/2, said A3 is given by the quantity 2·B2−A2, and said A1 is given by the quantity ((α+β)·B1−β·A2)/α, and said A4 is given by the quantity ((α+β)·B3−β·A3)/α.

### Claim 17 (depends on 16)

A method of processing an image representation as recited in claim 16, wherein the values of alpha and beta are selected from the group of combinations (α, β) consisting of (1,0), (3,1), (4,1), (5,3) and (7,1).

### Claim 18 (depends on 13)

A method of processing an image representation as recited in claim 13, wherein for said four pixels of said first kernel array consecutively designated as A1, A2, A3 and A4, for said corresponding three pixels of said second kernel array consecutively designated as B1, B2 and B3, said estimate of said corresponding at least one pixel of said first two-dimensional array of pixels comprises an estimate of said A2, wherein said estimate of said A2 is given by the quantity B2−(B3−B1)·K, wherein K is a constant, said A3 is given by the quantity 2·B2−A2, and said A1 is given by the quantity ((α+β)·B1−β·A2)/α, and said A4 is given by the quantity ((α+β)·B3−β·A3)/α.

### Claim 19 (depends on 18)

A method of processing an image representation as recited in claim 18, wherein said K is responsive to one or more user-settable parameters that control an appearance of said image.

### Claim 20 (depends on 18)

A method of processing an image representation as recited in claim 18, wherein the values of alpha and beta are selected from the group of combinations (α,β) consisting of (1,0), (3,1), (4,1), (5,3) and (7,1).

### Claim 21 (depends on 7)

A method of processing an image representation as recited in claim 7, wherein said dimensionality is two dimensional with equal row and column dimensions.

### Claim 22 (depends on 21)

A method of processing an image representation as recited in claim 21, wherein each said first kernel array comprises a three-by-three array of nine pixels, and each said second kernel array comprises a two-by-two array of four pixels.

### Claim 23 (depends on 21)

A method of processing an image representation as recited in claim 21, wherein each said first kernel array comprises a four-by-four array of sixteen pixels, and each said second kernel array comprises a three-by-three array of nine pixels.

### Claim 24 (depends on 21)

A method of processing an image representation as recited in claim 21, wherein each said first kernel array comprises a six-by-six array of thirty-six pixels, and each said second kernel array comprises a three-by-three array of nine pixels.

### Claim 25 (depends on 7)

A method of processing an image representation as recited in claim 7, wherein said second group of said third plurality of pixels is interleaved with said first group of said second plurality of pixels within a third two-dimensional array of pixels, and elements of said third plurality of pixels are interleaved with corresponding elements of said second plurality of pixels within a common said second kernel array common to each.

### Claim 26 (depends on 25)

A method of processing an image representation as recited in claim 25, wherein said elements of said third plurality of pixels are interleaved within said second kernel array at a relative location therewithin that is consistent for all second kernel arrays of said plurality of second kernel arrays.

### Claim 27 (depends on 1)

A method of processing an image representation as recited in claim 1, wherein said first group of said second plurality of pixels is contiguous and arranged in a contiguous fourth two-dimensional array of pixels so as to provide for directly displaying a representation of said digitized image having a relatively-lower resolution relative to a resolution of said digitized image of a first plurality of pixels in said first two-dimensional array of pixels.

### Claim 28 (depends on 1)

A method of processing an image representation as recited in claim 1, wherein said second group of said third plurality of pixels is interleaved with said first group of said second plurality of pixels within a third two-dimensional array of pixels.

### Claim 29 (depends on 28)

A method of processing an image representation as recited in claim 28, wherein said third two-dimensional array of pixels is equal in size and dimension to said first two-dimensional array of pixels.

### Claim 30 (depends on 1)

A method of processing an image representation as recited in claim 1, wherein prior to the operation of displaying said first two-dimensional array of pixels, further comprising successively repeating the operation of determining said at least one pixel of said first two-dimensional array of pixels one or more times, wherein each said first two-dimensional array of pixels resulting from a previous occurrence of said operation of determining said at least one pixel of said first two-dimensional array of pixels is used as said first group of said second plurality of pixels for the next occurrence of said operation determining said at least one pixel of said first two-dimensional array of pixels, and a different subset of pixels of said second group of said third plurality of pixels is used for each successive occurrence of said operation determining said at least one pixel of said first two-dimensional array of pixels.

### Claim 31 (depends on 30)

A method of processing an image representation as recited in claim 30, wherein at least one occurrence of said operation of determining said at least one pixel of said first two-dimensional array of pixels operates on only one of two dimensions, horizontal or vertical, of said fourth two-dimensional array of pixels by which said second plurality of pixels is organized.

### Claim 32 (depends on 30)

A method of processing an image representation as recited in claim 30, wherein different occurrences of said operation of determining said at least one pixel of said first two-dimensional array of pixels operate on different dimensions, horizontal and vertical, of said fourth two-dimensional array of pixels by which said second plurality of pixels is organized.

### Claim 33 (depends on 30)

A method of processing an image representation as recited in claim 30, wherein at least one occurrence of said operation of determining said at least one pixel of said first two-dimensional array of pixels simultaneously operates on both dimensions, horizontal and vertical, of said first two-dimensional array of pixels.