# US 2020/0288165 A1 · Image and video processing apparatuses and methods

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- Number: US 2020/0288165 A1
- Document ID: US20200288165A1
- Status: Published application
- Kind: A1
- Application number: 16/880,653
- Filed: 2020-05-21
- Published: 2020-09-10
- Earliest claimed: 2017-11-21
- Assignees: Huawei Technologies Co., Ltd.
- Applicants: Huawei Technologies Co., Ltd.
- Inventors: Itsik DVIR; Natan PETERFREUND; Dror IRONY; David DREZNER; Ady ECKER; Amiram ALLOUCH
- Web page: https://patentgrep.com/patent/US20200288165A1

## CPC

- H04N 19/12: Selection from among a plurality of transforms or standards, e.g. selection between discrete cosine transform [DCT] and sub-band transform or selection between H.263 and H.264
- H04N 19/547: Motion estimation performed in a transform domain
- H04N 19/157: Assigned coding mode, i.e. the coding mode being predefined or preselected to be further used for selection of another element or parameter
- H04N 19/176: the region being a block, e.g. a macroblock
- H04N 19/55: Motion estimation with spatial constraints, e.g. at image or region borders
- H04N 19/567: Motion estimation based on rate distortion criteria
- H04N 19/60: using transform coding
- H04N: PICTORIAL COMMUNICATION, e.g. TELEVISION

## Abstract

The invention relates to an image processing apparatus for compressing or decompressing a segment of an image. The segment includes a plurality of pixels, each pixel includes a pixel value and a pixel position defined by a first coordinate system. The pixel values of the plurality of pixels form a pixel value vector. The apparatus includes processing circuitry configured to compress and/or decompress the segment. Compressing the segment includes computing a plurality of expansion coefficients by expanding the pixel value vector into a plurality of basis vectors that are discrete approximations of solutions of a boundary value problem of the Helmholtz equation on the segment of the image in a second coordinate system rotated relative to the first coordinate system. Decompressing the segment includes computing the pixel value vector by forming a linear combination of the basis vectors using the plurality of expansion coefficients.

## Claims

### Claim 1

An image processing apparatus for compressing or decompressing a segment of an image, the segment comprising a plurality of pixels, each pixel comprising a pixel value and a pixel position defined by a first coordinate system, the pixel values of the plurality of pixels forming a pixel value vector, the apparatus comprising:
processing circuitry configured to compress and/or decompress the segment of the image,
wherein the processing circuitry is configured to, in compressing the segment, compute a plurality of expansion coefficients by expanding the pixel value vector into a plurality of basis vectors, the basis vectors being discrete approximations of solutions of a boundary value problem of the Helmholtz equation on the segment of the image in a second coordinate system, the second coordinate system being rotated relative to the first coordinate system by a rotation angle; and/or
wherein the processing circuitry is configured to, in decompressing the segment, compute the pixel value vector by forming a linear combination of the basis vectors using the plurality of expansion coefficients.

### Claim 2 (depends on 1)

The image processing apparatus of claim 1, wherein the processing circuitry is configured to represent a discretised Laplace operator of the Helmholtz equation as a system matrix A and to determine the basis vectors as eigenvectors of the system matrix A.

### Claim 3 (depends on 2)

The image processing apparatus of claim 2, wherein the processing circuitry is configured to represent the discretised Laplace operator of the Helmholtz equation on the basis of the following matrix:
∇
∥
2

=
1
4

h
2

[
sin


2

θ
4

sin
2

θ
-
sin


2

θ
4

cos
2

θ
-
8
4

cos
2

θ
-
sin


2

θ
4

sin
2

θ
sin


2

θ
]
,
wherein ∇∥2 denotes the discretised Laplace operator, θ denotes the rotation angle between the first coordinate system and the second coordinate system, and h denotes a horizontal distance between two subsequent pixels and a vertical distance between two subsequent pixels.

### Claim 4 (depends on 2)

The image processing apparatus of claim 2, wherein the processing circuitry is configured to generate the system matrix A on the basis of a plurality of boundary conditions defined for a boundary of the segment.

### Claim 5 (depends on 2)

The image processing apparatus of claim 2, wherein the processing circuitry is configured to define the discretized Laplace operator as a three-point stencil.

### Claim 6 (depends on 2)

The image processing apparatus of claim 2, wherein the plurality of pixels comprise a plurality of boundary pixels and a plurality of domain pixels, and wherein the processing circuitry is configured to generate the system matrix A by scanning the plurality of pixels of the segment based on a scanning order to define an order of the plurality of domain pixels of the segment and to determine a number of the plurality of domain pixels of the segment, wherein the number of the plurality of domain pixels of the segment defines a size K×K of the system matrix A.

### Claim 7 (depends on 6)

The image processing apparatus of claim 6, wherein the processing circuitry is configured to generate an i-th column of the system matrix A by centering the discretized Laplace operator on an i-th pixel of the plurality of domain pixels as defined by the scanning order.

### Claim 8 (depends on 7)

The image processing apparatus of claim 7, wherein the processing circuitry is configured to define the i-th column of the system matrix A based on a plurality of boundary conditions, wherein the plurality of boundary conditions comprise Dirichlet boundary conditions, Neumann boundary conditions, and/or mixed Dirichlet and Neumann boundary conditions.

### Claim 9 (depends on 2)

The image processing apparatus of claim 2, wherein the processing circuitry is further configured to determine eigenvalues of the system matrix A and to arrange the eigenvectors of the system matrix A in an increasing order.

### Claim 10

An image processing method for compressing or decompressing a segment of an image, the segment comprising a plurality of pixels, each pixel comprising a pixel value and a pixel position defined by a first coordinate system, the pixel values of the plurality of pixels forming a pixel value vector, the method comprising:
compressing the segment, wherein compressing the segment comprises computing a plurality of expansion coefficients by expanding the pixel value vector into a plurality of basis vectors, wherein the basis vectors are discrete approximations of solutions of a boundary value problem of the Helmholtz equation on the segment of the image in a second coordinate system, wherein the second coordinate system is rotated relative to the first coordinate system by a rotation angle within the image plane; and/or
decompressing the segment, wherein decompressing the segment comprises computing the pixel value vector by forming a linear combination of the basis vectors using the plurality of expansion coefficients.

### Claim 11 (depends on 2)

A video processing apparatus for encoding or decoding a video signal, wherein the video processing apparatus comprises:
an image processing apparatus according to claim 2,
wherein the video processing apparatus is configured, during encoding, to compress a segment of a residual image generated from the video signal and/or the video processing apparatus is configured, during decoding, to decompress a segment of a residual image generated from the video signal.

### Claim 12 (depends on 11)

The video processing apparatus of claim 11, wherein the eigenvectors of the system matrix A define a transformation matrix V, and
wherein for encoding and/or decoding the video signal, the processing circuitry is configured to scan column vectors of the transformation matrix V according to an increasing order of eigenvalues associated with the eigenvectors of the system matrix A.

### Claim 13 (depends on 11)

The video processing apparatus of claim 11, wherein the processing circuitry is further configured to determine an orthogonal set of transforms based on a rate distortion criterion.

### Claim 14 (depends on 11)

The video processing apparatus of claim 11, wherein the processing circuitry is further configured to determine a plurality of boundary conditions for the plurality of boundary pixels of the segment on the basis of another image segment of the same image or a different image of the video signal.

### Claim 15 (depends on 11)

The video processing apparatus of claim 11, wherein the processing circuitry is configured to choose, as the rotation angle between the first coordinate system and the second coordinate system, a direction angle associated with an intra prediction mode selected by the video processing apparatus for intra predicting the segment.

### Claim 16 (depends on 10)

A computer program comprising program code that, when executed on a computer, causes the computer to perform the method of claim 10.