KR102281037B1 - A method and an apparatus for extracting viewport - Google Patents

Abstract

The viewport extraction method according to the present invention converts coordinates for positions of pixels in a viewport area into coordinates in the UV area, calculates spherical surface coordinates corresponding to the converted UV area coordinates, and calculates the calculated spherical surface coordinates. It is possible to extract image information corresponding to .

Description

Viewport Extraction Method and Apparatus {A METHOD AND AN APPARATUS FOR EXTRACTING VIEWPORT}

The present invention relates to a viewport extraction method and apparatus.

As camera performance improves and network bandwidth increases, the demand for 360 VR video that requires high resolution and high bandwidth is also increasing. In order to view 360 VR video, a viewport that selectively outputs only a part of the entire 360 video is required. 360 VR image information is stored on the surface of a unit sphere in 3D space. When viewing only the image from the desired viewpoint through the viewport, after setting the desired viewpoint and the desired field of view (FOV), the image information of the unit sphere surface is projected onto the plane adjacent to the sphere to extract the image information through the viewport. .

Rectilinear projection, which is a conventional viewport extraction method commonly used, uses a plane, so the larger the FOV of the viewport, the greater the visual distortion.

US 2018-0040507 A

An object of the present invention is to solve the problems of the prior art by using a viewport extraction method using a curved surface.

An object of the present invention is to correct the coordinates so that the density of image information is evenly distributed in viewport extraction.

The technical problems to be achieved in the present invention are not limited to the technical problems mentioned above, and other technical problems not mentioned will be clearly understood by those of ordinary skill in the art to which the present invention belongs from the following description. will be able

A viewport extraction method and apparatus according to the present invention converts coordinates for a position of a pixel in a viewport area into coordinates in a UV area, calculates the spherical surface coordinates corresponding to the converted UV area coordinates, Image information corresponding to the calculated spherical surface coordinates may be extracted.

In the viewport extraction method and apparatus according to the present invention, the UV region may be a region used when calculating spherical surface coordinates containing image information.

In the viewport extraction method and apparatus according to the present invention, the UV region may be a flat surface or a curved surface.

In the viewport extraction method and apparatus according to the present invention, the curved surface is a part of an outer sphere circumscribed with the sphere containing the image information, and the radius of the outer sphere may be greater than or equal to the radius of the sphere containing the image information. there is.

In the viewport extraction method and apparatus according to the present invention, the conversion is performed by considering only the number of pixels in the horizontal direction and the vertical direction in the viewport area, without considering the horizontal and vertical lengths of the UV area, The horizontal and vertical lengths of the UV region may be determined in consideration of a field of view (FOV) of the viewport region.

In the viewport extraction method and apparatus according to the present invention, the conversion step may include a correction step of correcting the converted coordinates.

In the viewport extraction method and apparatus according to the present invention, in the correction step, the UV region is subdivided into at least two regions, and the distance between the coordinates of the first subdivided region is smaller than the distance between the coordinates of the second subdivided region. to correct the coordinates of at least one of the first subdivided region and the second subdivided region.

In the viewport extraction method and apparatus according to the present invention, the correction step is performed using a three-dimensional function, wherein the three-dimensional function has a slope of less than 1 within a range applied to the first subdivided area. , within a range applied to the second subdivided area, the slope of the function may be greater than 1.

In the viewport extraction method and apparatus according to the present invention, in the correction step, when the size of the viewport area or the UV area is less than or equal to a threshold size, the correction step of at least some of the subdivided areas may be skipped.

In the viewport extraction method and apparatus according to the present invention, the correction step is performed by applying a weight and an offset value, and the weight and the offset value may be the same or different for each subdivided area.

In the viewport extraction method and apparatus according to the present invention, the first area may be in the form of a circle or a rectangle based on the center of the UV area.

In the viewport extraction method and apparatus according to the present invention, the calculating step may include orthogonally projecting the converted UV region to the center of the spherical surface, and calculating the coordinates of the spherical surface corresponding to the coordinates of the orthographically projected UV region. can

In the viewport extraction method and apparatus according to the present invention, the position of the pixel may include a position of a pixel group composed of the pixels.

In the viewport extraction method and apparatus according to the present invention, the position of the pixel group may include a position of any one pixel included in the pixel group or an average value of a plurality of pixels included in the pixel group.

The features briefly summarized above with respect to the invention are merely exemplary aspects of the detailed description of the invention that follows, and do not limit the scope of the invention.

According to the present invention, by extracting a viewport using a curved surface, it is possible to reduce visual distortion that increases as the FOV increases.

According to the present invention, by correcting the coordinates, it is possible to further reduce the remaining visual distortion.

The effects obtainable in the present invention are not limited to the above-mentioned effects, and other effects not mentioned may be clearly understood by those of ordinary skill in the art to which the present invention belongs from the following description. will be.

1 is a diagram illustrating a flowchart of a Viewport extraction method.
2 is a diagram illustrating a 2D projection method on a plane using a rectilinear projection method.
3 is a diagram illustrating a 2D projection method on a plane using a stereographic projection method.
4 is a diagram illustrating a model of a viewport extraction method using a curved surface.
5 is a diagram showing a cross section of a model ( FIG. 4 ) of a viewport extraction method using a curved surface.
6 is a diagram illustrating a cubic function having a domain and a range of [0, 1] applied in the correction step.

Since the present invention can have various changes and can have various embodiments, specific embodiments are illustrated in the drawings and described in detail in the detailed description. However, this is not intended to limit the present invention to specific embodiments, and it should be understood to include all modifications, equivalents and substitutes included in the spirit and scope of the present invention. In describing each figure, like reference numerals have been used for like elements.

Terms such as first, second, etc. may be used to describe various elements, but the elements should not be limited by the terms. The above terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, a first component may be referred to as a second component, and similarly, a second component may also be referred to as a first component. The term 'and/or' includes a combination of a plurality of related listed items or any of a plurality of related listed items.

When a component is referred to as being “connected” or “connected” to another component, it is understood that the other component may be directly connected or connected to the other component, but other components may exist in between. it should be On the other hand, when it is said that a certain element is "directly connected" or "directly connected" to another element, it should be understood that the other element does not exist in the middle.

The terms used in the present application are only used to describe specific embodiments, and are not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly dictates otherwise. In the present application, terms such as “comprise” or “have” are intended to designate that a feature, number, step, operation, component, part, or combination thereof described in the specification exists, but one or more other features It should be understood that this does not preclude the existence or addition of numbers, steps, operations, components, parts, or combinations thereof.

Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the accompanying drawings. Hereinafter, the same reference numerals are used for the same components in the drawings, and repeated descriptions of the same components are omitted.

Since a person's viewing angle is limited to about 120 degrees, the user cannot view the panoramic image or the entire 360-degree image at once. Due to the limited viewing angle, the user only views a panoramic image or a partial image of a 360-degree image. A partial image corresponding to the user's viewing area among the entire area of the panoramic image or 360-degree image may be defined as a view port.

The view port may be classified into a static view port and a dynamic view port according to flexibility. A static view port means a view port that does not change position, and a dynamic view port means a view port whose position changes as the user's gaze changes. It is rare to use a static viewport for the entire 360-degree image, and most use a dynamic viewport whose position changes according to the user's gaze movement.

The panoramic image may be an image generated by stitching a plurality of images. The plurality of images may be images captured by a plurality of cameras, respectively. This is because the field of view of the image captured by the camera is limited according to the angle of view of the camera.

The 360-degree image may be an image having a degree of freedom of rotation based on a predetermined central axis among the panoramic images. For example, the 360-degree image may be an image having rotation degrees of freedom for at least one of Yaw, Roll, and Pitch.

Embodiments to be described later will be described with a focus on a 360-degree image, but applying the embodiments described later to a panoramic image other than a 360-degree image will be included in the technical scope of the present invention.

1 is a diagram illustrating a flowchart of a Viewport extraction method.

Referring to FIG. 1 , the viewport extraction method includes a transformation step (S100) of converting coordinates for positions of pixels in a viewport region into coordinates in a UV region; a calculation step (S101) of calculating spherical surface coordinates corresponding to the coordinates of the converted UV region; And it may include at least one of the extraction step (S102) of extracting the image information corresponding to the calculated spherical surface coordinates.

When the viewport extraction method is applied to an apparatus for encoding/decoding an image, it may be applied to extract a viewport image from a 360-degree image in the form of a sphere decoded through both projection and back-projection of the 360-degree image.

Hereinafter, a transformation step (S100) of converting coordinates for positions of pixels in a viewport region into coordinates in a UV region will be described.

The coordinates may be a 2D Cartesian coordinate system.

The coordinates for the positions of the pixels include coordinates for one pixel or coordinates for a group of pixels. The coordinates of the pixel group include the coordinates of the leftmost/right/top/bottom, the upper-left pixel, the lower-right pixel, the central pixel among the pixels of the corresponding pixel group, or the average value of the pixel coordinates in the pixel group. may include The average value may be a value calculated as an average value based on the same weight or a value calculated as an average value based on a different weight for each pixel. Here, the different weights may be determined in consideration of the pixel distance/position. Also, the coordinates of the pixel positions may be vector coordinates based on one coordinate.

For example, when 9 pixels in the viewport area form a group in a square shape or when 5 pixels in the viewport area form a group in a rhombus shape, the coordinates of the central pixel in the group are the coordinates of the pixel group. can be

For example, when one row or column of the viewport area forms one group, the coordinates of the pixels at the left/right or center of the group may be the coordinates of the group. In addition, coordinates calculated as an average value after multiplying the coordinates of the pixels in the row or column by a weight according to the distance may be the coordinates of the group.

The UV region may be a separate region for projecting a spherical surface containing image information. The region may have a curved or flat shape. The flat or curved surface may have a polygonal shape such as a triangle or a quadrangle or a circle shape. Also, at least one line of the polygon may have a curved shape. Specifically, in the case of a curved shape, the shapes may have a curved shape in the direction of the sphere containing the image information or the opposite direction. Also, in the case of a planar shape, the shapes may have an unfolded shape that is not bent in any direction.

Specifically, the curved surface may be a part of the outer sphere of the sphere including the image information. In this case, the radius of the outer sphere is r, which may be greater than or equal to the radius of the sphere including the image information. For example, when a sphere including image information is a unit sphere, r may be greater than or equal to 1.

The UV region may circumscribe the surface of the sphere including the image information or may be spaced apart by a predetermined distance. The predetermined distance may correspond to a distance n times the radius of the sphere including the image information, and n may include 1, 2, 3, or more natural numbers.

For example, referring to FIGS. 2 and 3 , the UV region is in the form of a plane having a rectangular shape and circumscribes a sphere surface including image information.

As an example, referring to FIG. 4 , the UV region is in the form of a curved surface having a rectangular shape, circumscribes the surface of the sphere containing the image information, and constitutes a part of the outer sphere larger than the radius of the sphere containing the image information. . Here, r of the outer sphere is greater than 1.

The shape, shape, location, or size of the UV region may be a predetermined fixed shape, shape, location, or size. In addition, the shape, shape, location, or size of the region may be variably determined from information related to the UV region. The information related to the UV region includes a horizontal or vertical field of view (FOV), the size or shape of the viewport region, the number of pixels or pixel groups in the viewport region, the type of image information, the amount or density of image information, A viewport projection technique, which will be described later, may be included. Here, the size may include a width, a height, or a ratio of the width to the height. All or part of the information related to the UV region may be encoded and signaled by an image encoding apparatus, or may be determined by a user input.

For example, the size of the UV region may be the same as the size of the viewport region. Alternatively, the size of the UV region may be different from the size of the viewport region. When the sizes are different from each other, the size of the UV region may be set to a size having the same ratio as the ratio of the width and height of the viewport region.

For example, when the FOVs in the horizontal or vertical directions are the same, the shape of the UV region may be a regular polyhedron or a circle shape. Specifically, when the polygon is a quadrangle, the shape of the UV region may have a square shape. On the other hand, when the FOVs in the horizontal or vertical directions are different from each other, the shape of the UV region may have a shape according to the FOV ratio. Specifically, when the polygon is a quadrilateral, the shape of the UV region may have a rectangular shape having the same width and height ratio as the FOV ratio.

The transformation of the coordinates may include calculating by the first equation when the UV region is a flat surface, and calculating by the second equation when the UV region is a curved surface. However, the present invention is not limited thereto, and a curved surface may be calculated by the first equation, and a flat surface may be calculated by the second equation. Alternatively, a part of the UV region may be calculated by the first equation, and the other part may be calculated by the second equation. For example, the first Equation and the second Equation may be defined as Equations 1 and 2 below.

,

는 UV영역의 가로, 세로 길이이며,

,

는 뷰포트 영역의 가로방향, 세로방향 화소의 개수이다. (u,v)는 UV영역의 좌표, (m,n)은 뷰포트 영역의 좌표이다.here,

,

is the horizontal and vertical length of the UV area,

,

is the number of horizontal and vertical pixels in the viewport area. (u,v) is the coordinates of the UV area, and (m,n) is the coordinates of the viewport area.

,

는 투영 기법에 따라 다른 값을 가질 수 있다. of Equation 1 above

,

may have different values depending on the projection technique.

,

는 아래 수학식 3에 의해 정의될 수 있다.As an example, FIG. 2 shows a case in which a Rectilinear projection is used,

,

may be defined by Equation 3 below.

와

는 각각 viewport의 가로방향, 세로방향에 대한 FOV(Field of view)이다.here,

Wow

is the FOV (Field of View) for the horizontal and vertical directions of the viewport, respectively.

,

는 아래 수학식 4에 의해 정의될 수 있다.As an example, FIG. 3 is a case in which stereographic projection is used,

,

may be defined by Equation 4 below.

와

는 각각 viewport의 가로방향, 세로방향에 대한 FOV(Field of view)이다.here,

Wow

is the FOV (Field of View) for the horizontal and vertical directions of the viewport, respectively.

Hereinafter, the calculation step (S101) of calculating the spherical surface coordinates corresponding to the converted UV region coordinates will be described.

The spherical surface coordinates may be coordinates of a 3D XYZ coordinate system. The 3D XYZ coordinate system may consist of a unit sphere with X, Y, and Z axes and a radius length of 1. Here, the unit sphere may include 360-degree image information on the corresponding surface.

One point on the surface of the unit sphere may be expressed by longitude (φ) and latitude (θ). The hardness φ may represent an angle in a counterclockwise direction with respect to the X axis, and the range may be [-π, π]. The latitude θ may represent an angle from the equator toward the Y axis, and the range may be [-π/2, π/2]. The coordinates (X, Y, Z) and (φ, θ) of a point on the surface of the unit sphere of the 3D XYZ coordinate system have the same relationship as in Equation 5 below.

,

)에 따라 전환될 수 있다. 구체적으로, 상기 전환은 아래 수학식 6에 의해 수행될 수 있다.Furthermore, the (X, Y, Z) coordinates are the latitude and longitude (

,

) can be converted according to Specifically, the conversion may be performed by Equation 6 below.

Here, (X', Y', Z') is the converted coordinate of (X, Y, Z).

Calculating the coordinates of the spherical surface may include obtaining coordinates of the projected spherical surface corresponding to the coordinates of the UV region by projecting the spherical surface to the UV region.

The projection may include a rectilinear projection or a stereographic projection.

The determination of the projection technique may be determined by a predetermined fixed technique, or may be variably determined based on projection-related information. The projection-related information may be determined based on at least one of the aforementioned parameters. The above-mentioned parameters include a field of view (FOV) in the horizontal or vertical direction, the size or shape of the viewport area, the number of pixels or pixel groups in the viewport area, the shape, shape, position, or size of the UV area, and image information. It may include at least one of a type and an amount or density of data of image information.

2 is a diagram illustrating a 2D projection method on a plane using a rectilinear projection method.

Rectilinear projection is a method of projecting the point of a sphere by orthographically projecting the point of the waterline down to the 2D area. According to the above method, the coordinates (u, v) of the 2D area and the coordinates (X, Y, Z) of the 3D sphere may have a relationship as in Equation 7 below.

,

는 UV영역의 가로, 세로 길이이고, 앞서 설명한 수학식 3에 의해 계산될 수 있다. 또한,

,

는 뷰포트 영역의 가로방향, 세로방향 화소의 개수이다.here,

,

is the horizontal and vertical lengths of the UV region, and can be calculated by Equation 3 described above. also,

,

is the number of horizontal and vertical pixels in the viewport area.

3 is a diagram illustrating a 2D projection method on a plane using a stereographic projection method.

Stereographic projection refers to a relationship between the coordinates (u, v) of the 2D area and the coordinates (X, Y, Z) of the 3D sphere as shown in Equation 8 below.

,

는 UV영역의 가로, 세로 길이이고, 앞서 설명한 수학식 4에 의해 계산될 수 있다.here,

,

is the horizontal and vertical lengths of the UV region, and can be calculated by Equation 4 described above.

4 is a model of a viewport extraction method using a curved surface, and FIG. 5 is a diagram illustrating a cross-section of a model ( FIG. 4 ) of a viewport extraction method using a curved surface.

A 2D projection method on a curved surface using a Rectilinear projection method will be described below with reference to FIGS. 4 and 5 .

First, referring to FIG. 4 , the curved surface ABCD is a part of the outer sphere circumscribed with the unit sphere, the radius of the outer sphere is r, and the center of the outer sphere is O' separated by r along the Z axis. In addition, the outer sphere is expressed by the equation shown in Equation (9).

Referring to FIG. 5 , in the 2D projection method on a curved surface using the rectilinear projection method, the coordinates (u, v) of the 2D area and the coordinates (X, Y, Z) of the 3D sphere may have a relationship as in Equation 10 below. .

,

는 아래의 수학식 11에 의해 정의될 수 있다.here,

,

may be defined by Equation 11 below.

는 Viewport의 세로방향 FOV이고,

은 외부 구의 중점 O'을 기준으로 하는 세로방향 각도이다.here,

is the vertical FOV of the viewport,

is the longitudinal angle with respect to the midpoint O' of the outer sphere.

The extraction step (S102) of extracting the image information corresponding to the calculated spherical surface coordinates refers to loading the spherical surface image information matching each of the corresponding viewport region coordinates into the viewport region.

The transformation step (S100) may further include a correction step of correcting the transformed coordinates.

The correction step may be selectively performed based on at least one of the above-described parameters. For example, if the size of the viewport area (or UV area) is less than or equal to a predetermined threshold size, the correction step may be skipped. Otherwise, the correction step may be performed. The threshold size may be a value pre-defined in the image encoding/decoding apparatus, and the image encoding apparatus may determine an optimal threshold size and encode it. The encoded threshold size may mean a minimum/maximum size for which coordinate correction is allowed. Alternatively, when the type of the UV region is a flat surface, the correction step may be skipped, and if the type of the UV region is a curved surface, the correction step may be performed.

The correction step may be performed for all of the UV region, or the correction step may be performed only for a part of the UV region. Here, the part may mean a central region of the UV region or an edge region within the UV region. Alternatively, a portion may be limited to the left/right edge region of the UV region, or may be limited to the upper/bottom edge region. Alternatively, the portion may be limited to at least one of each corner region (eg, upper left, lower left, upper right, lower right) of the UV region. The edge region includes T pixel lines from the boundary of the UV region, and T may be an integer of 1, 2, 3, 4, 5 or more. Depending on the position of the edge, the number of pixel lines included in the edge region may be different. For example, the left/right edge area where the correction step is performed may include more pixel lines than the upper/lower edge area.

For correction, the UV region may be largely divided into a central region and an edge region. Alternatively, the UV region may be divided into a center region, an edge region (excluding a corner region), and a corner region. However, this does not limit the number and position of the divided regions, and the UV region may be divided into four or more subdivided regions.

For example, in the correction step, the UV region is divided into a first region and a second region, and the distance between the coordinates of the first region is smaller than the distance between the coordinates of the first region or the second region. It may include correcting the coordinates of at least one of the two regions.

The first region may have a polygonal or circular shape with a center point of the UV region as a center. In this case, the second area may include all or part of the remaining area except for the first area in the UV area.

The correction according to the present invention may include a process of converting the pixel position (x,y) in the UV region into (x',y'). Corrected positions x' and y' may be obtained by applying predetermined weights w and offsets o to the x and y coordinates of the pixel position, respectively. Here, the weight w and the offset o may be integers including 0.

The weight wx for the x coordinate may include at least one of wx1, wx2, or wx3. The weight wy for the y coordinate may include at least one of wy1, wy2, or wy3. For example, the correction may be performed as in Equation 12 below.

Unlike the cubic equation, first, second, fourth, fifth, or higher order equations may also be applied.

The image encoding/decoding apparatus may define a plurality of equations for correction. Correction may be performed by selecting any one of a plurality of equations. Here, the selection is the size/shape of the viewport area, the size/shape of the UV area, the type of the UV area (eg, flat, curved, etc.), the size of at least one of a sphere containing image information or a circumscribed external sphere. (eg, a radius) and information such as a size ratio between the sphere and the outer sphere may be taken into consideration. To this end, the information may be encoded in the form of metadata and transmitted to the image decoding apparatus.

In addition, when the UV region is subdivided as described above, the same equation may be applied to each region, or different equations may be applied depending on the location of the region. A different equation may mean an equation in which at least one of a degree, a weight, and an offset is different. For example, when the UV region is subdivided into a central region, an edge (including a corner) region, and a boundary region from the boundary of the central region to the boundary of the edge, at least one of the central region or the edge region is expressed by the first equation However, the second equation may be applied to the boundary area.

The weight w and the offset o may be pre-defined fixed values or may be variably determined by at least one of the above-described parameters.

The weight w or offset o may increase or decrease in proportion to or inversely proportional to the size of the viewport region (or UV region). Here, the increase or decrease may include continuously increasing or decreasing according to the size of the viewport area (or UV area). Alternatively, it may include dividing the size into sections and increasing or decreasing the weight (w) or offset (o) in a stepwise fashion by setting a representative value of the section including the size.

In addition, the increase or decrease may have an upper limit or a lower limit. For example, even if the size of the viewport area (or UV area) becomes smaller or larger than a predetermined threshold, the weight or offset no longer changes and a constant weight or offset is applied. can have

The weight and offset values may differ according to the subdivided area of the viewport area (or UV area).

For example, the weight w or the offset o may be determined according to the location of the subdivided area. Specifically, when the UV region is subdivided into a central region, an edge region, and a corner region, a weight w or an offset o between the regions may be the same or different.

As another example, the weight w or the offset o may be determined according to the shape of the subdivided region. Specifically, when the UV region is in the form of a plane, the weight (w) or the offset (o) may have the same value as other subdivided regions, but in the case of a curved surface, the weight (w) or the offset (o) is different subdivision It may have a different value than the specified area.

6 is a diagram illustrating a cubic function having a domain and a range of [0, 1] applied in the correction step.

The correction may be performed through a cubic function having a curvature as shown in FIG. 6 . In u'=g(u) of FIG. 6 , the domain (u) and the range (g(u)) are normalized values and have ranges of [0, 1], respectively. In the graph of FIG. 6, the slope is less than 1 near u=0.5, and the slope is greater than 1 near u=1 or 0.

The following Equation 13 having the same function as the curvature may be applied to the UV region to correct it.

The distance between the coordinates of the converted pixel near the center position (u=0.5) of the UV region is physically closer, and the distance between the coordinates of the transformed pixel near the outer position of the UV region (u=0 or 1) The gap may be physically further apart. Through the correction, the image information density of the outer portion and the center portion of the UV region becomes similar, and distortion generated during the projection process may be reduced.

Claims (11)

The coordinates of the positions of pixels in the viewport area are converted into coordinates of a transformation coordinate region, wherein the transformation coordinate region is an area used when calculating spherical surface coordinates containing image information.
The transform coordinate region is subdivided into at least two regions, wherein the subdivided region includes a first subdivided region and a second subdivided region.
correcting the coordinates of at least one of the first subdivided region and the second subdivided region so that the distance between the coordinates of the first subdivided region is smaller than the distance between the coordinates of the second subdivided region;
calculating the spherical surface coordinates corresponding to the coordinates of the corrected transformation coordinate region,
Extracting image information corresponding to the calculated spherical surface coordinates,
The transformation coordinate area is a curved surface,
The horizontal and vertical lengths of the transformation coordinate area are determined in consideration of a field of view (FOV) of the viewport area,
The transformation is performed in consideration of only the number of pixels in the horizontal direction and the vertical direction in the viewport area, without considering the horizontal and vertical lengths of the transformation coordinate area,
The correction comprises skipping correction of at least some of the subdivided regions when the size of the viewport region or the transformation coordinate region is less than or equal to a threshold size. The method of claim 1,
The curved surface is a part of the outer sphere circumscribed to the sphere containing the image information,
The radius of the outer sphere is greater than or equal to the radius of the sphere containing the image information, the video decoding apparatus. delete delete According to claim 1,
The correction is performed using a three-dimensional function,
wherein the three-dimensional function has a slope of less than 1 within a range applied to the first subdivided area, and a slope of the function greater than 1 within a range applied to the second subdivided area, video decoding device. delete According to claim 1,
The correction is performed by applying a weight and an offset value,
The weight and the offset value are the same or different for each of the subdivided regions. According to claim 1,
The first subdivision region, characterized in that the shape of a circle or a rectangle based on the center of the transformation coordinate region, image decoding apparatus. The method of claim 1,
The calculation comprises orthographically projecting the transformed transformed coordinate region to the center of the spherical surface, and calculating the coordinates of the spherical surface corresponding to the coordinates of the orthographically projected transformed coordinate region. The method of claim 1,
The position of the pixel includes a position of a pixel group composed of the pixels. 11. The method of claim 10,
The position of the pixel group includes a position of any one pixel included in the pixel group or an average value of a plurality of pixels included in the pixel group.

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