CN116824085A - Quasi-uniform spherical image segmentation and general convolution operation method - Google Patents

Quasi-uniform spherical image segmentation and general convolution operation method Download PDF

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CN116824085A
CN116824085A CN202310388254.4A CN202310388254A CN116824085A CN 116824085 A CN116824085 A CN 116824085A CN 202310388254 A CN202310388254 A CN 202310388254A CN 116824085 A CN116824085 A CN 116824085A
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解杨敏
肖尧
高志远
仇文玮
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University of Shanghai for Science and Technology
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Abstract

The application belongs to the field of mobile robots and environmental sensors, and particularly relates to a quasi-uniform spherical image segmentation and general convolution operation method. The quasi-uniform spherical image segmentation method comprises the following steps: s1, acquiring a spherical image, mapping the spherical image onto a unit spherical surface S, and gradually subdividing the unit spherical surface S into spherical triangles with quasi-equal areas; s2, establishing an electrostatic repulsion physical model, and optimizing the vertex position of the spherical triangle through the electrostatic repulsion physical model; and S3, carrying out geodesic Voronoi polygonal division on the unit spherical surface S based on the optimized spherical triangle vertex to obtain a quasi-uniformly divided unit spherical surface S. The general convolution operation method of the quasi-uniform spherical image comprises the following steps: convolution, pooling or upsampling of the spherical image providing a quasi-uniform segmentation. The application can solve the problem of uneven sampling of the spherical image pixels, and remarkably improves the segmentation capability of the high-fidelity small object in the segmentation research of the spherical image CNN example.

Description

Quasi-uniform spherical image segmentation and general convolution operation method
Technical Field
The application belongs to the field of mobile robots and environmental sensors, and particularly relates to a quasi-uniform spherical image segmentation and general convolution operation method.
Background
The purpose of the spherical image pixel segmentation is to obtain uniformly distributed spherical pixels, thereby improving the semantic segmentation performance of the spherical image CNN. Spherical images have a wide field of view, which is more advantageous in mobile robot and environmental sensing applications. The research of the structure of the spherical image CNN always has the problem of uneven sampling, and limits on semantic segmentation performance. In order to ensure distortion-free and image continuity of a spherical image, it is required that the pixels of the sphere are uniformly segmented and have a regular pattern of pixels.
In the prior art, an icosahedron four-time subdivision method is adopted for the spherical image pixel segmentation. Specifically, the triangle surface of the icosahedron is divided into four smaller triangles, and the operations are iterated, or the triangles are directly projected onto a spherical surface to generate pixel segmentation, or the triangles are replaced by hexagons before projection, but the overlapping of the edges of the subsequent icosahedron and pixel shape distortion caused by projection are not considered, so that pixel lack uniformity is generated.
It is therefore desirable to have a solution that overcomes or at least alleviates at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The application aims to provide a quasi-uniform spherical image segmentation and general convolution operation method, which aims to solve the problems of spherical image distortion and discontinuity caused by uneven segmentation of spherical image pixels in the prior art.
The technical scheme of the application is as follows:
a first aspect of the present application provides a quasi-uniform spherical image segmentation method, comprising:
s1, acquiring a spherical image, mapping the spherical image onto a unit spherical surface S, and gradually subdividing the unit spherical surface S into spherical triangles with quasi-equal areas;
s2, establishing an electrostatic repulsion physical model, and optimizing the vertex position of the spherical triangle through the electrostatic repulsion physical model;
and S3, carrying out geodesic Voronoi polygonal division on the unit spherical surface S based on the optimized spherical triangle vertex to obtain a quasi-uniformly divided unit spherical surface S.
In at least one embodiment of the present application, in S1, the step-by-step subdivision of the unit sphere S into spherical triangles with quasi-equal areas includes:
s1.1, defining a regular icosahedron inscribed in the unit spherical surface S as a 0-level surface, wherein the 0-level surface comprises 12 vertexes and 20 regular triangles;
s1.2, gradually subdividing the unit spherical surface S from 1 level to N level by adopting a quasi-equal area method to obtain an N-level spherical surface, wherein N is more than 0, and N is an odd number;
s1.3, the spherical obtuse angle triangles obtained by N-level subdivision are connected through a large arc, the obtuse angle vertexes of two spherical obtuse angle triangles sharing the same obtuse angle opposite sides are eliminated, two spherical acute angle triangles are obtained, and the vertex positions of the spherical triangles are not changed in the process.
In at least one embodiment of the present application, in S1.2, the step-by-step subdivision of the unit sphere S by using a quasi-equal area method is performed from 1 to N steps, to obtain an N-step sphere, including:
s1.2.1, performing 1-level quasi-equal area subdivision on the unit sphere S, including:
obtaining projection points of the geometric centers of all regular triangles in the 0-level surface on the unit spherical surface S, connecting the projection points with the vertexes of the corresponding regular triangles through a large arc on the unit spherical surface S, and connecting the vertexes of the regular triangles through the large arc to obtain a 1-level spherical surface, wherein the 1-level spherical surface comprises 32 vertexes and 60 spherical triangles;
wherein each regular triangle corresponds to three spherical triangles with equal areas;
s1.2.2 the unit sphere S is subdivided into N-level quasi-equal areas, n=2 to N, and the method includes:
halving the area of each spherical triangle in the n-1 level spherical surface to obtain an n level spherical surface;
the unit spherical surface S is subjected to 2-N-level quasi-equal area subdivision step by step to obtain an N-level spherical surface, wherein a spherical triangle in the N-level spherical surface is defined as T i The vertex set of the spherical triangle isThe vertex position set of the spherical triangle is +.>
In at least one embodiment of the present application, S1.2.2, the halving the area of each sphere triangle in the n-1 sphere results in an n-sphere, comprising:
taking the spherical center of the unit spherical surface S as an origin, and establishing a spherical coordinate system;
the vertex coordinates of the spherical triangle in the n-1 level spherical surface are obtained as follows: v (V) A ,V B ,V C ；
The area of the spherical triangle is: [ V A ,V B ,V C ]＝A+B+C-π；
Wherein A, B, C are dihedral angles of spherical triangles respectively;
calculating the side length a of the longest side of the spherical triangle as follows: a=arccoss (V B ·V C )；
Calculating a coordinate point V on the unit sphere S by a formula (1) D So that the spherical triangle area V A ,V B ,V D ]And [ V A ,V D ,V C ]Equal;
wherein ,
v is formed on the unit sphere S by a large arc A And V is equal to D Connecting to obtain an n-level spherical surface;
in the N-level sphere, the number of vertexes of the sphere triangle is N v ＝2 n-1 X 30+2, number of spherical triangles N s ＝2 n-1 ×60。
In at least one embodiment of the present application, in S2, the establishing an electrostatic repulsive force physical model, and optimizing the vertex position of the spherical triangle by using the electrostatic repulsive force physical model includes:
s2.1, defining that each vertex has the same polarity charge, and establishing an electrostatic repulsive force physical model:
wherein ,Fi For the electrostatic resultant force of the ith charged vertex, V i For the position corresponding to the ith charged vertex, V j C is a constant for the position corresponding to the jth charged vertex;
s2.2, acquiring an electrostatic force balance equation when the charged peak reaches an electrostatic force balance state:
||V i * || 2 ＝1
wherein ,Vi * Is the vertex position V i The optimized position;
solving an electrostatic force balance equation to obtain an optimized vertex position V i * The spherical triangle is T i * The vertex set isVertex position set is +.>
In at least one embodiment of the present application, in S3, the performing geodesic Voronoi polygon division on the unit sphere S based on the optimized spherical triangle vertex to obtain a quasi-uniformly divided unit sphere S includes:
s3.1, acquiring spherical triangle T i * Center point O of (2) i Wherein the center point O i Is spherical triangle T i * And T is i * The center of a circumcircle of a large spherical triangle formed by adjacent three spherical triangles is at the projection point of the unit spherical surface S;
s3.2 will be N on the unit sphere S i * The central points of all spherical triangles serving as vertexes are sequentially connected through large arcs according to adjacent sequences to obtain quasi-uniformly divided unit spherical surfaces S, wherein the quasi-uniformly divided unit spherical surfaces S comprise N v A plurality of closed spherical polygonal areas R i Each spherical polygonal region R i Corresponding to a spherical image pixel;
in the spherical polygonal region R i Any sphere point and R i Optimized vertex position V in region i * Distance of less than or equal to R i Any sphere point in the region and the optimized vertex position V j * Distance of j+.i:
R i ＝{p∈S：||p-V i * ||≤||p-V j * ||，for j＝1...，N v }
wherein ,Ri Is the ith spherical polygonal area, p is any point on the sphere, V i * For the optimized position of the ith vertex, V j * The position of the jth vertex after optimization;
all spherical polygonal areas R i The middle part comprises 12 spherical surfaces fiveEdge region and N v -12 spherical hexagonal areas.
A second aspect of the present application provides a general convolution operation method for a quasi-uniform spherical image, for performing convolution operation, pooling or upsampling on a quasi-uniformly segmented unit spherical surface S obtained by the quasi-uniform spherical image segmentation method as described above, including:
alignment of N on a uniformly divided unit sphere S v The 12 spherical hexagonal regions are convolved, pooled or upsampled, wherein,
alignment of N on a uniformly divided unit sphere S v -12 spherical hexagonal areas are convolved, comprising:
defining a spherical polygonal region R i The k-turn adjacent pixels of (a) are:
wherein ,D(Ri ，R j ) Is from R i To R j The minimum number of spherical polygons passed;
defining a spherical polygonal region R i The K-turn convolution kernel of (2) is:
alignment of N on a uniformly divided unit sphere S v -12 spherical hexagonal regions are subjected to a single-turn convolution operation, a multi-turn convolution operation, a stride convolution operation, a transpose convolution operation, or a hole convolution operation, wherein,
operation one: single-or multi-turn convolution operation
Convolved pixel value P i The method comprises the following steps:
wherein ,Wm For a convolution kernel of k turnsWeight of the mth element, I m Is omega (R) i M is the number of convolution kernel elements in the M-th image pixel value in K);
and (3) operation II: stride convolution operation
Taking a plurality of spherical polygons as sliding step length to obtain a sliding curve R i To R i The direction of the single circle of adjacent pixels is a stride direction, and single circle convolution operation or multi-circle convolution operation is carried out;
and (3) operation III: transposed convolution operation
Zero padding expansion is carried out on the pixels of the input image, and the image subjected to the zero padding expansion enables adjacent pixels R of the original image i ，R j Satisfy D (R) i ，R j ) =2, and the single-turn neighboring pixel value of the original pixel in the zero-padded extended image is 0;
performing stride single-circle convolution operation with the step length of 1 on all spherical pixels subjected to zero padding expansion;
and (4) operation four: cavity convolution operation
Will be R i A pixel with a stride length of 2 along six stride directions as a center, and a pixel point R i A total of 7 pixels, defined as R i Is effective in the pixel region;
carrying out single-circle convolution operation on the effective pixels of all the pixels in the spherical hexagonal area;
alignment of N on a uniformly divided unit sphere S v Performing pooling operation on 12 spherical hexagonal areas, and obtaining a low-pool-level pixel set L from a high-pool-level pixel set H; defining odd-numbered levels as pool levels, wherein the pooling operation is to take four adjacent pixel blocks in H as pooling cores, and downsampling from H to L;
alignment of N on a uniformly divided unit sphere S v Up-sampling operation is carried out on 12 spherical hexagonal areas, and a high-pool level pixel set H is obtained from a low-pool level pixel set L; wherein, defining odd number level as pool level, and the pixel value not belonging to L in H is obtained by linear interpolation calculation of pixels in L.
A third aspect of the present application provides a quasi-uniform spherical image segmentation and general convolution operation device, including:
the unit spherical surface S is subdivided step by step into spherical triangles with quasi-equal areas, wherein the spherical surface S is used for acquiring a spherical image, mapping the spherical image onto the unit spherical surface S, and subdividing the unit spherical surface S step by step;
the vertex optimization module is used for establishing an electrostatic repulsion physical model and optimizing the vertex position of the spherical triangle through the electrostatic repulsion physical model;
the polygon dividing module is used for carrying out geodesic Voronoi polygon division on the unit spherical surface S based on the optimized spherical triangle vertexes to obtain a unit spherical surface S which is divided in a quasi-uniform manner;
and the convolution operation module is used for carrying out convolution operation, pooling or up-sampling aiming at the unit spherical surface S which is uniformly divided.
A fourth aspect of the application provides an electronic device comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, the processor implementing a quasi-uniform spherical image segmentation method as described above when executing the computer program.
A fifth aspect of the present application provides a computer readable storage medium storing a computer program which, when executed by a processor, enables the quasi-uniform spherical image segmentation method as described above.
The application has at least the following beneficial technical effects:
compared with the traditional four-segmentation method, quasi-equivalent method and optimized quasi-equivalent method, the quasi-uniform spherical image segmentation method reduces the area variance of the spherical triangle by more than half, so that the uniformity of the divided spherical pixels is obviously better than that of the traditional method; furthermore, the spherical image has more uniformly distributed pixels, so that the distortion condition of the image is greatly reduced, and the integrity of the image is ensured; the CNN is implemented by using the method for instance segmentation, and has smaller average cross-over ratio (mIoU), so that the segmentation capability of the high-fidelity small object is remarkably improved.
Drawings
FIG. 1 is a flow chart of a method of quasi-uniform spherical image segmentation in accordance with one embodiment of the present application;
FIG. 2 is a 0-level facet schematic of one embodiment of the present application;
FIG. 3 is a schematic illustration of progressive subdivision of a unit sphere according to one embodiment of the present application;
FIG. 4 is a schematic illustration of an area halving of a spherical triangle according to one embodiment of the application;
FIG. 5 is a schematic view of spherical obtuse triangle reconstruction in accordance with one embodiment of the present application;
FIG. 6 is a schematic diagram of a unit sphere after progressive subdivision in accordance with one embodiment of the present application;
FIG. 7 is a schematic illustration of Voronoi polygon partitioning in accordance with one embodiment of the present application;
FIG. 8 is a single-turn convolution schematic of one embodiment of the present disclosure;
FIG. 9 is a schematic illustration of a multi-turn convolution of one embodiment of the present disclosure;
FIG. 10 is a schematic diagram of a stride convolution according to an embodiment of the present disclosure;
FIG. 11 is a transposed convolution schematic of one embodiment of the present application;
FIG. 12 is a schematic illustration of hole convolution according to one embodiment of the present disclosure;
FIG. 13 is a schematic diagram of pooling and upsampling according to one embodiment of the present application;
FIG. 14 is a schematic diagram of a device for performing quasi-uniform spherical image segmentation and general convolution operation according to an embodiment of the present application;
fig. 15 is a schematic structural diagram of a computer device suitable for use in implementing the terminal or server of the embodiment of the present application.
wherein ：
100-unit spherical surface S progressive subdivision module; 200-vertex optimization module; 300-polygon dividing module; 400-convolution operation module; 500-a computer device; 501-CPU;502-ROM;503-RAM; 504-bus; 505-I/O interface; 506-an input section; 507-an output section; 508-a storage portion; 509-a communication section; 510-a driver; 511-removable media.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application become more apparent, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the application. The embodiments described below by referring to the drawings are illustrative and intended to explain the present application and should not be construed as limiting the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
In the description of the present application, it should be understood that the terms "center," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, merely to facilitate describing the present application and simplify the description, and do not indicate or imply that the devices or elements being referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the scope of the present application.
The application is described in further detail below with reference to fig. 1 to 15.
A first aspect of the present application provides a quasi-uniform spherical image segmentation method, as shown in fig. 1, comprising the steps of:
s1, acquiring a spherical image, mapping the spherical image onto a unit spherical surface S, and gradually subdividing the unit spherical surface S into spherical triangles with quasi-equal areas;
s2, establishing an electrostatic repulsive force physical model, and optimizing the vertex position of the spherical triangle through the electrostatic repulsive force physical model;
s3, carrying out geodesic Voronoi polygon division on the unit spherical surface S based on the optimized spherical triangle vertex to obtain a unit spherical surface S which is divided quasi-uniformly;
the application relates to a quasi-uniform spherical image segmentation method, which comprises the steps of firstly obtaining a spherical image as input, mapping the spherical image onto a unit spherical surface S, and gradually subdividing the unit spherical surface S into spherical triangles with quasi-uniform areas by adopting a quasi-uniform area method, wherein the spherical triangles comprise vertexes positioned on the unit spherical surface S and large arcs connected among the vertexes.
In a preferred embodiment of the present application, the number of times of performing quasi-equal area subdivision is defined as a level, and the unit sphere S is subdivided step by step as follows:
s1.1, defining a regular icosahedron inscribed in a unit spherical surface S as a 0-level surface, wherein the 0-level surface comprises 12 vertexes and 20 regular triangles, and referring to FIG. 2;
s1.2, gradually subdividing the unit spherical surface into 1-N levels by adopting a quasi-equal area method to obtain an N-level spherical surface, wherein N is more than 0, and N is an odd number.
S1.2, specifically comprises:
s1.2.1, carrying out 1-level quasi-equal area subdivision on the unit spherical surface S, wherein the method comprises the following steps of:
obtaining a projection point of the geometric center of each regular triangle in the 0-level geometric surface on a unit spherical surface S, connecting the projection point with the vertex of the corresponding regular triangle through a large arc on the unit spherical surface S, and connecting the vertexes of the regular triangle through the large arc to obtain a 1-level spherical surface, wherein the 1-level spherical surface comprises 32 vertexes and 60 spherical triangles;
wherein each regular triangle corresponds to three spherical triangles with equal areas;
s1.2.2 the unit sphere S is subdivided into N-level quasi-equal areas, n=2 to N, including:
halving the area of each spherical triangle in the n-1 level spherical surface to obtain an n-level spherical surface, see fig. 3;
the unit spherical surface S is subjected to 2-N-level quasi-equal area subdivision step by step to obtain an N-level spherical surface, wherein a spherical triangle in the N-level spherical surface is defined as T i The vertex set of the spherical triangle isThe vertex position set of the spherical triangle is
As shown in fig. 4, in this embodiment, the area of each spherical triangle in the n-1 level spherical surface is halved to obtain an n level spherical surface, which includes:
taking the spherical center of the unit spherical surface S as an origin, and establishing a spherical coordinate system;
the vertex coordinates of the spherical triangle in the n-1 level spherical surface are obtained as follows: v (V) A ，V B ，V C ；
The area of the spherical triangle is: [ V A ，V B ，V C ]＝A+B+C-π；
Wherein A, B, C are dihedral angles of spherical triangles respectively;
calculating the side length a of the longest side of the spherical triangle as follows: a=arccoss (V B ·V C )；
Calculating a coordinate point VD on the unit sphere S through a formula (1) so as to ensure the triangular area [ V ] of the sphere A ，V B ，V D ]And [ V A ，V D ，V C ]Equal;
wherein ,
vertex V corresponding to the longest side is formed on unit sphere S through a large arc A With sitting onPunctuation V D Connecting to obtain an n-level spherical surface;
in an N-stage sphere, the number of vertexes of the sphere triangle is N v ＝2 n-1 X 30+2, number of spherical triangles N s ＝2 n-1 X 60, the vertices of all spherical triangles are quasi-uniform points.
According to the mode, the areas of all spherical triangles on the unit spherical surface S are halved, and finally the spherical triangle T with N subdivided is obtained i The vertex set of the spherical triangle isThe vertex position set of the spherical triangle is +.>
S1.3, reconstructing spherical obtuse triangles obtained by N-level subdivision, wherein N is an odd number. The obtuse vertices of two spherical obtuse triangles sharing the same obtuse edge are connected by a large arc, and the shared obtuse edge is eliminated to obtain two spherical acute triangles, as shown in fig. 5. The process does not change the vertex position of the spherical triangle.
According to the quasi-uniform spherical image segmentation method, after the unit spherical surface S is subdivided step by step, the vertex position of the spherical triangle on the unit spherical surface S needs to be optimized.
In a preferred embodiment of the present application, the position of the vertex of the spherical triangle is optimized by an electrostatic repulsive force physical model, which specifically includes:
s2.1, defining that each vertex has the same polarity charge, and establishing an electrostatic repulsive force physical model:
wherein ,Fi For the electrostatic resultant force of the ith charged vertex, V i For the position corresponding to the ith charged vertex, V j C is a constant for the position corresponding to the jth charged vertex;
s2.2, acquiring an electrostatic force balance equation when the charged peak reaches an electrostatic force balance state:
||V i * || 2 ＝1
wherein ,Vi * Is the vertex position V i The optimized position;
solving an electrostatic force balance equation to obtain an optimized vertex position V i * The spherical triangle is T i * The vertex set isVertex position set is +.>
Under the driving of electrostatic force, the charged vertex reaches an electrostatic force balance state, an optimized vertex position set is obtained by solving an electrostatic force balance equation, the vertex position of the spherical triangle after optimization is changed, and the spherical triangle topological structure is kept unchanged.
Further, in S3, the unit sphere S is divided into the geodesic Voronoi polygons based on the optimized spherical triangle vertices, to obtain a quasi-uniformly divided unit sphere S, which includes:
s3.1, acquiring spherical triangle T i * Center point O of (2) i Wherein the center point O i Is spherical triangle T i * And T is i * The center of a circumcircle of a large spherical triangle formed by adjacent three spherical triangles is at the projection point of the unit spherical surface S;
s3.2 will be N on the unit sphere S i * The central points of all spherical triangles serving as vertexes are sequentially connected through large arcs according to adjacent sequences to obtain unit spherical surfaces S which are divided in a quasi-uniform mode, wherein the unit spherical surfaces S comprise N v A plurality of closed spherical polygonal areas R i Each spherical polygonRegion R i Corresponds to a spherical image pixel as shown in fig. 7. In the spherical polygonal region R i Any sphere point and R i Optimized vertex position V in region i * Distance of less than or equal to R i Any sphere point in the region and the optimized vertex position V j * Distance of j+.i:
R i ＝{p∈S：||p-V i * ||≤||p-V j * ||，for j＝1...，N v }
wherein ,Ri Is the ith spherical polygonal area, p is any point on the sphere, V i * For the optimized position of the ith vertex, V j * The position of the jth vertex after optimization.
The quasi-uniform spherical image segmentation method of the application optimizes the vertexesThe division can be divided into two types, one is: 12 vertices at the initial 0-level division, with only 5 adjacent vertices around such vertices; the other is: all N (N)>0) Vertices generated after the classification, N in total v -12 vertices, such vertices being surrounded by 6 adjacent vertices. N is shared on a unit sphere S which is divided into quasi-uniform segments after the geodesic Voronoi polygon is divided v The spherical polygon, wherein the spherical polygon area corresponding to the 12 vertexes of the optimized 0-level surface is a spherical pentagon, and the rest N is the same as the spherical pentagon v The spherical polygon area corresponding to the 12 optimized vertexes is spherical hexagon, and the obtained spherical polygon corresponds to the spherical image pixel.
The second aspect of the present application provides a general convolution operation method for a quasi-uniform spherical image, which is used for performing convolution operation, pooling or up-sampling on a unit spherical surface S which is uniformly segmented, and specifically comprises:
alignment of N on a uniformly divided unit sphere S v The 12 spherical hexagonal regions are convolved, pooled or upsampled, wherein,
alignment of uniformly segmented unit spheresN on S v -12 spherical hexagonal areas are convolved, comprising:
defining a spherical polygonal region R i The k-turn adjacent pixels of (a) are:
wherein ,D(Ri ，R j ) Is from R i To R j The minimum number of spherical polygons passed;
defining a spherical polygonal region R i The K-turn convolution kernel of (2) is:
alignment of N on a uniformly divided unit sphere S v -12 spherical hexagonal regions are subjected to a single-turn convolution operation, a multi-turn convolution operation, a stride convolution operation, a transpose convolution operation, or a hole convolution operation, wherein,
operation one: single-or multi-turn convolution operation
Single-circle convolution operation or multi-circle convolution operation to obtain a convolved pixel value P i ：
wherein ,Wm Weight of mth element of the convolution kernel of k circles, I m Is omega (R) i M is the number of convolution kernel elements in the M-th image pixel value in K);
and (3) operation II: stride convolution operation
The stride convolution operation uses several spherical polygons as sliding steps to obtain R i To R i The direction of the single turn adjacent pixels is a single turn (multi-turn) convolution operation of the stride direction.
And (3) operation III: transposed convolution operation
Input image pixelsZero padding expansion, wherein the image subjected to zero padding expansion enables adjacent pixels R of the original image to be formed i ，R i Satisfy D (R) i ，R j ) =2, and the single-turn neighboring pixel value of the original pixel in the zero-padded extended image is 0;
and then performing stride single-circle convolution operation with the step length of 1 on all spherical pixels subjected to zero padding expansion.
And (4) operation four: cavity convolution operation
By R i A pixel with a stride length of 2 along six stride directions as a center, and a pixel point R i A total of 7 pixels, defined as R i A valid pixel of the location;
and then carrying out single-circle convolution operation on the effective pixels of all the pixels in the spherical hexagonal area.
The application relates to a general convolution operation method of a quasi-uniform spherical image, which further comprises the following steps:
alignment of N on a uniformly divided unit sphere S v Performing pooling operation on 12 spherical hexagonal areas, and obtaining a low-pool-level pixel set L from a high-pool-level pixel set H;
an odd level is defined as a pool level. The high-pool level pixel set is defined as H, the low-pool level pixel set is defined as L, and the requirements are satisfied thatThe pooling operation is downsampling from H to L with four adjacent pixel blocks in H as the pooling kernel. The pool operation can be implemented using a conventional 2-dimensional pooling approach.
The application relates to a general convolution operation method of a quasi-uniform spherical image, which further comprises the following steps:
alignment of N on a uniformly divided unit sphere S v Up-sampling operation is carried out on 12 spherical hexagonal areas, and a high-pool level pixel set H is obtained from a low-pool level pixel set L;
an odd level is defined as a pool level. The high-pool level pixel set is defined as H, the low-pool level pixel set is defined as L, and the requirements are satisfied thatPixel structure slaveThe value of the pixel which does not belong to L in H is obtained by linear interpolation calculation of the pixel in L.
The application relates to a general convolution operation method of a quasi-uniform spherical image, which comprises single-circle convolution, multi-circle convolution, stride convolution, transposition convolution and cavity convolution, wherein the back propagation process is consistent with the back propagation of two-dimensional convolution. Wherein the convolution kernel of the single-turn convolution is shown in fig. 8, and the convolution kernel of the multi-turn convolution is shown in fig. 9. Stride convolution as in FIG. 10, with several spherical polygons as sliding steps to form R i To R i The direction of a single turn of adjacent pixels is a single turn (multiple turns) convolution of the stride direction. Transpose convolution as in fig. 11, the process is as follows: zero padding expansion is carried out on the pixels of the input image, and the image subjected to the zero padding expansion enables adjacent pixels R of the original image i ，R j Satisfy D (R) i ，R j ) =2, and the single-turn neighboring pixel value of the original pixel in the zero-padded image is 0, and then the step-by-step single-turn convolution with a step length of 1 is performed on all spherical pixels after zero-padded expansion. As in fig. 12, the holes are convolved with R i A pixel with a stride length of 2 along six stride directions as a center, and a pixel point R i A total of 7 pixels, defined as R i The valid pixels of a location are then convolved in a single turn for all locations.
In the general convolution operation method for the quasi-uniform spherical image, as shown in fig. 13, the unit spherical surface S is pooled, and an odd number level is defined as a pool level. The high-pool level pixel set is defined as H, the low-pool level pixel set is defined as L, and the requirements are satisfied thatThe pooling operation takes four adjacent pixel blocks in H as a pooling core, downsampling from H to L, and the pooling operation can be realized by adopting a traditional 2-dimensional pooling method. In fig. 13, the up-sampling of the unit sphere S changes the pixel structure from L to H, and the pixel value of H not belonging to L is obtained by linear interpolation of the pixels in L.
Compared with the traditional four-segmentation method, quasi-equivalent method and optimized quasi-equivalent method, the area variance of the spherical triangle obtained by the method is reduced by more than half, so that the uniformity of the divided spherical pixels is obviously better than that of the traditional method. The spherical image provided by the application has more uniformly distributed pixels, so that the distortion condition of the image is greatly reduced, and the integrity of the image is ensured. The method is used for implementing CNN for instance segmentation, and has smaller average cross-over ratio (mIoU), so that the segmentation capability of the high-fidelity small object is remarkably improved.
Based on the above-mentioned quasi-uniform spherical image segmentation and general convolution operation method, the third aspect of the present application further provides a quasi-uniform spherical image segmentation and general convolution operation device, as shown in fig. 14, including:
the unit sphere S is subdivided step by step into spherical triangles with quasi-equal areas, wherein the spherical triangles are used for acquiring spherical images, mapping the spherical images onto the unit sphere S and subdividing the unit sphere S step by step;
the vertex optimization module is used for establishing an electrostatic repulsion physical model and optimizing the vertex position of the spherical triangle through the electrostatic repulsion physical model;
the polygon dividing module is used for carrying out geodesic Voronoi polygon division on the unit spherical surface S based on the optimized spherical triangle vertexes to obtain a unit spherical surface S which is divided quasi-uniformly;
and the convolution operation module is used for carrying out convolution operation, pooling or up-sampling aiming at the unit spherical surface S which is uniformly divided.
In another aspect of the present application, a computer device is provided, comprising a processor, a memory, and a computer program stored on the memory and executable on the processor, the processor executing the computer program for implementing the quasi-uniform spherical image segmentation method described above.
Referring now to FIG. 15, there is illustrated a schematic diagram of a computer device 500 suitable for use in implementing embodiments of the present application. The computer device shown in fig. 15 is only one example, and should not impose any limitation on the functions and scope of use of the embodiments of the present application.
As shown in fig. 15, the computer device 500 includes a Central Processing Unit (CPU) 501, which can perform various appropriate actions and processes according to a program stored in a Read Only Memory (ROM) 502 or a program loaded from a storage section 508 into a Random Access Memory (RAM) 503. In the RAM503, various programs and data required for the operation of the device 500 are also stored. The CPU501, ROM502, and RAM503 are connected to each other through a bus 504. An input/output (I/O) interface 505 is also connected to bus 504.
The following components are connected to the I/O interface 505: an input section 506 including a keyboard, a mouse, and the like; an output portion 507 including a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), and the like, and a speaker, and the like; a storage portion 508 including a hard disk and the like; and a communication section 509 including a network interface card such as a LAN card, a modem, or the like. The communication section 509 performs communication processing via a network such as the internet. The drive 510 is also connected to the I/O interface 505 as needed. A removable medium 511 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like is mounted on the drive 510 as needed so that a computer program read therefrom is mounted into the storage section 508 as needed.
In particular, according to embodiments of the present application, the processes described above with reference to flowcharts may be implemented as computer software programs. For example, embodiments of the present application include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method shown in the flowcharts. In such an embodiment, the computer program may be downloaded and installed from a network through the communication portion 509, and/or installed from the removable medium 511. The above-described functions defined in the method of the present application are performed when the computer program is executed by a Central Processing Unit (CPU) 501. The computer storage medium of the present application may be a computer readable signal medium or a computer readable storage medium, or any combination of the two. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In the present application, however, the computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, with the computer-readable program code embodied therein. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, fiber optic cable, RF, etc., or any suitable combination of the foregoing.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The modules or units described in the embodiments of the present application may be implemented by software, or may be implemented by hardware. The modules or units described may also be provided in a processor, the names of which do not in some cases constitute a limitation of the module or unit itself.
As another aspect, the present application also provides a computer-readable storage medium, which may be included in the apparatus described in the above embodiment; or may be present alone without being fitted into the device. The computer readable storage medium carries one or more programs which when executed by the apparatus process data according to the quasi-uniform spherical image pixel processing method.
The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present application should be included in the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (10)

1. A quasi-uniform spherical image segmentation method, comprising:
s1, acquiring a spherical image, mapping the spherical image onto a unit spherical surface S, and gradually subdividing the unit spherical surface S into spherical triangles with quasi-equal areas;
s2, establishing an electrostatic repulsion physical model, and optimizing the vertex position of the spherical triangle through the electrostatic repulsion physical model;
and S3, carrying out geodesic Voronoi polygonal division on the unit spherical surface S based on the optimized spherical triangle vertex to obtain a quasi-uniformly divided unit spherical surface S.
2. The quasi-uniform spherical image segmentation method according to claim 1, wherein in S1, the step-by-step subdivision of the unit spherical surface S into spherical triangles of quasi-equal area comprises:
s1.1, defining a regular icosahedron inscribed in the unit spherical surface S as a 0-level surface, wherein the 0-level surface comprises 12 vertexes and 20 regular triangles;
s1.2, gradually subdividing the unit spherical surface S from 1 level to N level by adopting a quasi-equal area method to obtain an N-level spherical surface, wherein N is more than 0, and N is an odd number;
s1.3, the spherical obtuse angle triangles obtained by N-level subdivision are connected through a large arc, the obtuse angle vertexes of two spherical obtuse angle triangles sharing the same obtuse angle opposite sides are eliminated, two spherical acute angle triangles are obtained, and the vertex positions of the spherical triangles are not changed in the process.
3. The method for dividing a quasi-uniform spherical image according to claim 2, wherein in S1.2, the unit spherical surface S is subdivided step by adopting a quasi-equal area method from 1 to N levels to obtain N levels of spherical surfaces, comprising:
s1.2.1, performing 1-level quasi-equal area subdivision on the unit sphere S, including:
obtaining projection points of the geometric centers of all regular triangles in the 0-level surface on the unit spherical surface S, connecting the projection points with the vertexes of the corresponding regular triangles through a large arc on the unit spherical surface S, and connecting the vertexes of the regular triangles through the large arc to obtain a 1-level spherical surface, wherein the 1-level spherical surface comprises 32 vertexes and 60 spherical triangles;
wherein each regular triangle corresponds to three spherical triangles with equal areas;
s1.2.2 the unit sphere S is subdivided into N-level quasi-equal areas, n=2 to N, and the method includes:
halving the area of each spherical triangle in the n-1 level spherical surface to obtain an n level spherical surface;
the unit spherical surface S is gradually added by the step of circulationPerforming quasi-equal area subdivision on the stages from 2 to N stages to obtain N stages of spherical surfaces, wherein spherical triangles in the N stages of spherical surfaces are defined as T i The vertex set of the spherical triangle isThe vertex position set of the spherical triangle is +.>
4. A quasi-uniform spherical image segmentation method according to claim 3, wherein in S1.2.2, the halving the area of each spherical triangle in the n-1 class of spheres to obtain n class of spheres comprises:
taking the spherical center of the unit spherical surface S as an origin, and establishing a spherical coordinate system;
the vertex coordinates of the spherical triangle in the n-1 level spherical surface are obtained as follows: v (V) A ,V B ,V C ；
The area of the spherical triangle is: [ V A ,V B ,V C ]＝A+B+C-π；
Wherein A, B, C are dihedral angles of spherical triangles respectively;
calculating the side length a of the longest side of the spherical triangle as follows: a=arccoss (V B ·V C )；
Calculating a coordinate point V on the unit sphere S by a formula (1) D So that the spherical triangle area V A ,V B ,V D ]And [ V A ,V D ,V C ]Equal;
wherein ,
v is formed on the unit sphere S by a large arc A And V is equal to D Connecting to obtain an n-level spherical surface;
in the N-level sphere, the number of vertexes of the sphere triangle is N v ＝2 n-1 X 30+2, number of spherical triangles N s ＝2 n-1 ×60。
5. The quasi-uniform spherical image segmentation method according to claim 1, wherein in S2, the establishing an electrostatic repulsive force physical model, and optimizing the vertex position of the spherical triangle by the electrostatic repulsive force physical model comprises:
s2.1, defining that each vertex has the same polarity charge, and establishing an electrostatic repulsive force physical model:
wherein ,Fi For the electrostatic resultant force of the ith charged vertex, V i For the position corresponding to the ith charged vertex, V j C is a constant for the position corresponding to the jth charged vertex;
s2.2, acquiring an electrostatic force balance equation when the charged peak reaches an electrostatic force balance state:
wherein ,Vi * Is the vertex position V i The optimized position;
solving an electrostatic force balance equation to obtain an optimized vertex position V i * The spherical triangle is T i * The vertex set isVertex position set is +.>
6. The method for dividing a quasi-uniform spherical image according to claim 1, wherein in S3, the unit spherical surface S is divided into a geodesic Voronoi polygon based on the optimized spherical triangle vertices, so as to obtain a quasi-uniform divided unit spherical surface S, which comprises:
s3.1, acquiring spherical triangle T i * Center point O of (2) i Wherein the center point O i Is spherical triangle T i * And T is i * The center of a circumcircle of a large spherical triangle formed by adjacent three spherical triangles is at the projection point of the unit spherical surface S;
s3.2 will be N on the unit sphere S i * The central points of all spherical triangles serving as vertexes are sequentially connected through large arcs according to adjacent sequences to obtain quasi-uniformly divided unit spherical surfaces S, wherein the quasi-uniformly divided unit spherical surfaces S comprise N v A plurality of closed spherical polygonal areas R i Each spherical polygonal region R i Corresponding to a spherical image pixel;
in the spherical polygonal region R i Any sphere point and R i Optimized vertex position V in region i * Distance of less than or equal to R i Any sphere point in the region and the optimized vertex position V j * Distance of j+.i:
R i ＝{p∈S:||p-V i * ||≤||p-V j * ||,for j＝1...,N v }
wherein ,Ri Is the ith spherical polygonal area, p is any point on the sphere, V i * For the optimized position of the ith vertex, V j * The position of the jth vertex after optimization;
all spherical polygonal areas R i Comprises 12 spherical pentagonal regions and N v -12 spherical hexagonal areas.
7. A general convolution operation method for a quasi-uniform spherical image, which is used for carrying out convolution operation, pooling or up-sampling on a quasi-uniform segmented unit spherical surface S obtained by the quasi-uniform spherical image segmentation method as claimed in claim 6, and is characterized by comprising:
alignment of N on a uniformly divided unit sphere S v The 12 spherical hexagonal regions are convolved, pooled or upsampled, wherein,
alignment of N on a uniformly divided unit sphere S v -12 spherical hexagonal areas are convolved, comprising:
defining a spherical polygonal region R i The k-turn adjacent pixels of (a) are:
wherein ,D(Ri ,R j ) Is from R i To R j The minimum number of spherical polygons passed;
defining a spherical polygonal region R i The K-turn convolution kernel of (2) is:
alignment of N on a uniformly divided unit sphere S v Carrying out single-circle convolution operation and multiple circles on 12 spherical hexagonal areasConvolution operations, stride convolution operations, transpose convolution operations, or hole convolution operations, wherein,
operation one: single-or multi-turn convolution operation
Convolved pixel value P i The method comprises the following steps:
wherein ,Wm Weight of mth element of the convolution kernel of k circles, I m Is omega (R) i M is the number of convolution kernel elements in the M-th image pixel value in K);
and (3) operation II: stride convolution operation
Taking a plurality of spherical polygons as sliding step length to obtain a sliding curve R i To R i The direction of the single circle of adjacent pixels is a stride direction, and single circle convolution operation or multi-circle convolution operation is carried out;
and (3) operation III: transposed convolution operation
Zero padding expansion is carried out on the pixels of the input image, and the image subjected to the zero padding expansion enables adjacent pixels R of the original image i ,R j Satisfy D (R) i ,R j ) =2, and the single-turn neighboring pixel value of the original pixel in the zero-padded extended image is 0;
performing stride single-circle convolution operation with the step length of 1 on all spherical pixels subjected to zero padding expansion;
and (4) operation four: cavity convolution operation
Will be R i A pixel with a stride length of 2 along six stride directions as a center, and a pixel point R i A total of 7 pixels, defined as R i Is effective in the pixel region;
carrying out single-circle convolution operation on the effective pixels of all the pixels in the spherical hexagonal area;
alignment of N on a uniformly divided unit sphere S v Performing pooling operation on 12 spherical hexagonal areas, and obtaining a low-pool-level pixel set L from a high-pool-level pixel set H; wherein, the odd level is defined as a pool level, the pooling operation takes four adjacent pixel blocks in H as a pooling core,downsampling from H to L;
alignment of N on a uniformly divided unit sphere S v Up-sampling operation is carried out on 12 spherical hexagonal areas, and a high-pool level pixel set H is obtained from a low-pool level pixel set L; wherein, defining odd number level as pool level, and the pixel value not belonging to L in H is obtained by linear interpolation calculation of pixels in L.
8. A quasi-uniform spherical image segmentation and general convolution operation device, comprising:
the unit spherical surface S is subdivided step by step into spherical triangles with quasi-equal areas, wherein the spherical surface S is used for acquiring a spherical image, mapping the spherical image onto the unit spherical surface S, and subdividing the unit spherical surface S step by step;
the vertex optimization module is used for establishing an electrostatic repulsion physical model and optimizing the vertex position of the spherical triangle through the electrostatic repulsion physical model;
the polygon dividing module is used for carrying out geodesic Voronoi polygon division on the unit spherical surface S based on the optimized spherical triangle vertexes to obtain a unit spherical surface S which is divided in a quasi-uniform manner;
and the convolution operation module is used for carrying out convolution operation, pooling or up-sampling aiming at the unit spherical surface S which is uniformly divided.
9. An electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the quasi-uniform spherical image segmentation method according to any one of claims 1 to 7 when the computer program is executed by the processor.
10. A computer readable storage medium storing a computer program, wherein the computer program is capable of implementing the quasi-uniform spherical image segmentation method according to any one of claims 1 to 7 when executed by a processor.
CN202310388254.4A 2023-04-12 2023-04-12 Quasi-uniform spherical image segmentation and general convolution operation method Pending CN116824085A (en)

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