KR101223940B1 - Method of distinguishing neighbor relationship between two cells which are located at any distance in multiple-resolution octree structure - Google Patents

Abstract

The present invention relates to a method of determining a neighbor relationship between two cells spaced at an arbitrary distance in a multi-resolution octree structure. In particular, the present invention relates to a method of determining neighboring relationships between two adjacent cells simply and quickly using simple arithmetic and GCD operations. The present invention relates to a method for determining a neighbor relationship between two cells spaced at a certain distance in a resolution octree structure. The present invention can provide a method of determining a neighbor relationship between two cells spaced at an arbitrary distance in a multi-resolution octree structure capable of determining a neighbor relationship between two cells simply and quickly using simple arithmetic and GCD operation.

Description

METHODE OF DISTINGUISHING NEIGHBOR RELATIONSHIP BETWEEN TWO CELLS WHICH ARE LOCATED AT ANY DISTANCE IN MULTIPLE-RESOLUTION OCTREE STRUCTURE}

The present invention relates to a method for determining neighboring relations between two cells spaced at arbitrary distances in a multiresolution octree structure. The present invention relates to a method for determining a neighbor relationship between two cells spaced at a certain distance in a resolution octree structure.

Multi-resolution Octree Representation (MOR), a method of modeling a three-dimensional workspace in the form of a cell occupancy map, is recognized as one of the best standards. However, as a cell-based representation, the multi-resolution octree representation is a characteristic entity of the three-dimensional workspace and has inherent limitations in expressing the walls, obstacles, and free spaces to be definable.

The existing neighbor detection method between two cells is "S. Samet The Design and Analysis of Spatial Data Structures Reading, MA: Addison-Wesley, 1990." proposed by Samet. Samet proposed a method of finding neighboring cells in a given direction for pointer octrees based on a search of common ancestors. Besançon proposed an algorithm change and encoding technique in "J. E. Besan'on, Vision par Ordinateur en Deux et Trois Dimensions. Paris, France: Eyrolles, 1988, pp. 341-353." Bollard and Brown also described the tree from the initial cell to the common ancestor in "I. Gargantini, Linear oct-trees for fast processing of three-dimensional objects, Computer Graphics and Image Processing 20 (1982) 365-374." We proposed a retrograde technique for finding neighbors in structures. This method is designed to minimize backtracking from the logic function to verify the neighboring state between two cells based on the tree's circular structure. Boros's proposed "V ㆆ r ㆆ s. J," A strategy for repetitive neighbor finding in octree representations, "Image and vision computing, 2000, 18 (14): pp. 1085-1091" We propose a matrix based on the method of finding octrees using the location of binary code of neighbor search gain. Fayye, Choi, in "Payeur, P.," An Optimized Computational Technique for Free Space Localization in Probabilistic Environment Models ", IEEE Transactions on Instrumentation and Measurement, vol. 55, no 5, pp. 1734-1746, October 2006. A method for finding 26 directions of multi-resolution octree representations is proposed for adjacent cells. Here, in general, adjacent rule sets have proposed a hierarchical addressing scheme of a cell encrypted with a lookup table and a series of mathematical rules. In addition, it was used simultaneously that the selected cell was adjacent to another cell when the relationship between the direction and the rule set of possibilities was defined.

In addition to the methods described above, many studies on object recognition are known. However, known methods are difficult to determine simply and quickly adjacent cells.

An object of the present invention is to provide a simple and fast method for determining the neighbor relationship between two octree cells separated by an arbitrary distance from an octree structure.

In order to achieve the above object, the present invention provides a method for encoding an address of octree cells, encoding an address of the encoded octree cells to a coordinate value, and determining neighboring relationships of the octree cells encoded to the coordinate value. In the multi-resolution octree structure characterized in that it comprises a step of providing a method for determining the neighbor relationship between two cells separated by a certain distance. The encoding of the address of the octree cells may include assigning a unique address value to each octree cell in the octree structure according to the octree depth level, such that the address difference between neighboring octree cells in the octree structure is constant. Encoding the address of the octree cells to indicate thermal regularity. The encoding of the address of the encoded octree cells into a coordinate value may include obtaining an address value of an octree cell that is symmetrical with the selected octree cell by using the sequence regularity, and obtaining a symmetric relationship with the selected octree cell. And encoding an octree cell in the coordinate value represented in the octree coordinate system. The determining of neighboring relationships of the octree cells encoded with the coordinate values includes calculating a distance between two octree cells encoded with the coordinate values and determining whether the neighboring cells are neighbors with each other. Encoding the address of the encoded octree cells into a coordinate value may include assigning an address by a positive integer from 1 to 8 based on upper, left, and rear corners of the octree cell;

, y축 방향 옥트리 셀의 주소 차이값의 증감값 집합

, z축 방향 옥트리 셀의 주소 차이값의 증감값 집합

중 어느 하나에 속하는 증감값 패턴을 갖고, 각 축의 증가방향으로는 +값이며, 각 축의 감소방향으로는 -값이다. 상기 주소 차이값의 증감값은

이며, 상기

는 연산되는 x축과 y축 및 z축 중 어느 하나이고, 상기

는 인덱스이며, 상기

는 각 축에 대한 깊이 레벨 0인 ADV이며 x축일 때 1, y축일 때 4, z축일 때 2의 값을 가진다. 상기 인코딩된 옥트리 셀들의 주소를 좌표값으로 인코딩하는 단계는, 유효한 이웃 셀의 주소값이 되기 위한 기본적인 규칙조건과, 대칭위치에 있는 옥트리 셀의 주소를 규칙적으로 대체할 수 있는 유효숫자가 저장된 대칭셀의 유효숫자 테이블을 이용하여 이웃셀들의 주소값을 찾아내는 것을 특징으로 하며, 상기 유효한 이웃 셀의 주소값이 되기 위한 기본조건은, 1부터 8까지의 양의 정수만 주소 인코딩에 사용되는 제1조건, 주소의 길이는 반드시 같아야 하는 제2조건, 주소의 맨 마지막의 한 자리 숫자는 동일하지 않아야 하는 제3조건, 주소의 각 자리의 숫자는 유효숫자 테이블에 따른 숫자만 위치하는 제4조건을 포함한다. 상기 인코딩된 옥트리 셀들의 주소를 좌표값으로 인코딩하는 단계는,

에 의해 수행되며, 상기

는 연산되는 x축과 y축 및 z축 중 어느 하나이고, 상기

는 인덱스이며, 상기

는 각 축에 대한 깊이 레벨 0인 ADV이며 x축일 때 1, y축일 때 4, z축일 때 2의 값을 가진다. 상기 좌표값으로 인코딩된 옥트리 셀들의 이웃관계를 판별하는 단계는,

에 의해 수행되며, 상기

는 2진수를 10진수로 변환하는 것을 의미하며, 상기

는 연산되는 x축과 y축 및 z축 중 어느 하나를 의미하고, 상기

는 선택된 주소이며, 상기

는 각 축 어레이의 최대 인덱스이고, 상기

는 각 축에 대한 깊이 레벨 0인 ADV이며 x축일 때 1, y축일 때 4, z축일 때 2의 값을 가진다.Repeatingly increasing the number of digits of the address value according to the octree depth level of the octree cell and adding the new digit address value after the existing digit address value. Encoding the address of the encoded octree cells into a coordinate value includes dividing the octree cells into small pieces to increase the octree depth level. The encoding of the encoded octree cells into coordinates may include setting an octree coordinate system having the left and right directions as the x-axis, the up and down directions as the y-axis, and the front and rear directions as the z-axis, based on the center of gravity of the octree cells. And making the address values assigned to neighboring octree cells in the octree structure have a direction based on the x-axis, y-axis, and z-axis directions of the octree coordinate system. The sequence regularity of the address difference values of neighboring octree cells in the octree structure is a set of increase and decrease values of the address difference values of the octree cells in the x-axis direction.

set of increments of address difference value of octree in y-axis direction

set of increments of address difference value of octree in z-axis direction

It has a value increasing / lowering pattern belonging to any one of them, and is positive in the increasing direction of each axis and negative in the decreasing direction of each axis. The increase / decrease value of the address difference value is

And said

Is any one of the x-axis, the y-axis, and the z-axis to be calculated.

Is an index, and

Is an ADV with a depth level of 0 for each axis and has a value of 1 for the x-axis, 4 for the y-axis, and 2 for the z-axis. The encoding of the address of the encoded octree cells into a coordinate value includes a basic rule condition for becoming an address value of a valid neighbor cell, and a symmetric storing significant figures that can regularly replace an address of an octree cell at a symmetric position. The address value of neighboring cells is found by using a significant number table of a cell. The basic condition for becoming an address value of a valid neighbor cell is a first condition in which only positive integers from 1 to 8 are used for address encoding. , A second condition that the length of the address must be the same, a third condition that the last digit of the address must not be the same, and a fourth condition where only the number in the significant digits table is located. do. Encoding the address of the encoded octree cells into a coordinate value,

Is performed by and said

Is any one of the x-axis, the y-axis, and the z-axis to be calculated.

Is an index, and

Is an ADV with a depth level of 0 for each axis and has a value of 1 for the x-axis, 4 for the y-axis, and 2 for the z-axis. The step of determining the neighbor relationship of the octree cells encoded by the coordinate value,

Is performed by and said

Means convert a binary number to a decimal number,

Means any one of the x-axis, y-axis, and z-axis to be calculated,

Is the selected address,

Is the maximum index of each axis array,

Is an ADV with a depth level of 0 for each axis and has a value of 1 for the x-axis, 4 for the y-axis, and 2 for the z-axis.

The present invention can provide a method of determining a neighbor relationship between two cells spaced at an arbitrary distance in a multi-resolution octree structure capable of determining a neighbor relationship between two cells simply and quickly using simple arithmetic and GCD operation.

1 is a conceptual diagram of a neighbor relationship determination method between two cells spaced at an arbitrary distance in a multi-resolution octree structure according to the present invention.
2 is a conceptual diagram of an address encoding method of an octree structure according to the present invention.
3 is an octree coordinate diagram according to the present invention.
4 is an exemplary conceptual diagram of an address array of x, y, and z axes in the present invention.
5 is an exemplary conceptual diagram of a method for determining neighboring octree cells in a MOR according to the present invention.
6 is an exemplary conceptual diagram of the nearest neighboring ADV relationship in the present invention.
7 is a view showing an experimental appearance in a 3DWM environment in the present invention.
8 is a view showing the octree clustering results in the MOR of the 3DWM in the present invention.
9 is a view showing the results of octree point grouping according to Experiment 1 in the present invention.
10 is a view showing the octree point grouping results according to Experiment 2 in the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

It will be apparent to those skilled in the art that the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, It is provided to let you know. Like reference numerals refer to like elements throughout.

1 is a conceptual diagram of a method of determining a neighbor relationship between two cells spaced apart at an arbitrary distance in a multiresolution octree structure according to the present invention, and FIG. 2 is a conceptual diagram of an address encoding method of an octree structure according to the present invention. FIG. 3 is an octree coordinate diagram according to the present invention, and FIG. 4 is an exemplary conceptual diagram of an address array of x, y, and z axes in the present invention. 5 is an exemplary conceptual diagram of a method for determining neighboring octree cells in a MOR in the present invention, and FIG. 6 is an exemplary conceptual diagram of a neighboring ADV relationship in the present invention. FIG. 7 is a view illustrating an experimental view in a 3DWM environment in the present invention, and FIG. 8 is a view illustrating octree clustering results in a MOR of 3DWM in the present invention. 9 is a view showing the results of octree point grouping according to Experiment 1 in the present invention, Figure 10 is a view showing the results of octree point grouping according to Experiment 2 in the present invention.

In the multi-resolution octree structure according to the present invention, a neighbor relationship determination method between two cells spaced at an arbitrary distance may include collecting three-dimensional data (S ₁ ), generating an address encoding and an octree, as shown in FIG. 1. and the step (S _2), which includes the octree clustering stage (S _3).

In the step of collecting three-dimensional data (S ₁ ), the three-dimensional data is collected based on an image photographed using a camera or the like.

In step S ₂ of generating an address encoding and an octree, an address encoding is performed using the collected three-dimensional data to generate an octree. This step of encoding and generating an octree (S ₂ ) comprises the steps of encoding the addresses of the octree cells (S _2-1 ), encoding the addresses of the encoded octree cells with coordinate values (S _2-2 ), And determining the neighbor relationship (S _2-3 ).

Encoding the address of the octree cells (S _2-1 ) gives each cell in the octree structure a unique address value whose value increases with the octree depth level, so that the address difference value between neighboring cells in the octree structure is reduced. Address encoding of the octree cells is performed to represent a constant sequence regularity.

As shown in FIG. 2, in the octree structure having the x-axis plane, the y-axis plane, and the z-axis plane, the address encoding of the octree structure that speaks a positive integer from 1 to 8 from the upper left of the x-axis is continuously repeated. The push back method is used to add a new integer address value to the last number of the existing address value, which increases the number of address values by the octree depth level. That is, as shown in FIG. 3, 1, 2, 3, and 4 are spoken from the upper left of the x-axis in the octree cell, and 7, at the lower left of the y-axis, 8, z at the lower right of the y-axis. 5 is spoken at the bottom left of one axis, and 6 at the bottom right of the other z-axis. By using the octree cell, for example, dividing the octree cell by level 1, the octree cell is doubled. As shown in FIG. 3, in the case of the upper left of the y-axis surface of the octree cell, the octree cell close to the address 3 of the octree cell may be represented by 33, and the octree cell close to the address 3 of the octree cell but also close to the address 4. Can be represented by 34. In addition, an octree cell close to addresses 3 and 7 of an octree cell may be represented by 37, and an octree cell close to addresses 3 and 8 of the octree cell may be represented by 38. In addition, an address is assigned to each octree cell in this way, thereby generating a difference value between the octree cells. Hereinafter, the present invention defines address difference values between octree cells as Address Difference Values (ADVs). In addition, the encoded address has a specific regular value for the z-axis, y-axis, and x-axis directions of the octree coordinates.

Referring to FIG. 4, as in the aforementioned octree coordinates, cells adjacent to each other in the x-axis direction (FIG. 4A) have addresses 1 and 2 and have an ADV of 1. In this case, when the octree cell is decomposed to a depth of level 1, an octree cell having an address of 1 is an octree cell having an address of 11 adjacent to an octree cell of address 1 and an octree having an address of 12 adjacent to an octree cell of address 2. Can be broken down into cells. Also, an octree cell having an address of 2 may be decomposed into an octree cell having an address of 21 adjacent to an octree cell of address 1 and an octree cell having an address of 22 adjacent to an octree cell of address 2. At this time, neighboring octree cells at the depth of level 2 have ADVs of 1 and 9. When an octree cell with a depth of level 2 is decomposed into an octree with a depth of level 3, the depth of level 2 with addresses of 1 and 2 since the x-axis plane has addresses of 1, 2, 3, and 4 in the octree coordinates. Add directionality for addresses 3 and 4 in the octree cell address of. That is, an octree cell having an address of 11 may be decomposed into 131 close to an octree cell of address 3 and 141 close to an octree cell of address 4. In addition, an octree cell having an address of 12 may be decomposed into 132 adjacent to an octree cell of address 3 and 142 adjacent to an octree cell of address 4. An octree cell having an address of 21 may be decomposed into 231 proximate to an octree cell at address 3, and 241 proximate to an octree cell at address 4, and an octree cell having an address of 22 at 232 proximate to an octree cell at address 3, It can be resolved to 242 close to the octree cell at address 4. At this time, the octree cell decomposed to the depth of level 3 has an ADV of 1, 9, and 89. This address difference value has a specific pattern as the level of the decomposition depth is increased, and includes the ADV for the previous depth level when the depth level is increased.

Table 1 shows the characteristics of the address differences. Here, index 0 means depth level 1.

Index X axis Y axis Z axis 0 One 4 2 One 9 36 18 2 89 356 178 3 889 3556 1778 4 8889 35556 17778 5 88889 355556 177778 ... ... ... ... n-1 8… (8)… 9 3 ... (5)... 6 One… (7)... 8

Referring to Table 1, the ADV has a 1 when the depth level is 0 with respect to the x-axis, and has an ADV of 1 and 9 when the depth level is 1. Also, if the depth level is 2, it has an ADV of 1, 9, 89. If the depth level is 0 for the y-axis, the ADV has a value of 4. If the depth level is 1, the ADV has an ADV of 4 and 36. In addition, when the depth level is 0 with respect to the z-axis, the ADV is 2, and when the depth level is 1, the ADV is 2 and 18. As the depth of the x-axis increases to 3 or more, 8 is added between 8 and 9, and in the y-axis, 5 is added between 3 and 6. In addition, in the z-axis, 7 is repeatedly added between 1 and 8. That is, the ADV of the y-axis has a value four times that of the x-axis, and has an ADV value of twice that of the z-axis. This may be formulated as in Equation 1 below.

는 x축과 y축 및 z축이다. 또한,

는 표1의 인덱스이고,

는 각 축에 대한 깊이 레벨 0인 ADV이며 x축일 때 1, y축일 때 4, z축일 때 2의 값을 가진다.here,

Are the x-axis, the y-axis, and the z-axis. Also,

Is the index of Table 1,

Is an ADV with a depth level of 0 for each axis and has a value of 1 for the x-axis, 4 for the y-axis, and 2 for the z-axis.

According to Equation 1, for example, when the depth level of the octree cell is 2 with respect to the x-axis, it has a value of 89 as in the result of Equation 2.

Encoding the address of the encoded octree cells into a coordinate value (S _2-2 ) is performed by using the numerical regularity of the address difference value of each of the address encoded octree cells. The address value is obtained and the two are encoded using a simple mathematical operation to the coordinate values represented in the octree coordinate system. This is performed by encoding the addresses of the above-described octree cells (S _2-1 ). This may be performed by converting the address of the selected octree cell into a coordinate value indicating a position with respect to the octree coordinate using the ADV characteristic. This value is later useful for understanding direct or indirect neighboring relationships between octree cells of varying sizes. In this case, in order to obtain coordinate values of the selected cell of the octree coordinates, opposite pairs are required. Opposite pairs are based on the xy plane (the plane formed by the x and y axes) and the yz plane (the plane formed by the y and z axes) and the zx plane (the plane formed by the z and x axes) of the octree coordinates. A pair of octree cells located next to each other opposite to each other. This relates to the property that addresses 1 to 8 can only be seen in certain directions of three-dimensional octree cells, which can be summarized in Table 2 below.

Table 2 shows opposite numbers in octree cells.

number X axis Y axis Z axis One 2 5 3 2 One 6 4 3 4 7 One 4 3 8 2 5 6 One 7 6 5 2 8 7 8 3 5 8 7 4 6

Referring to Table 2, address 2 on the x-axis faces address 5 on the y-axis and address 3 on the z-axis. Also, address 1 on the x-axis faces address 6 on the y-axis and address 4 on the z-axis. Through Table 2, all numeric conversions of selected octree cell addresses in the required directions of the z-axis, y-axis, and x-axis bring opposite pairs, which can be generated from Equation 3 below.

는 선택된 주소의 대향 쌍 주소이며,

는 x축과 y축 및 z축이다. 또한,

는 선택된 주소를 의미한다. 이때,

는 표2의 대향 쌍 주소를 포함한다.here,

Is the opposite pair address of the selected address,

Are the x-axis, the y-axis, and the z-axis. Also,

Means selected address. At this time,

Contains the opposite pair addresses in Table 2.

사이에 십진수 값 결과는 단정수 값으로, 이러한 이진 패턴의 변환(n은 해당하는 옥트리 구조에서 최대 깊이 레벨 값이다)값은 옥트리 좌표의 좌표값으로 이용될 수 있다. 이는 수학식1과 수학식2를 기반으로 아래의 수학식4와 같이 공식화할 수 있다.In addition, two octree cells of the opposite pair relationship also have one ADV, which is defined as the opposite pair of ADV, that is, OADV (Opposite pair's ADV). The OADV can be calculated by its inference from the address in the opposite pair relationship of the selected address. In addition, OADV is so characteristic that all OADVs have a unique value on a specific axis from the selection of one of the z-axis, y-axis, and x-axis of the octree structure with a certain level. Accordingly, the cell address selected in the octree can be generalized, and the OADV using this attribute is slightly calculated to adjust the value indicating the position of the octree structure. It can also be observed that a binary pattern is obtained by this value divided by twice the initial value of the corresponding direction of the OADV. Where 0 and

The decimal value result in between is a single integer value, and the conversion of this binary pattern (n is the maximum depth level value in the corresponding octree structure) can be used as the coordinate value of the octree coordinate. This may be formulated as Equation 4 below based on Equations 1 and 2.

는 2진수를 10진수로 변환하는 것을 의미하며,

는 연산되는 x축과 y축 및 z축 중 어느 하나를 의미한다.

는 선택된 주소이며,

는 각 축 어레이의 최대 인덱스를 의미한다. 또한,

는 각 축에 대한 깊이 레벨 0인 ADV이며 x축일 때 1, y축일 때 4, z축일 때 2의 값을 가진다.here,

Means convert binary to decimal,

Denotes any one of the x-axis, the y-axis, and the z-axis to be calculated.

Is the selected address,

Is the maximum index of each axis array. Also,

Is an ADV with a depth level of 0 for each axis and has a value of 1 for the x-axis, 4 for the y-axis, and 2 for the z-axis.

From Equation 4, the sign of the coordinate value uses the same sign of the OADV, and one OADV (all three) may be generated for each of the z-axis, y-axis, and x-axis directions of the selected one octree cell address. . These coordinate values are used to calculate distances between octree cells or to determine adjacent relationships of cells.

When comparing two randomly selected octree cells of varying sizes, two octree cells do not belong to one object in the collected three-dimensional data and one of the two octree cells belongs to another object, or belongs to the same object. It can maintain a certain distance with respect to the x-axis, y-axis and z-axis direction. In the case of two randomly selected octree cells having the same size, the two octree cells may be the same octree cell or may belong to the same object to maintain a certain distance with respect to the x-axis, y-axis, and z-axis directions.

In the step of determining the neighbor relationship (S _2-3 ), the distance between two arbitrary cells having the same or different size changed to the value of the octree coordinate system is calculated to determine whether they are neighbors with each other.

로 정의하고 이보다 한 단계 높은 깊이 레벨인 옥트리 셀을

로 정의한다. 또한, 두 개의 옥트리 셀의 레벨 사이의 차이를

로 정의하며, 각각의 방향의 OCV의 부호로부터 미리 정의된 보상값을

로 정의할 수 있다. 이때, 보상값

는 옥트리 좌표 내의 OCV의 동일한 양수의 차이로부터 정의되며, 이것은 선택된 두 개의 옥트리 셀은 서로 다르거나 동일함으로부터 동일방향 OCV의 부호일 때 0과 1의 값을 가진다. 물론, 좌표값 중에서 x만을 비교하는 경우

로 정의할 수 있다. 또한, 동일한 방법으로

와

를 계산할 수 있고, 이 방법은 동일한 깊이 레벨로 두개의 다른 레벨을 가진 옥트리 구조의 셀들의 단일화 절차와,

와

및

는 높은 깊이 레벨의 단일화 이후 두 개의 죄표값의 차이의 크기가 된다. 이러한 값은 옥트리 셀의 최대 개수, N을 포함하는 차이의 절대값에 의해 두 개의 옥트리 셀 사이의 거리를 얻을 수 있으며, 높은 깊이 레벨 옥트리 셀들 내로 낮은 깊이 레벨 옥트리 셀들의 분할의 예에서 가상적으로 생성될 수 있다.Referring to FIG. 5, octree cells having different sizes and low depth levels are illustrated.

Define an octree cell that is one level deeper.

. Also, the difference between the levels of two octree cells

The compensation value defined in advance from the sign of the OCV in each direction

Can be defined as At this time, the compensation value

Is defined from the same positive difference of the OCV in the octree coordinates, which has values of 0 and 1 when the two selected octree cells are different or identical to each other in the same direction OCV. Of course, when comparing only x among coordinate values

Can be defined as Also, in the same way

Wow

In this method, a method of unifying cells of an octree structure having two different levels with the same depth level,

Wow

And

Is the magnitude of the difference between the two sinus values after the unification of the high depth level. This value can be obtained from the example of partitioning low depth level octree cells into high depth level octree cells, which can be obtained by the maximum number of octree cells, the absolute value of the difference including N, Can be.

로 표현될 수 있으며, 도 5는 그 예를 보여준다.This process is as shown in Equation 5 below.

It can be expressed as, Figure 5 shows an example.

는 다른 부호인 두 개의 OCV를 선택했을 때 1이며, 동일한 부호인 두 개의 OCV를 선택했을 때는 0의 값을 가진다. 또한,

는 레벨 L과 레벨 H의 차이값이며,

일 때

의 값을 가진다.here,

Is 1 when two OCVs with different signs are selected and has a value of 0 when two OCVs with the same sign are selected. Also,

Is the difference between level L and level H,

when

Lt; / RTI >

와

처럼 선택된 두 개의 옥트리 셀이 2인 차이값

를 가지면, 수학식5로부터

인 결과값

와,

인 결과값

를 얻을 수 있다. 이 결과는 선택된 두 개의 옥트리 셀 사이의 셀 거리에 직접적으로 사용될 수 있으며, 0은 선택된 두 개의 옥트리 셀이 경계 내에 있거나 선택된 두 개의 옥트리 셀이 겹쳐진 것을 의미한다. 만약,

의 최종거리가 r보다 작을 경우 인접 관계를 가지고 있는 것이며, 사용자가 내부 경계선 거리 r을 1과 동일하게 했을 때 숫자 1은 대부분이 모든 방향으로 인접한 옥트리 셀이다.As shown in Figure 5,

Wow

Difference between two selected octree cells

If from the equation (5)

Result

Wow,

Result

Can be obtained. This result can be used directly for the cell distance between two selected octree cells, where 0 means that the two selected octree cells are within the boundary or the selected two octree cells overlap. if,

If the final distance of is less than r, then there is a contiguous relationship. When the user makes the inner boundary distance r equal to 1, the number 1 is mostly octree cells in all directions.

Based on the addresses of selected octree cells with the same level and combinations thereof, 26 addresses can be quickly generated using six ADVs from the directions -x, + x, -y, + y, -z and + z. In general, except for octree cells located at boundaries and vertices, the octree has the closest octree cells through six faces, twelve borders, and eight vertices. Here, it is essential that the ADV is computed before the other adjacent ADVs by six neighboring relationship determination methods between two cells spaced at an arbitrary distance in the multi-resolution octree structure according to the present invention.

The octree coordinates made through the OADV of the octree cell address selected by the method described above have a special relationship with the maximum number of octree cells that the depth level of the corresponding octree structure can have as many as one column or one row. Is the largest common digit (Greatest Common Digit, GCD, hereinafter GCD) relationship.

Table 3 shows a sample of ADV divided with one column from the X-axis on the octree. Where ADDR is the selected octree address and OPP is the opposite pair of selected addresses. In addition, SIGN is the sine of OADV and OCV is the octree coordinate value. GCD is the maximum common number of both OCV and 2 ³ , and (-) ADV is the ADV in the -X direction. In addition, (+) ADV is ADV in the + X direction.

ADDR OPP SIGN OCV GCD (-) ADV (+) ADV 1131 2242 + 7 One One 1132 2241 6 2 -One 9 1141 2232 5 One -9 One 1142 2231 4 4 -One 89 1231 2142 3 One -89 One 1232 2141 2 2 -One 9 1241 2132 One One -9 One 1242 2131 0 8 -One 889 2131 1242 - 0 8 -889 One 2132 1241 One One -One 9 2141 1232 2 2 -9 One 2142 1231 3 One -One 89 2231 1142 4 4 -89 One 2232 1141 5 One -One 9 2241 1132 6 2 -9 One 2242 1131 7 One -One

이므로, 표1에 나타난 바와 같이, x축에서 첫 번째 ADV값(첫번째 인덱스)은 첫 번째 펙터값 1이 된다. OADV의 부호가 양이므로 +x 방향으로 ADV값을 보여주고 그 값은 1이 된다. 또한, 반대 방향 ADV를 계산하기 위해, 최초 방향과 다른 인접한 옥트리 셀의 ADV값을 이용할 수 있다. 예를 들어, -x 방향에서 주소값 1441의 ADV는 +x 방향에서 1132의 ADV값과 같음을 알 수 있다. 이러한 값을 얻기 위해, 주소값 1132의 OADV와 기대되는 옥트리 셀의 최대 개수 사이에서 GCD가 연산될 수 있다. 하지만, GCD는 주소값 1141의 좌표값에 1을 더한 좌표값과 추가적인 연산 없이 도출된 옥트리 셀의 결과의 최대 개수 사이에서 연산된다. 또한, 이러한 결과로서, GCD값 2를 얻을 수 있다. 이때, 2는

이므로 표1에서 1개의 x축에 의해 보여진 두 번째 인자 9를 선택할 수 있다. ADV의 부호는 반대 방향이므로 음수이다. 좌표값은 좌표값이 접경하기 위해 속한 셀의 경우 극값(extremal value)을 가지고 있다. 이때, 어떤 ADV도 양인 OADV에서 - 방향에 존재할 수 있으며, 음인 OADV에서 +방향에 존재할 수 있으므로 연산은 필요없다. 이러한 방법으로 생성된 6 방향에서의 ADV는 동시에 선택한 옥트리 셀 주소뿐만 아니라 인접한 옥트리 셀의 주소까지 생성할 수 있다. 도 6에 도시된 바와 같이, 동일한 라인으로 인접한 12개의 이웃한 옥트리 셀은 12개의 조합으로부터 만들어진 새로운 ADV를 생성할 수 있다.Table 3 shows the ADV distribution with one column from the example of the x-axis and GCD values of the octree structure at depth level 4. Referring to Table 3, for example, the address value 1441 has a final GCD value of 1. GCD value of 1

Therefore, as shown in Table 1, the first ADV value (first index) on the x-axis becomes the first factor value 1. Since the sign of OADV is positive, ADV value is shown in + x direction and its value becomes 1. In addition, to calculate the opposite direction ADV, the ADV value of the adjacent octree cell different from the original direction may be used. For example, it can be seen that the ADV of the address value 1441 in the -x direction is the same as the ADV value of 1132 in the + x direction. To obtain this value, the GCD can be computed between the OADV of address value 1132 and the maximum number of octree cells expected. However, the GCD is calculated between the coordinate value of the address value 1141 plus 1 and the maximum number of results of the octree cell derived without further calculation. As a result of this, the GCD value 2 can be obtained. 2 is

In Table 1, you can select the second factor 9 shown by one x-axis. The sign of ADV is negative because it is in the opposite direction. The coordinate value has an extreme value in the cell to which the coordinate value belongs. At this time, since any ADV may exist in the negative direction in the positive OADV and negative in the negative direction of the OADV, no operation is required. In this way, the ADVs generated in the six directions can generate not only the selected octree cell address but also the addresses of adjacent octree cells. As shown in FIG. 6, twelve neighboring octree cells adjacent to the same line may generate a new ADV made from twelve combinations.

FIG. 7 shows that the robot arm picks up an object by recognizing the object in a 3D Workspace Modeling, by Sukhan Lee (3DWM) experimental environment. 8 to 10 show three-dimensional point clouds, tables and octree cells. Here, two experiments were performed in the experimental environment of 3DWM in FIGS. 9 and 10, and all of the same processor operations were repeated 100 times. 9 and 10, the detailed openGL rendering result of octree point grouping can reduce the time wasted to find neighboring octree cells in a multi-resolution octree representation (MOR). The results are shown in Table 4 below.

Table 4 shows the experimental results of octree clustering in the octree structure. Here, Lv # (1 to 9) is the octree cell generation amount at each depth level, and the sum is the total amount of octree cell generation. M1 is a neighbor relationship discrimination method and a processing time (MSEC) between two cells spaced at an arbitrary distance in the multi-resolution octree structure according to the present invention, and M2 is Payeur's method and processing time (MSEC). M3 is a common backtracking method and processing time (MSEC).

Experiment # 1 Lv1 Lv2 Lv3 Lv4 Lv5 Lv6 Lv7 Lv8 Lv9 Sum M1 M2 M3 Level6 0 0 0 0 One 78 0 0 0 79 0 0 94 Level7 0 0 0 0 One 11 200 0 0 212 0 47 781 Level8 0 0 0 0 One 11 30 405 0 447 0 172 4094 Level9 0 0 0 0 One 11 30 41 996 1079 16 1015 29094 Experiment # 2 Lv1 Lv2 Lv3 Lv4 Lv5 Lv6 Lv7 Lv8 Lv9 Sum M1 M2 M3 Level6 0 0 0 0 One 132 0 0 0 113 0 15 250 Level7 0 0 0 0 One 12 336 0 0 349 0 94 2110 Level8 0 0 0 0 One 12 34 906 0 953 0 734 18813 Level9 0 0 0 0 One 12 34 102 2221 2370 62 4812 N / A

Referring to Table 4, in the multi-resolution octree structure according to the present invention, it can be seen that the neighboring relationship between two cells spaced at an arbitrary distance is significantly reduced in processing time compared to the conventional Payeur and general backtracking methods. have.

As described above, in the multi-resolution octree structure according to the present invention, the neighbor relationship determination method between two cells spaced at an arbitrary distance is simple, and the neighboring relationship between two cells spaced at an arbitrary distance from the octree structure is simplified by using a simple algorithm and GCD operation. It can be done quickly.

Although described above with reference to the drawings and embodiments, those skilled in the art can be variously modified and changed within the scope of the invention without departing from the spirit of the invention described in the claims below. I can understand. For example, each step described in the present invention may be programmed inside the computer, or each step may be implemented in a modular manner such as a chip.

Claims (12)

Encoding the addresses of the octree cells;
Encoding the address of the encoded octree cells into a coordinate value, and
And determining neighboring relationships of the octree cells encoded by the coordinate values. 2. The method according to claim 1,
Encoding the address of the octree cells,
Each octree cell in the octree structure is assigned a unique address value whose value is increased according to the octree depth level, so that the address difference of the octree cells in the octree structure indicates a constant sequence regularity. And a method of determining neighboring relationships between two cells spaced at an arbitrary distance in a multiresolution octree structure. The method according to claim 2,
Encoding the address of the encoded octree cells into a coordinate value,
Coordinates value of an octree cell having a symmetrical relation with a selected octree cell among encoded octree cells using the sequence regularity, and an octree cell having a symmetric relation with the selected octree cell is represented in an octree coordinate system And determining a neighbor relationship between two cells spaced apart at an arbitrary distance in a multiresolution octree structure. The method according to claim 3,
The step of determining the neighbor relationship of the octree cells encoded by the coordinate value,
And calculating whether a distance between two octree cells encoded by the coordinate value is adjacent to each other, thereby determining whether or not the neighbors are adjacent to each other in a multi-resolution octree structure. The method according to claim 2,
Encoding the address of the encoded octree cells into a coordinate value,
Addressing a positive integer from 1 to 8 based on the top, left, and back corners of the octree cell;
Repetitively increasing the number of digits of the address value according to the octree depth level of the octree cell to add an address value of a new number of digits after the existing number of digits to an arbitrary distance in the multi-resolution octree structure. Method of determining neighboring relationship between two distant cells. The method according to claim 5,
Encoding the address of the encoded octree cells into a coordinate value,
And dividing the octree cells into smaller ones to increase the octree depth level. 2. A method of determining neighboring relationships between two cells spaced at an arbitrary distance in a multi-resolution octree structure. The method according to claim 1,
Encoding the address of the encoded octree cells into a coordinate value,
Setting an octree coordinate system having the x-axis as the left and right directions, the y-axis as the vertical axis, and the z-axis as the front and rear directions, with the center of gravity of the octree cell as the origin;
Arbitrary addressing in a multi-resolution octree structure, comprising the step of causing an address value assigned to neighboring octree cells in the octree structure to have a direction relative to the x-axis, y-axis, and z-axis directions of the octree coordinate system. Method of determining neighbor relationship between two cells separated by distance. The method of claim 7,
The sequence regularity of the address difference values of neighboring octree cells in the octree structure is a set of increase and decrease values of the address difference values of the octree cells in the x-axis direction.

set of increments of address difference value of octree in y-axis direction

set of increments of address difference value of octree in z-axis direction

Determination of neighboring relations between two cells separated by an arbitrary distance in a multi-resolution octree structure, characterized by having an increase / decrease pattern belonging to any one of them, and a positive value in an increasing direction of each axis, and a negative value in a decreasing direction of each axis. Way. The method according to claim 8,
The increase / decrease value of the address difference value is

Is,
Here, the address difference values (ADVs) are address difference values between octree cells,
remind

Is either the x-axis, the y-axis, and the z-axis being computed,
remind

Is an index,
remind

Determining the neighbor relationship between two cells separated by a certain distance in the multi-resolution octree structure, characterized in that ADV having a depth level of 0 for each axis, 1 in the x-axis, 4 in the y-axis, 2 in the z-axis Way. The method according to claim 1,
Encoding the address of the encoded octree cells into a coordinate value,
Finding the address value of neighboring cells using basic rule condition to be the address value of a valid neighbor cell and the significant number table of the symmetric cell that stores the significant digits that can regularly replace the address of the octree cell in the symmetric position The basic condition for an address value of a valid neighbor cell includes: a first condition in which only positive integers from 1 to 8 are used for address encoding, a second condition in which the length of the address must be the same, and the end of the address The third condition that one digit of must not be the same, the fourth digit of each address of the address includes a fourth condition where only the number according to the significant number table is located. Method of determining neighbor relationship between two cells. The method of claim 10,
Encoding the address of the encoded octree cells into a coordinate value,

Is performed by
Here, the address difference values (ADVs) are address difference values between octree cells,
remind

Is either the x-axis, the y-axis, and the z-axis being computed,
remind

Is an index,
remind

Determining the neighbor relationship between two cells separated by a certain distance in the multi-resolution octree structure, characterized in that ADV having a depth level of 0 for each axis, 1 in the x-axis, 4 in the y-axis, 2 in the z-axis Way. The method according to claim 1,
The step of determining the neighbor relationship of the octree cells encoded by the coordinate value,

Is performed by
Here, the OCV is an octree coordinate value, the ADV (Address Difference values) is an address difference value between the octree cells, the OADV (Opposite pair's ADV) is the opposite pair ADV,

Is,

ego,
remind

Means convert binary to decimal,
remind

Means any one of the x-axis, y-axis, and z-axis being computed,
remind

Is the selected address,
remind

Is the opposite pair address of the selected address,
remind

Is the index of each axis array,
remind

Is the maximum index of each axis array,
remind

Determining the neighbor relationship between two cells separated by a certain distance in the multi-resolution octree structure, characterized in that ADV having a depth level of 0 for each axis, 1 in the x-axis, 4 in the y-axis, 2 in the z-axis Way.

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