WO2025035646A1 - 一种支持表达不确定性层次空间信息的轨迹可视化方法 - Google Patents

一种支持表达不确定性层次空间信息的轨迹可视化方法 Download PDF

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WO2025035646A1
WO2025035646A1 PCT/CN2023/134764 CN2023134764W WO2025035646A1 WO 2025035646 A1 WO2025035646 A1 WO 2025035646A1 CN 2023134764 W CN2023134764 W CN 2023134764W WO 2025035646 A1 WO2025035646 A1 WO 2025035646A1
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uncertain
nodes
trajectory
spatial information
leaf
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袁晓如
郭宇涵
罗煜楚
鲁可儿
李林芳
杨海峥
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Peking University
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/26—Visual data mining; Browsing structured data
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/29—Geographical information databases

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  • the present invention belongs to the field of visualization, and in particular relates to a trajectory visualization method supporting the expression of uncertain hierarchical spatial information.
  • trajectory visualization methods are based on geographic maps, directly drawing trajectory paths or clustering trajectory data before drawing.
  • coding methods such as fuzziness, color, and size are used to indicate uncertainty.
  • the spatial uncertainty in the data is significant, the clustering of a large number of ambiguous locations on the geographic map can easily lead to misunderstandings and make it difficult to reveal the trajectory characteristics.
  • the present invention aims to provide a trajectory visualization method that supports the expression of uncertainty hierarchical spatial information.
  • trajectory data with uncertainty hierarchical spatial information the points in the trajectory are organized into nested circular structures according to the extracted spatial uncertainty hierarchy.
  • the location of a certain place is placed inside the circle, and the location of an uncertain place is placed on the circle's boundary, with directed edges representing the movement between the two places.
  • the optimal layout of abstract map nodes is obtained through constraints such as geographic space and link relationships, thereby avoiding misunderstandings caused by drawing uncertain places on geographic maps, while retaining known information and related relationships to the greatest extent, objectively and effectively revealing trajectory characteristics, and laying a solid foundation for the development of spatial information visualization.
  • a trajectory visualization method supporting the expression of uncertainty hierarchical spatial information comprising the following steps:
  • step S2 performing abstract map node layout according to the spatial uncertainty level extracted in step S1;
  • the trajectory path is drawn using quadratic Bezier curves.
  • the tree nodes in the spatial uncertainty hierarchy extracted in step S1 are divided into non-leaf nodes, determined leaf nodes and uncertain leaf nodes.
  • Determined leaf nodes refer to leaf nodes without non-leaf sibling nodes
  • uncertain leaf nodes refer to leaf nodes with non-leaf sibling nodes.
  • step S2 the locations in the trajectory are organized into a nested circular structure according to the extracted spatial uncertainty hierarchy, and the locations with determined positions are placed inside the circle, and the uncertain locations are placed at the boundary of the circle.
  • the abstract map node layout process in step S2 considers the spatial uncertainty level, link relationship and geographical location of the nodes.
  • step S2 includes the following sub-steps:
  • step S21 the internal nodes with the same parent node are represented as a group of circles, and the circular tree graph layout algorithm is applied. Starting from the leaf nodes, the circles are compactly arranged from the inside to the outside from the bottom up. During the internal node layout process, the edge chain is maintained, and the edge chain is initialized to three tangent circles. Thereafter, two adjacent circles on the edge chain are selected each time, and the new circle is placed at the tangent point.
  • step S22 for each uncertain leaf node, the center of gravity of its neighboring nodes is first calculated, and the center of gravity of the parent node of the uncertain leaf node is connected with the center of gravity of the neighboring nodes to obtain a ray. The intersection of the ray and the parent node boundary is the center of gravity of the uncertain leaf node. If the newly placed uncertain leaf node coincides with the position of an existing uncertain leaf node, a small offset is added until there is no overlap between the uncertain leaf nodes.
  • trajectory path in step S3 is represented by directed edges between abstract map nodes.
  • the edge width between two nodes in the trajectory path in step S3 encodes the number of trajectories from the starting point to the end point.
  • the beneficial technical effect of the present invention is that: using a trajectory visualization method disclosed in the present invention that supports the expression of uncertain hierarchical spatial information can effectively display trajectory data with hierarchical spatial uncertainty, avoid misunderstandings caused by uncertain locations, and objectively and effectively reveal trajectory characteristics, such as aggregation and dispersion, laying a reliable foundation for the development of spatial information visualization.
  • FIG1 is a schematic diagram of a process of constructing an abstract map using a trajectory visualization method supporting the expression of uncertain hierarchical spatial information according to Embodiment 1 of the present invention
  • (a) is the actual spatial level
  • (b) is the uncertainty spatial information, such as the city or province to which the institution belongs is unknown
  • (c) is the uncertainty spatial level
  • (d) is the abstract map structure
  • FIG2 is a schematic diagram of a process of performing abstract map node layout using a trajectory visualization method supporting the expression of uncertain hierarchical spatial information according to Embodiment 1 of the present invention
  • FIG. 3 is an abstract map constructed using a trajectory visualization method supporting the expression of uncertain hierarchical spatial information as described in Example 1.
  • an embodiment of the present invention provides a trajectory visualization method that supports expressing uncertain hierarchical spatial information, and the method includes the following steps:
  • the spatial uncertainty level is extracted from the spatial data to be expressed.
  • the actual spatial information includes the complete hierarchical information from “country” to “institution” as shown in the figure.
  • the spatial data can be expressed as an uncertainty hierarchy as shown in Figure (c).
  • Non-leaf nodes are non-leaf nodes, such as "country”, “province”, and "city”, which represent upper-level regions and have a certain geographical location.
  • Determined leaf nodes refer to leaf nodes without non-leaf sibling nodes, such as institution nodes with known locations.
  • Uncertain leaf nodes refer to leaf nodes with non-leaf sibling nodes, such as institution nodes with unknown locations.
  • step S2 Perform abstract map node layout based on the spatial uncertainty hierarchy extracted in step S1.
  • non-leaf nodes and definite leaf nodes are laid out in a circular tree graph, and uncertain leaf nodes are placed at the boundary of their parent nodes.
  • the abstract map node layout is divided into two sub-steps.
  • non-leaf nodes and certain leaf nodes are collectively referred to as internal nodes, and uncertain leaf nodes are called boundary nodes.
  • the internal node positions are determined, with the goal of preserving the relative geospatial position relationship; then the boundary node positions are determined, with the goal of minimizing the trajectory path length.
  • step S2 includes the following steps:
  • the internal nodes with the same parent node are represented as a group of circles.
  • the circular treemap layout algorithm is applied to arrange the circles compactly from the inside out.
  • the edge chain is maintained.
  • the edge chain is initialized as three tangent circles. After that, two adjacent circles on the edge chain are selected each time, and the new circle is placed at the tangent point with them, so that after the new circle is added, the angle relationship between all circles is consistent with the real geographic
  • the spatial angle relationship has the smallest difference.
  • the circles are nested hierarchically from bottom to top.
  • the area of the leaf node maps the number of trajectories passing through the node.
  • Cm represents the center of the mth circle
  • the hollow circles are the three tangent circles Cm -1 , Cm and Cm +1 that have been determined, and the circles are placed one by one.
  • the solid circle C is the newly inserted circle, and the newly inserted circle C is placed at the tangent point with the two adjacent circles Cm and Cm +1 on the edge chain.
  • Pm represents the geographical location coordinates corresponding to the mth circle, and the new circle C is set on the boundary so that the two adjacent circles with the minimum geographical angle loss are tangent.
  • For each boundary node first calculate the center of gravity of its neighboring nodes, connect the center of its parent node with the center of gravity of the neighboring nodes, and the intersection of the ray and the parent node boundary is the center of the boundary node. If the newly placed boundary node overlaps with the position of an existing boundary node, increase the offset slightly until there is no overlap.
  • the centers of neighbor nodes of the boundary node center C are C 1 , C 2 , C 3 and C 4 respectively, and the center of gravity of the neighbor nodes is G.
  • the parent node is a dotted circle with Cp as the center.
  • the center of the boundary node C is located at the intersection of the ray from the parent node center Cp to the center of gravity of its neighbor nodes G and the circumference of the parent node.
  • the position of C can be calculated by the angle ⁇ of the ray CpG and the radius of the circle Cp.
  • the trajectory path is drawn using quadratic Bezier curves.
  • the trajectory is represented by directed edges between nodes, drawn using quadratic Bezier curves, and the width of the edge between two nodes encodes the number of trajectories from the start point to the end point.
  • the trajectory visualization method disclosed by the present invention supports the expression of uncertain hierarchical spatial information.
  • the optimal layout of abstract map nodes is obtained through constraints such as geographic space and link relationships, thereby avoiding It avoids misunderstandings caused by drawing uncertain locations on geographic maps, while retaining known information and related relationships to the greatest extent. It can objectively and effectively reveal trajectory characteristics and lay a solid foundation for the development of spatial information visualization.

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Abstract

一种支持表达不确定性层次空间信息的轨迹可视化方法，属于可视化领域，基于实际空间信息，从待表达空间数据中提取空间不确定性层次；依据提取的空间不确定性层次，进行抽象地图节点布局，将轨迹中地点按空间不确定性层次组织为嵌套圆形结构，将位置确定的地点置于圆形内部，不确定地点置于圆形边界，使用二次贝塞尔曲线进行轨迹路径绘制。该方法针对具有不确定性层次空间信息的轨迹数据，通过地理空间、链接关系等约束条件获得抽象地图节点优化布局，从而避免在地理地图上绘制不确定地点带来的误解，同时最大程度保留已知信息和相关关系，能够客观有效揭示轨迹特征，为空间信息可视化发展奠定可靠基础。

Description

一种支持表达不确定性层次空间信息的轨迹可视化方法 技术领域
本发明属于可视化领域，具体涉及一种支持表达不确定性层次空间信息的轨迹可视化方法。
背景技术
可视化是数据时代用以进行数据表达的重要手段,轨迹可视化可以帮助理解与分析轨迹数据中的移动特征，是可视化领域的经典研究方向。
已有轨迹可视化方法大多基于地理地图，直接绘制轨迹路径或对轨迹数据进行聚集后进行绘制。对于轨迹中不确定的地点信息，则采用模糊、颜色、大小等编码方式表明不确定性。然而，当数据中空间不确定性显著时，大量具有模糊性的地点在地理地图上的聚集易带来误解，且难以揭示轨迹特征。
发明内容
针对现有技术中存在的缺陷，本发明的目的在于提供一种支持表达不确定性层次空间信息的轨迹可视化方法，针对具有不确定性层次空间信息的轨迹数据，将轨迹中地点按提取的空间不确定性层次组织为嵌套圆形结 构，将位置确定的地点置于圆形内部，不确定地点置于圆形边界，以有向边表示两地点间的移动。通过地理空间、链接关系等约束条件获得抽象地图节点优化布局，从而避免在地理地图上绘制不确定地点带来的误解，同时最大程度保留已知信息和相关关系，客观有效揭示轨迹特征，为空间信息可视化发展奠定可靠基础。
为达到以上目的，本发明采用的技术方案是：
一种支持表达不确定性层次空间信息的轨迹可视化方法，所述方法包括以下步骤：
S1、基于实际空间信息，从待表达空间数据中提取空间不确定性层次；
S2、依据步骤S1中提取的空间不确定性层次，进行抽象地图节点布局；
S3、基于抽象地图节点布局，使用二次贝塞尔曲线进行轨迹路径绘制。
进一步，步骤S1中提取的空间不确定性层次中树节点分为非叶子节点、确定叶子节点和不确定叶子节点，确定叶子节点指无非叶兄弟节点的叶子节点，不确定叶子节点指有非叶兄弟节点的叶子节点。
进一步，步骤S2中将轨迹中地点按提取的空间不确定性层次组织为嵌套圆形结构，将位置确定的地点置于圆形内部，不确定地点置于圆形边界。
进一步，步骤S2中进行抽象地图节点布局过程考虑节点所在的空间不确定性层次、链接关系和地理位置。
进一步，步骤S2包括以下子步骤：
S21、应用圆形树图布局算法进行内部节点布局，所述内部节点包括非叶子节点和确定叶子节点；
S22、将不确定叶子节点布局于所述不确定叶子节点的父节点边界。
进一步，步骤S21中将具有同一父节点的内部节点表示为一组圆形，应用圆形树图布局算法，从叶子节点开始，自下而上将圆形由内而外紧凑排布，在内部节点布局过程中，维持边缘链，边缘链初始化为三个相切的圆形，之后每次选取边缘链上两个相邻圆形，将新的圆形置于与其相切处。
进一步，步骤S22中对于每个不确定叶子节点，首先计算其邻居节点的重心位置，将所述不确定叶子节点的父节点圆心与邻居节点重心相连得到一条射线，所述射线与父节点边界交点即为所述不确定叶子节点圆心，如果新放置的不确定叶子节点与已有不确定叶子节点位置重合，则增加微小偏移量，直到不确定叶子节点之间没有重合。
进一步，步骤S3中所述轨迹路径以抽象地图节点间有向边表示。
进一步，步骤S3中所述轨迹路径中两节点间连边宽度编码由起点到终点的轨迹数量。
本发明的有益技术效果在于：采用本发明所公开的一种支持表达不确定性层次空间信息的轨迹可视化方法，能够有效展示具有层次空间不确定性的轨迹数据，避免不确定地点所带来的误解，且能客观有效揭示轨迹特征，如聚集、分散，为空间信息可视化发展奠定可靠基础。
附图说明
图1为采用本发明实施例一所述的一种支持表达不确定性层次空间信息的轨迹可视化方法构造抽象地图过程示意图；
其中(a)为实际空间层次，(b)为不确定性空间信息，如机构所属城市或省份未知，(c)为不确定性空间层次(d)为抽象地图结构；
图2为采用本发明实施例一所述的一种支持表达不确定性层次空间信息的轨迹可视化方法进行抽象地图节点布局过程示意图；
图3为采用实施例一所述的一种支持表达不确定性层次空间信息的轨迹可视化方法构造的抽象地图。
具体实施方式
下面结合附图和具体实施方式对本发明作进一步描述。
实施例一
如图1所示，本发明实施例提供一种支持表达不确定性层次空间信息的轨迹可视化方法，所述方法包括以下步骤：
S1、基于实际空间信息，从待表达空间数据中提取空间不确定性层次。
如图1所示，在本实施例中，以“国家-省份-城市-机构”层次结构空间信息为例，其中如图1(a)所示，实际空间信息包含图中所示由“国家”到“机构”完整层次信息。
如图1(b)所示，然而在一些情形下，如对于历史数据，可能仅知道“机构”存在，而不知其所属城市或省份，根据不同层次空间不确定性，可将空间数据表达为如图(c)所示的不确定性层次结构，深度越低的机构节点具有 越高的不确定性。后续步骤中可根据(c)中提取的不确定性层次结构，构造如(d)所示的抽象地图。
图1(c)中不确定性层次树节点可分为三类：非叶节点、确定叶子节点和不确定叶子节点。非叶节点即非叶子节点，如“国家”“省份”“城市”，代表上层区域，具有确定的地理位置。确定叶子节点指无非叶兄弟节点的叶子节点，如位置已知的机构节点。不确定叶子节点指有非叶兄弟节点的叶子节点，如位置未知的机构节点。
S2、依据步骤S1中提取的空间不确定性层次，进行抽象地图节点布局。
如图1(d)所示，非叶节点和确定叶子节点按圆形树图布局，不确定叶子节点置于其父节点边界。
考虑到节点层次约束、链接关系(即有轨迹路径相连的节点应较为接近)和地理位置(即节点布局应近似真实地理位置关系)，抽象地图节点布局分为两个子步骤。为便于说明布局算法，下将非叶节点和确定叶子节点统称为内部节点，将不确定叶子节点成为边界节点。
如图2所示，首先确定内部节点位置，目标是保留相对地理空间位置关系；然后确定边界节点位置，目标是最小化轨迹路径长度。
即步骤S2包括以下步骤：
S21、应用圆形树图布局算法进行内部节点布局。
将具有同一父节点的内部节点表示为一组圆形，应用圆形树图布局算法，将圆形由内而外紧凑排布。在布局过程中，维持边缘链。边缘链初始化为三个相切的圆形，之后每次选取边缘链上两个相邻圆形，将新的圆形置于与其相切处，使得新圆形加入后，所有圆形之间角度关系与真实地理 空间角度关系相差最小。从叶子节点开始，自下而上将圆形按层次嵌套。叶子节点面积映射经过该节点的轨迹数量。
如图2(a)所示，Cm表示第m个圆形的圆心，空心圆为已确定布局的三个相切的圆形Cm-1、Cm和Cm+1，逐次放置圆形，实心圆C为新插入的圆形，新插入的圆形C置于与边缘链上两个相邻圆形Cm和Cm+1相切处。Pm则表示第m个圆形所对应的地理位置坐标，新圆C设置于边界上使得地理角度损失最小的两相邻圆形相切。
S22、将边界节点布局于其父节点边界。
对于每个边界节点，首先计算其邻居节点的重心位置，将其父节点圆心与邻居节点重心相连，该射线与父节点边界交点即为边界节点圆心。如果新放置的边界节点与已有边界节点位置重合，则增加微小偏移量，直到没有重合。
如图2(b)所示，边界节点圆心C的邻居节点圆心分别为C1、C2、C3和C4，邻居节点的重心位置为G。父节点为虚线圆，圆中心为Cp，边界节点圆心C位于由父节点中心Cp指向其邻居节点重心G的射线与父节点圆周交点上。例如图2(b)中，由射线CpG角度α和圆Cp半径可计算得到C位置。
S3、基于抽象地图节点布局，使用二次贝塞尔曲线进行轨迹路径绘制。
如图3所示，轨迹以节点间有向边表示，使用二次贝塞尔曲线绘制，两节点间连边宽度编码由起点到终点的轨迹数量。
通过上述实施例可以看出，本发明公开的一种支持表达不确定性层次空间信息的轨迹可视化方法，针对具有不确定性层次空间信息的轨迹数据，通过地理空间、链接关系等约束条件获得抽象地图节点优化布局，从而避 免在地理地图上绘制不确定地点带来的误解，同时最大程度保留已知信息和相关关系，能够客观有效揭示轨迹特征，为空间信息可视化发展奠定可靠基础。
本发明所述的方法并不限于具体实施方式中所述的实施例，本领域技术人员根据本发明的技术方案得出其他的实施方式，同样属于本发明的技术创新范围。

Claims (9)

  1. 一种支持表达不确定性层次空间信息的轨迹可视化方法，所述方法包括以下步骤：
    S1、基于实际空间信息，从待表达空间数据中提取空间不确定性层次；
    S2、依据步骤S1中提取的空间不确定性层次，进行抽象地图节点布局；
    S3、基于抽象地图节点布局，使用二次贝塞尔曲线进行轨迹路径绘制。
  2. 如权利要求1所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S1中提取的空间不确定性层次中树节点分为非叶子节点、确定叶子节点和不确定叶子节点，确定叶子节点指无非叶兄弟节点的叶子节点，不确定叶子节点指有非叶兄弟节点的叶子节点。
  3. 如权利要求1所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S2中将轨迹中地点按提取的空间不确定性层次组织为嵌套圆形结构，将位置确定的地点置于圆形内部，不确定地点置于圆形边界。
  4. 如权利要求1所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S2中进行抽象地图节点布局过程考虑节点所在的空间不确定性层次、链接关系和地理位置。
  5. 如权利要求2所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于，步骤S2包括以下子步骤：
    S21、应用圆形树图布局算法进行内部节点布局，所述内部节点包括非叶子节点和确定叶子节点；
    S22、将不确定叶子节点布局于所述不确定叶子节点的父节点边界。
  6. 如权利要求5所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S21中将具有同一父节点的内部节点表示为一组圆形，应用圆形树图布局算法，从叶子节点开始，自下而上将圆形由内而外紧凑排布，在内部节点布局过程中，维持边缘链，边缘链初始化为三个相切的圆形，之后每次选取边缘链上两个相邻圆形，将新的圆形置于与其相切处。
  7. 如权利要求5所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S22中对于每个不确定叶子节点，首先计算其邻居节点的重心位置，将所述不确定叶子节点的父节点圆心与邻居节点重心相连得到一条射线，所述射线与父节点边界交点即为所述不确定叶子节点圆心，如果新放置的不确定叶子节点与已有不确定叶子节点位置重合，则增加微小偏移量，直到不确定叶子节点之间没有重合。
  8. 如权利要求1所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S3中所述轨迹路径以抽象地图节点间有向边表示。
  9. 如权利要求8所述的一种支持表达不确定性层次空间信息的轨迹可视化方法，其特征在于：步骤S3中所述轨迹路径中两节点间连边宽度编码由起点到终点的轨迹数量。
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