在抽象空间中的深度测量的水平集
A Cholaquidis1, R Fraiman1, L Moreno2
1Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay.
概括
镜头深度是用公尺空间来衡量的,现在已经定义为一般空间. 它的经验形式汇聚到真正的镜头深度,水平集始终估计人口对应物.
科学领域:
- * 数学的统计学
- * 计量空间理论 * 计量空间理论
背景情况:
- *大多数深度测量仅限于欧几里德空间.
- * 镜头深度已经扩展到一般的米制空间.
- *这种扩展允许深度测量的更广泛的应用.
研究的目的:
- * 在一般的度量空间中建立实证镜头深度的理论性质.
- *为了证明实证镜头深度水平集与其人口对应的趋同.
- * 为了证明经验水平集作为人口水平集的估计器的一致性.
主要方法:
- * 使用镜头深度的定义来表示一个点在两个随机球的交叉点上的概率.
- * 应用Painlevé-Kuratowski意义上的收定理来实现集合的收.
- *使用豪斯多夫距离来评估经验估计者的一致性.
主要成果:
- * 经验证实了透镜深度水平集与可分离和完整的度量空间中的人口水平集的融合.
- * 证明实证水平集及其边界是对紧集的豪斯多夫距离的一致估计器.
- *通过两个现实生活中的例子分析了镜头深度的实际实用性.
结论:
- * 经验性镜头深度可用于在一般的度量空间中可靠地估计总体镜头深度.
- * 理论发现支持在米制空间内的统计分析中使用镜头深度.
- * 该研究验证了透镜深度作为具有实际应用的强大的统计工具.
相关概念视频
Depth Perception and Spatial Vision
745
Depth perception is the ability to perceive objects three-dimensionally. It relies on two types of cues: binocular and monocular. Binocular cues depend on the combination of images from both eyes and how the eyes work together. Since the eyes are in slightly different positions, each eye captures a slightly different image. This disparity between images, known as binocular disparity, helps the brain interpret depth. When the brain compares these images, it determines the distance to an object.
745
Interval Level of Measurement
15.4K
For effective statistical analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...
15.4K
Design Example: Measuring Distance Between Two Points with Obstructions
67
When measuring distances in areas with physical obstructions, such as a lake in a field, surveyors must employ techniques to calculate accurate lengths without direct line measurements. One effective method is the offset technique, which allows for precise distance estimation over inaccessible stretches.In this scenario, a surveyor must measure a side of an area that crosses a lake. Since the measuring tape cannot span the lake, the surveyor begins by establishing a baseline that aligns with...
67
Collisions in Multiple Dimensions: Introduction
5.5K
It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
5.5K
Collisions in Multiple Dimensions: Problem Solving
4.3K
In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
4.3K
Differential Leveling
224
Differential leveling is a precise method in surveying used to determine the elevation difference between two points. Its primary goal is to establish accurate vertical measurements to create level surfaces or grade lines critical for designing and constructing infrastructures such as roads, bridges, and buildings.The procedure for differential leveling begins with setting up and leveling the instrument at a point where the benchmark can be seen. The level rod is held on the benchmark (BM), and...
224


