scholarly journals Boltzmann Entropy for the Spatial Information of Raster Data

2019 ◽  
Vol 1 ◽  
pp. 1-1 ◽  
Author(s):  
Peichao Gao ◽  
Hong Zhang ◽  
Zhilin Li
Keyword(s):  
Boltzmann Equation ◽  
Information Content ◽  
Shannon Entropy ◽  
Spatial Data ◽  
Spatial Information ◽  
Statistical Information ◽  
Boltzmann Entropy ◽  
Raster Data ◽  
Data Set ◽  
The Boltzmann Equation

<p><strong>Abstract.</strong> Entropy is an important concept that originated in thermodynamics. It is the subject of the famous Second Law of Thermodynamics, which states that “the entropy of a closed system increases continuously and irrevocably toward a maximum” (Huettner 1976, 102) or “the disorder in the universe always increases” (Framer and Cook 2013, 21). Accordingly, it has been widely regarded as an ideal measure of disorder. Its computation can be theoretically performed according to the Boltzmann equation, which was proposed by the Austrian physicist Ludwig Boltzmann in 1872. In practice, however, the Boltzmann equation involves two problems that are difficult to solve, that is the definition of the macrostate of a system and the determination of the number of possible microstates in the microstate. As noted by the American sociologist Kenneth Bailey, “when the notion of entropy is extended beyond physics, researchers may not be certain how to specify and measure the macrostate/microstate relations” (Bailey 2009, 151). As a result, this entropy (also referred to as Boltzmann entropy and thermodynamic entropy) has remained largely at a conceptual level.</p><p> In practice, the widely used entropy is actually proposed by the American mathematician, electrical engineer, and cryptographer Claude Elwood Shannon in 1948, hence the term Shannon entropy. Shannon entropy was proposed to quantify the statistical disorder of telegraph messages in the area of communications. The quantification result was interpreted as the information content of a telegraph message, hence also the term information entropy. This entropy has served as the cornerstone of information theory and was introduced to various fields including chemistry, biology, and geography. It has been widely utilized to quantify the information content of geographic data (or spatial data) in either a vector format (i.e., vector data) or a raster format (i.e., raster data). However, only the statistical information of spatial data can be quantified by using Shannon entropy. The spatial information is ignored by Shannon entropy; for example, a grey image and its corresponding error image share the same Shannon entropy.</p><p> Therefore, considerable efforts have been made to improve the suitability of Shannon entropy for spatial data, and a number of improved Shannon entropies have been put forward. Rather than further improving Shannon entropy, this study introduces a novel strategy, namely shifting back from Shannon entropy to Boltzmann entropy. There are two advantages of employing Boltzmann entropy. First, as previously mentioned, Boltzmann entropy is the ideal, standard measure of disorder or information. It is theoretically capable of quantifying not only the statistical information but also the spatial information of a data set. Second, Boltzmann entropy can serve as the bridge between spatial patterns and thermodynamic interpretations. In this sense, the Boltzmann entropy of spatial data may have wider applications. In this study, Boltzmann entropy is employed to quantify the spatial information of raster data, such as images, raster maps, digital elevation models, landscape mosaics, and landscape gradients. To this end, the macrostate of raster data is defined, and the number of all possible microstates in the macrostate is determined. To demonstrate the usefulness of Boltzmann entropy, it is applied to satellite remote sensing image processing, and a comparison is made between its performance and that of Shannon entropy.</p>

scholarly journals Improvements to Information Entropy for Raster Spatial Data: A Thermodynamic-based Evaluation

2019 ◽  
Vol 1 ◽  
pp. 1-1
Author(s):  
Hong Zhang ◽  
Peichao Gao ◽  
Zhilin Li
Keyword(s):  
Information Theory ◽  
Information Content ◽  
Information Entropy ◽  
Spatial Data ◽  
Spatial Information ◽  
Comprehensive Evaluation ◽  
Statistical Information ◽  
Late 20Th Century ◽  
Spatial Datasets ◽  
Spatial Dataset

<p><strong>Abstract.</strong> Spatial information is fundamentally important to our daily life. It has been estimated by many scholars that almost 80 percent or more of all information in this world are spatially referenced and can be regarded as spatial information. Given such importance, a discipline called spatial information theory has been formed since the late 20th century. In addition, international conferences on spatial information have been frequently held. For example, COSIT (Conference on Spatial Information Theory) was established in 1993 and are held every two years all over the world.</p><p>In spatial information theory, one fundamental question is how to measure the amount of information (i.e., information content) of a spatial dataset. A widely used method is to employ entropy, which is proposed by the American mathematician Claude Shannon in 1948 and usually referred to as Shannon entropy or information entropy. This information entropy was originally designed to measure the statistical information content of a telegraph message. However, a spatial dataset such as a map or a remote sensing image contains not only statistical information but also spatial information, which cannot be measured by using the information entropy.</p><p>As a consequence, considerable efforts have been made to improve the information entropy for spatial datasets in either a vector format of a raster format. There are two basic lines of thought. The first is to improve the information entropy by defining how to calculate its probability parameters, and the other is to introduce new parameters into the formula of the information entropy. The former results in a number of improved information entropies, while the latter leads to a series of variants of the information entropy. Both seem to be capable of distinguishing different spatial datasets, but there is a lack of comprehensive evaluation of their performance in measuring spatial information.</p><p>This study first presents a state-of-the-art review of the improvements to the information entropy for the information content of spatial datasets in a raster format (i.e., raster spatial data, such as a grey image and a digital elevation model). Then, it presents a comprehensive evaluation of the resultant measures (either improved information entropies or variants of the information entropy) according to the Second Law of Thermodynamics. A set of evaluation criteria were proposed, as well as corresponding measures. All resultant measures were ranked accordingly.</p><p>The results reported in this study should be useful for entropic spatial data analysis. For example, in image fusion, a crucial question is how to evaluate the performance of a fusion algorithm. This evaluation is usually achieved by using the information entropy to measure the increase in the information content during the fusion. It can now be performed by the best-improved information entropy reported in this study.</p>

scholarly journals A Head/Tail Breaks-Based Method for Efficiently Estimating the Absolute Boltzmann Entropy of Numerical Raster Data

2020 ◽  
Vol 9 (2) ◽  
pp. 103 ◽  
Author(s):  
Hong Zhang ◽  
Zhiwei Wu
Keyword(s):  
Shannon Entropy ◽  
Spatial Data ◽  
Computation Time ◽  
Original Method ◽  
Efficient Computation ◽  
Boltzmann Entropy ◽  
Raster Data ◽  
Digital Elevation ◽  
The Absolute ◽  
Heavy Tailed

Shannon entropy is the most popular method for quantifying information in a system. However, Shannon entropy is considered incapable of quantifying spatial data, such as raster data, hence it has not been applied to such datasets. Recently, a method for calculating the Boltzmann entropy of numerical raster data was proposed, but it is not efficient as it involves a series of numerical processes. We aimed to improve the computational efficiency of this method by borrowing the idea of head and tail breaks. This paper relaxed the condition of head and tail breaks and classified data with a heavy-tailed distribution. The average of the data values in a given class was regarded as its representative value, and this was substituted into a linear function to obtain the full expression of the relationship between classification level and Boltzmann entropy. The function was used to estimate the absolute Boltzmann entropy of the data. Our experimental results show that the proposed method is both practical and efficient; computation time was reduced to about 1% of the original method when dealing with eight 600 × 600 pixel digital elevation models.

INFORMATION THEORY OF CARTOGRAPHY: A FRAMEWORK FOR ENTROPY-BASED CARTOGRAPHIC COMMUNICATION THEORY

2020 ◽  
Vol XLIII-B4-2020 ◽  
pp. 11-16
Author(s):  
Z. Li
Keyword(s):  
Information Theory ◽  
Communication Theory ◽  
Spatial Information ◽  
Digital Communication ◽  
Spatial Configuration ◽  
Statistical Information ◽  
Fundamental Theory ◽  
Boltzmann Entropy ◽  
Spatial Objects ◽  
Thematic Information

Abstract. Map is an effective communication means. It carries and transmits spatial information about spatial objects and phenomena, from map makers to map users. Therefore, cartography can be regarded as a communication system. Efforts has been made on the application of Shannon Information theory developed in digital communication to cartography to establish an information theory of cartography, or simply cartographic information theory (or map information theory). There was a boom during the period from later 1960s to early 1980s. Since later 1980s, researcher have almost given up the dream of establishing the information theory of cartography because they met a bottleneck problem. That is, Shannon entropy is only able to characterize the statistical information of map symbols but not capable of characterizing the spatial configuration (patterns) of map symbols. Fortunately, break-through has been made, i.e. the building of entropy models for metric and thematic information as well as a feasible computational model for Boltzmann entropy. This paper will review the evolutional processes, examine the bottleneck problems and the solutions, and finally propose a framework for the information theory of cartography. It is expected that such a theory will become the most fundamental theory of cartography in the big data era.

A seismic to simulation unconventional workflow using automated fault-detection attributes

2017 ◽  
Vol 5 (3) ◽  
pp. SJ41-SJ48 ◽  
Author(s):  
Jesse Lomask ◽  
Luisalic Hernandez ◽  
Veronica Liceras ◽  
Amit Kumar ◽  
Anna Khadeeva
Keyword(s):  
Seismic Data ◽  
Spatial Information ◽  
Spatial Location ◽  
Statistical Information ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Data Set ◽  
Fault Indicator ◽  
Well Data ◽  
Additional Constraints

Natural fracture networks (NFNs) are used in unconventional reservoir simulators to model pressure and saturation changes in fractured rocks. These fracture networks are often derived from well data or well data combined with a variety of seismic-derived attributes to provide spatial information away from the wells. In cases in which there is a correlation between faults and fractures, the use of a fault indicator can provide additional constraints on the spatial location of the natural fractures. We use a fault attribute based on fault-oriented semblance as a secondary conditioner for the generation of NFNs. In addition, the distribution of automatically extracted faults from the fault-oriented semblance is used to augment the well-derived statistics for natural fracture generation. Without the benefit of this automated fault-extraction solution, to manually extract the fault-statistical information from the seismic data would be prohibitively tedious and time consuming. Finally, we determine, on a 3D field unconventional data set, that the use of fault-oriented semblance results in simulations that are significantly more geologically reasonable.

scholarly journals Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 381 ◽  
Author(s):  
Hong Zhang ◽  
Zhiwei Wu ◽  
Tian Lan ◽  
Yanyu Chen ◽  
Peichao Gao
Keyword(s):  
Spatial Data ◽  
Software Tool ◽  
Data File ◽  
Landscape Patterns ◽  
Wasserstein Metric ◽  
Boltzmann Entropy ◽  
Landscape Mosaic ◽  
Numerical Work ◽  
Data Set ◽  
User Friendly

Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human–computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient.

On Searching for the Most Informative Spatial Pattern

1978 ◽  
Vol 10 (7) ◽  
pp. 747-779 ◽  
Author(s):  
M Batty ◽  
R Sammons
Keyword(s):  
Los Angeles ◽  
Shannon Entropy ◽  
Spatial Data ◽  
Simple Algorithm ◽  
Information Measure ◽  
Data Set ◽  
Maximum Information ◽  
Equal Area ◽  
The Best Approximation ◽  
Spatial Analyst

This paper is concerned with an inquiry into the way in which the organisation of a spatial data set affects the interpretation of the spatial phenomena which it records, in terms of its underlying pattern or density. It is argued that the number and configuration of zones affects the level of information which is imparted to the spatial analyst, and thus the quest becomes one in which the data set is to be reorganised spatially to impart maximum information. The paper sets out to define an appropriate measure of information and an algorithm designed to optimise its value. The information measure developed is in essence a modified Shannon entropy, modified to account for uneven zonal configurations and converging to Shannon entropy when the zoning system is equal-area and the distribution the best approximation to the density. The measure has some well-known aggregation properties which are presented and several interpretations of its form in spatial terms are made. Empirical measurements of this information measure on the distribution of population in seven metropolitan areas indicate that by aggregation of zones to equal areas, increases in information might be possible and a clearer picture of the underlying density perceived. Accordingly a simple algorithm embodying an heuristic to optimise towards the equal-area norm is developed and applied to the Los Angeles region. The results, in fact, indicate that information cannot be improved in this case, and this leads to a reexamination of the nature of the problem and to suggestions for further research.

scholarly journals FEASIBILITY OF INTEGRATED TRANSPORT NETWORK MODEL IN LITHUANIA

Transport ◽  
2014 ◽  
Vol 29 (4) ◽  
pp. 346-354 ◽  
Author(s):  
Lina Papšienė ◽  
Andrius Balčiūnas ◽  
Giedrė Beconytė ◽  
Danas Motiejauskas ◽  
Denis Romanovas ◽  
...  
Keyword(s):  
Spatial Data ◽  
Data Model ◽  
Emergency Services ◽  
Spatial Information ◽  
Cost Benefit ◽  
Transport Network ◽  
Guidance Document ◽  
Transport Networks ◽  
Data Set ◽  
Integrated Transport Network

Availability of up-to-date and detailed spatial data on transport networks is very important for sustainable development. As Directive 2007/2/EC of 14 March 2007 establishing an Infrastructure for Spatial Information in the European Community (INSPIRE) targets transport networks data as one of the first priority data themes to be harmonized across Europe, the specification for transport network dataset has been developed and adopted as guidance document for all Member States. The specification provides a common model for road, rail, air, water and cable transport networks and related infrastructure. Integrated transport network database can be used for routing of vehicles, taking into account all limitations of the road network, for transport planning, emergency services. In order to achieve the benefits related to common use of up-to-date information and to interoperable data for these tasks, all transport network elements must be accurately mapped in a consistent logical network. Unfortunately, in Lithuania there is no single continuous and extensive spatial data set (geographic database) of transport networks. The authors analysed the possibilities of building joint INSPIRE databases from different transport datasets, and indicated the best data sources for road and railway transport, as well as actions of improvement have to be taken. The research and successful experiment has showed that the more extensive INSPIRE transport data model can be implemented using ArcGIS data model. This concept and the model will serve as an important prop for development of policy of national and transboundary spatial data integration in countries with similar situation. INSPIRE implementation guidelines are compatible with national interest and must be followed, but technical feasibility and cost-benefit considerations must be taken into account.

DARCY RIBEIRO UNIVERSITY CAMPUS MAP – 2017- TECHNICAL NOTE

2018 ◽  
Vol 7 (2) ◽  
Author(s):  
Rafael Sanzio Araújo dos Anjos ◽  
Jose Leandro de Araujo Conceição ◽  
Jõao Emanuel ◽  
Matheus Nunes
Keyword(s):  
Spatial Data ◽  
Spatial Information ◽  
Technical Note ◽  
University Campus ◽  
Communication Tool ◽  
Sources Of Information ◽  
Data Manipulation ◽  
Geographic Space ◽  
The Many ◽  
New Generation

The spatial information regarding the use of territory is one of the many strategies used to answer and to inform about what happened, what is happening and what may happen in geographic space. Therefore, the mapping of land use as a communication tool for the spatial data made significant progress in improving sources of information, especially over the last few decades, with new generation remote sensing products for data manipulation.

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