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This presentation discusses the regional changes quantitatively in the 200 years through the overlay analysis of the present map and the INŌ’s map made by Tadataka INO in 1821 (Figure 1). INO surveyed the coastline and major roads on foot. He investigated not only survey lines, but also various geographic information such as rivers, lakes, mountains, village names, castles, temples, administrative boundaries, etc. Visualizing all of the 214 sheets of the INŌ’s large-scale map with Geographic Information Systems (GIS), we can analyse the national land condition seamlessly at the end of the Edo era.Methodological point of view, we have serious problems including the scale, projection, identification of geographic features and so on, when we compare the old map with the present. In this connection, digitalizing the INŌ’s map as the GIS data is very useful to examine the spatial transformation scientifically during the 200 years. The digital INŌ’s map was constructed by employing the geo-reference function of GIS with the triangulation method. The survey line was converted into the line feature of vector data, and the place names were converted into the point feature of raster data. The distance of the survey line was measured by GIS-based geometric operation.We obtained the following findings. The distributions of villages, ports, and facilities in western Japan were denser than those in eastern Japan in the 19th century. This was caused not only by the difference in natural environment and landform but also by socioeconomic factors including the locations of the castle towns and industrial activities. The regional structure has been dramatically transformed by the modernization of the political system, transportation system, and industrial development in reclaimed areas (Figure 2). It is concluded that most parts of changes in regional characteristics have been attained by overcoming the natural constraints. However, the difference in the political system has also been influential to the formation of the present regional system.

Compared with regular quadrilateral grid, regular hexagonal grid is isotropy and has higher cell compactness and sampling density. This gives regular hexagonal grid advantages in visual display, spatial analysis, and many other aspects. However, the studies of raster data mainly focus on regular quadrilateral grid, and various encoding methods are also focused on it. The researches on hexagonal raster data are relatively insufficient.In this paper, encoding and compression for regular hexagonal grid are studied. By introducing Gosper curve which has good spatial aggregation and takes into account the morphological structure of regular hexagonal grid, the bidirectional correlation between Gosper curve and regular hexagonal grid is established. Then, a new encoding framework is built to determine the Gosper coding of each grid unit. The lossless compression is completed by performing run-length coding on adjacent coding sets in the target region.

Cost distance is one of the fundamental functions in geographic information systems (GIS), which has been used in various applications such as route planning, construction of Thiessen polygons and distance weighted interpolation. Conventional 2D cost distance function, due to its limited movement directions (either 4 or 8 neighbourhood cells) in the raster data model, overestimates the least cost and the problem is especially severe with a homogeneous friction surface. 3D cost distance function removes the limitation that movement must occur on a planar surface. It can therefore take into account tunnels and bridges when calculating least cost paths. In addition, it can also be used in many other application domains which deal with 3D geospatial data such as in atmospheric science, geology, and oceanography. Based on the method in Tomlin (2010), which can completely eliminate the overestimation when traveling on a homogeneous friction surface, this research proposes an algorithm that calculates accurate least cost with both homogeneous and heterogeneous friction in 3D space. When extending the cost distance function from 2D to 3D, the number of voxels in the propagation front increases significantly and efficiency is an imperative issue. This research also improves the computational efficiency by developing a data structure that combines a binary heap and a hash table. Our results show that the proposed algorithm can calculate accurate 3D cost distance in a homogeneous friction space, and the proposed data structure (i.e., heap plus hash table) not only significantly reduces the algorithm’s runtime but also benefits more in 3D than in 2D. In addition, we have applied the method in a 3D drone delivery routing application in a city environment (Figure 1). Additional applications, such as calculating groundwater flow paths of least hydraulic resistance in a heterogeneous 3D hydraulic conductivity field, are currently under development.

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.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.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.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.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.