Waldo Tobler | University of California, Santa Barbara (original) (raw)
Papers by Waldo Tobler
Theories of Mapping Practice and Cartographic Representation, 2011
Theories of Mapping Practice and Cartographic Representation, 2011
... Muehrcke, P. "Population Slope Maps," Unpub... more ... Muehrcke, P. "Population Slope Maps," Unpublished MA thesis, Department of Geography, University of Michigan, 1966. ... H. "On the Interpretation of State Vectors and Local Transformation Oper-ators," Colloquium on Simulation, Univer-sity of Kansas Computer Contribution 22 ...
Journal of the American Statistical Association, 1979
Census enumerations are usually packaged in irregularly shaped geographical regions. Interior val... more Census enumerations are usually packaged in irregularly shaped geographical regions. Interior values can be interpolated for such regions, without specification of "control points," by using an analogy to elliptical partial differential equations. A solution pro- cedure is suggested, ...
International journal of population geography : IJPG, 1997
We report on a project that converted subnational population data to a raster of cells on the ear... more We report on a project that converted subnational population data to a raster of cells on the earth. We note that studies using satellites as collection devices yield results indexed by latitude and longitude. Thus it makes sense to assemble the terrestrial arrangement of people in a compatible manner. This alternative is explored here, using latitude/longitude quadrilaterals as bins for population information. This format also has considerable advantages for analytical studies. Ways of achieving the objective include, among others, simple centroid sorts, interpolation, or gridding of polygons. The results to date of putting world boundary coordinates together with estimates of the number of people are described. The estimated 1994 population of 219 countries, subdivided into 19,032 polygons, has been assigned to over six million five minute by five minute quadrilaterals covering the world. These results are available over the Internet. The grid extends from latitude 57°S to 72°N, and covers 360° of longitude. Just under 31% of the (1548 by 4320) grid cells are populated. The number of people in these countries is estimated to be 5.6 billion, spread over 132 million km 2 of land. Extensions needed include continuous updating, additional social variables, improved interpolation methods, correlation with global change studies, and more detailed information for some parts of the world.
program to demonstrate this, with five commodities, including strawberries, wheat, otherfoodstuff... more program to demonstrate this, with five commodities, including strawberries, wheat, otherfoodstuffs, and Cadillacs. Given the other inputs I could demonstrate computer printouts of circularly arranged optimalland uses, and could even run the program with multiple market places to get mixtures of partially concentric patterns,and could include a climatic gradient to get non-circular patterns. All this was done off-line, in a
Different image processing techniques have been tested and compared on data derived from gamma-an... more Different image processing techniques have been tested and compared on data derived from gamma-angiography images to detect the boundary of the left ventricle. The method involves a preprocessing step, followed by the edge detection itself. The best preprocessing is a nonlinear "variant" filtering, where each pixel is replaced by the average of the 3 X 3 neighborhood having the smallest variance. The edge detector giving the best contour is a Sobel operator. A second-order high-pass Butterworth filter also provides a good segmentation.
It is important that cartographers, and others who use geographic information, understand the pro... more It is important that cartographers, and others who use geographic information, understand the procedures used to adjust empirical measurements made for the purpose of specifying locations. Two new graphical interpretations of reconciling distance or directional observations are presented in this paper. These graphics are consistent with standard practice, but treat the problems in a somewhat more general, non—mathematical manner, facilitating understanding. An example is given using driving distances to obtain a map configuration for points in the United States. Land surveying consists of geometric measurements made on the surface of the earth. Since it is known that all measurements are, to some extent, wrong, it is appropriate that surveying errors should be recognized explicitly. When this is done, it is possible to attempt to compensate for these — unavoidable — measurement errors. The process of compensation is known as survey adjustment. From a pedagogical point of view, it is...
Urban Geography, 1995
It is now over one hundred years since Ravenstein published his "Laws of Migration". How have the... more It is now over one hundred years since Ravenstein published his "Laws of Migration". How have these laws fared? His paper also includes a map of "Currents of Migration", not mentioned in the text. Thornthwaite also compared migration to currents, but did not follow through with this analogy. Others have used similar terminology. More recent migration studies may yield new laws.
Transportation Research Part A: General, 1985
A geographically continuous movement model can be deduced from the quadraw transshipment problem ... more A geographically continuous movement model can be deduced from the quadraw transshipment problem by consldermg the transportation network. as a &Crete mesh The resultmg system of coupled Helmholz equations can be consIdered to solve simultaneously the spanally contmuous vewons of the traffic "chstnbut~on" and "awgnment" problems The associated Lagran~lan funcnons are smnlar to the potentials of clawcal flow theory Numerical methods Implement the procedure
The Canadian Geographer/Le Géographe canadien, 1963
The Professional Geographer, 1964
The Professional Geographer, 1957
Several other related studies were undertaken. Special attention was given to certain methodologi... more Several other related studies were undertaken. Special attention was given to certain methodological problems including statistical anaIyses of the accuracy of the photographically collected data.' In this part of the work it was discovered that the discrepancies in the photographic observations were distributed non-randomly, a situation which provided the basis for constructing preliminary correction factors through knowledge of the nature, amount, and direction of the errors.
Papers in Regional Science, 2005
Papers in Regional Science, 2005
Papers of the Regional Science Association, 1969
Theories of Mapping Practice and Cartographic Representation, 2011
Theories of Mapping Practice and Cartographic Representation, 2011
... Muehrcke, P. "Population Slope Maps," Unpub... more ... Muehrcke, P. "Population Slope Maps," Unpublished MA thesis, Department of Geography, University of Michigan, 1966. ... H. "On the Interpretation of State Vectors and Local Transformation Oper-ators," Colloquium on Simulation, Univer-sity of Kansas Computer Contribution 22 ...
Journal of the American Statistical Association, 1979
Census enumerations are usually packaged in irregularly shaped geographical regions. Interior val... more Census enumerations are usually packaged in irregularly shaped geographical regions. Interior values can be interpolated for such regions, without specification of "control points," by using an analogy to elliptical partial differential equations. A solution pro- cedure is suggested, ...
International journal of population geography : IJPG, 1997
We report on a project that converted subnational population data to a raster of cells on the ear... more We report on a project that converted subnational population data to a raster of cells on the earth. We note that studies using satellites as collection devices yield results indexed by latitude and longitude. Thus it makes sense to assemble the terrestrial arrangement of people in a compatible manner. This alternative is explored here, using latitude/longitude quadrilaterals as bins for population information. This format also has considerable advantages for analytical studies. Ways of achieving the objective include, among others, simple centroid sorts, interpolation, or gridding of polygons. The results to date of putting world boundary coordinates together with estimates of the number of people are described. The estimated 1994 population of 219 countries, subdivided into 19,032 polygons, has been assigned to over six million five minute by five minute quadrilaterals covering the world. These results are available over the Internet. The grid extends from latitude 57°S to 72°N, and covers 360° of longitude. Just under 31% of the (1548 by 4320) grid cells are populated. The number of people in these countries is estimated to be 5.6 billion, spread over 132 million km 2 of land. Extensions needed include continuous updating, additional social variables, improved interpolation methods, correlation with global change studies, and more detailed information for some parts of the world.
program to demonstrate this, with five commodities, including strawberries, wheat, otherfoodstuff... more program to demonstrate this, with five commodities, including strawberries, wheat, otherfoodstuffs, and Cadillacs. Given the other inputs I could demonstrate computer printouts of circularly arranged optimalland uses, and could even run the program with multiple market places to get mixtures of partially concentric patterns,and could include a climatic gradient to get non-circular patterns. All this was done off-line, in a
Different image processing techniques have been tested and compared on data derived from gamma-an... more Different image processing techniques have been tested and compared on data derived from gamma-angiography images to detect the boundary of the left ventricle. The method involves a preprocessing step, followed by the edge detection itself. The best preprocessing is a nonlinear "variant" filtering, where each pixel is replaced by the average of the 3 X 3 neighborhood having the smallest variance. The edge detector giving the best contour is a Sobel operator. A second-order high-pass Butterworth filter also provides a good segmentation.
It is important that cartographers, and others who use geographic information, understand the pro... more It is important that cartographers, and others who use geographic information, understand the procedures used to adjust empirical measurements made for the purpose of specifying locations. Two new graphical interpretations of reconciling distance or directional observations are presented in this paper. These graphics are consistent with standard practice, but treat the problems in a somewhat more general, non—mathematical manner, facilitating understanding. An example is given using driving distances to obtain a map configuration for points in the United States. Land surveying consists of geometric measurements made on the surface of the earth. Since it is known that all measurements are, to some extent, wrong, it is appropriate that surveying errors should be recognized explicitly. When this is done, it is possible to attempt to compensate for these — unavoidable — measurement errors. The process of compensation is known as survey adjustment. From a pedagogical point of view, it is...
Urban Geography, 1995
It is now over one hundred years since Ravenstein published his "Laws of Migration". How have the... more It is now over one hundred years since Ravenstein published his "Laws of Migration". How have these laws fared? His paper also includes a map of "Currents of Migration", not mentioned in the text. Thornthwaite also compared migration to currents, but did not follow through with this analogy. Others have used similar terminology. More recent migration studies may yield new laws.
Transportation Research Part A: General, 1985
A geographically continuous movement model can be deduced from the quadraw transshipment problem ... more A geographically continuous movement model can be deduced from the quadraw transshipment problem by consldermg the transportation network. as a &Crete mesh The resultmg system of coupled Helmholz equations can be consIdered to solve simultaneously the spanally contmuous vewons of the traffic "chstnbut~on" and "awgnment" problems The associated Lagran~lan funcnons are smnlar to the potentials of clawcal flow theory Numerical methods Implement the procedure
The Canadian Geographer/Le Géographe canadien, 1963
The Professional Geographer, 1964
The Professional Geographer, 1957
Several other related studies were undertaken. Special attention was given to certain methodologi... more Several other related studies were undertaken. Special attention was given to certain methodological problems including statistical anaIyses of the accuracy of the photographically collected data.' In this part of the work it was discovered that the discrepancies in the photographic observations were distributed non-randomly, a situation which provided the basis for constructing preliminary correction factors through knowledge of the nature, amount, and direction of the errors.
Papers in Regional Science, 2005
Papers in Regional Science, 2005
Papers of the Regional Science Association, 1969