Breaking Out of Cell Prison: Aggregate Cell Constructs


Micha Pazner, Associate Professor

Department of Geography

The University of Western Ontario


June 1, 1998


This paper describes current work on Aggregate Pixel Constructs and their multivariate data modeling applications for researching bodies of information. The basic problem is envisioning large multivariate datasets in the context of what has been referred to as Ńthe interface of the display with the userń by NATO IST-13/TG-002 Visualization for Massive Military Datasets.

Local Table Maps (LTM) are a specific example of an aggregate cell construct. Local Tables Maps are image-based representations created using a multi-cell block. In the example, embeddded in each 4x4 =16 cell block are six cell tiles representing a micro 'table' that holds a value for one of six variables. Each variable cell can have only one of the following "Traffic Light" hues: Red, Yellow, Green. Gray is used to turn a variable's traffic light "OFF" in a visual sense. Keeping the data values for each variable in separate numeric ranges permits the individual variation of thresholding of hues. This means that each variable 'traffic light' can be tuned differently, and that this tuning can be easily adjusted. The alerting Red hue is generally used to flag extreme or high values.

Local Table Maps allow us to map and record the interrelation of several carto/graphic variables, on a single image, at each location, for a very large number of locations (e.g. millions of pixels), with minimal loss of information, and fairly economically. Local Table Maps can be overlayed on conventional map and or graph elements such as points, lines, areas, or surfaces. Therefore, a hybrid Map-Table construct is further mixed in with additional graphic elements, allowing for more a contextual, information rich, and visually diverse multivariate information display.

The case for cell aggregate constructs is made based on the severe limitations to using the single pixel ¸ which can only represent information using a single graphic element: tone or color. Moving away from the single cell to cell aggregates enables the deployment of visual variables such as: color, length, width, orientation, shape, size, pattern and texture can be designed and implemented for optimal visualization impact (Buttenfield, 1993) (Bertin, 1983). Aggregate pixel designs have a special ability to take into account the classic elements of photointerpretation. Therefore the aggregate-cell-map maker has control over designing elements of interpretation (Avery and Berlin, 1992). We are not only able to interpret a given external representation, but are also better able to design, generate, and manipulate the external representation. Tufte (1990) stresses in his book: ŃEscaping (this) flatland is the essential task of envisioning information...ń Should we not seek to break out of the prison cell in our quest to escape flatland? Current image processing program have brought single cell image processing to the desktop. The case is made here for the need and utility of multi-cell pattern processing software facilities in future generations of image processing software. This would allow users to make and read images containing multi-celled constructs.

This study uses a raster (image based) geographic information system (GIS) to create and manipulate the aggregate cell patterns (Tomlin, 1990) (Pazner, 1995). The procedure for creating multi-cell constructs is based on a unique spatial/neighborhood overlay approach. In these image-maps the basic assumption of each cell representing a single location is relaxed to permit multiple cells per original location. Every cell is transformed in the local table map into a patterned matrix of output cells¸the multi-cell block. The key step in the procedure is a GIS model that generates an internal block addressing system. The addressing system is created using spatial, arithmetic and logic operations. For example, in the case of creating the LTM, a dual periodicity relative deviation model is used. The whole procedure, including the internal addressing model, is stored as a script ("macro") in the software used, which in this case is a raster GIS for desktop computers (PC and Macintosh) made by ThinkSpace Inc. and called Map­Factory. Most, if not all of the capabilities needed to create aggregate cell constructs exist in other similar systems such as Idrisi (Clark University, MA).

How can aggregate cell constructs, such as local table maps, be used? The interpretation of aggregate cell maps involves explicit comparison of the inter-relation of variables mapped deliberately for co-examination. The resultant maps reveal macro interaction patterns, while retaining in a zoomed-in micro view, full and easily visualized hue and numeric information for every variable at each location. Consequently, aggregate cell constructs can be used effectively for co-visualizing multivariate interrelation. Local table maps represent an interesting cross between a modern pixel-based image and a map composed of cartographic ╬table symbolsÔ with a legend key. The potential exists to reap the advantages of interpreting image data while reading simple cartographic table symbols. In reading a local table map, there is an emphasis on comparing between the variables that are depicted on the map. This is an exercise in interpreting isolated-and-joined elements that is different from the interpretation of normal imagery. Our LTM shows from 6 to 9 variables: 6 micro tabulated variables: elevation, steepness, orientation, drainage, impervious, and soil. In addition, areas of hydrology and vegetation are depicted as conventional themes and the terrain is shown using shaded relief.

Aggregate cell constructs, even when made using a GIS, are applicable not only to maps, but also to graphs. Graphing applications come under the rubric of Spatialization using GIS. The term Spatialization refers to the spatial representation and processing of non-spatial information such as numeric arrays, tables, graphs, text, etc. The term GRASP (GRaph and Array Spatial Processing) was coined and is used by Pazner for raster GIS based spatialization applications. Selected references on Spatialization and GRASP include: (Kuhn, 1996) (Malczewski et al., 1997), (Pazner, 1994), (Scott and Pazner, 1992) and (Skupin and Buttenfield, 1997). Examples of Spatialization/GRASP work include:

1. Multiple Comparative Overlays (by Anderson et al. , 1998)

2. Graphic Timetables (Scott and Pazner, 1992)

3. GIS modeling of Color Model Spaces (Pazner, 1998)

4. Line Graphs: Transect Profiles (Ripley and Pazner, 1998)

5. Scatterplot Modeling (Pazner and Liu, 1992)


Concluding Comments

The aggregate cell model is unique in that it approaches the map overlay problem in a non-standard way; that is based on changing the cell resolution and uses multi-cell constructs, to achieve a spatial neighborhood based overlay, in which micro graphical tables, icon elements, and conventional themes (0D-3D) can be placed.

Possible applications for Local Table Maps includes work that involves learning about information: coincidence, context, conditions, comparison, interrelation, interaction, anomalies, change detection, classification, hypotheses generation, explanation, causality, and location. One type of application that appears particularly suitable is Exploratory Data Visualization (EDV). Where "Data" can be: Variables, Criteria, Indices, Gradients, Error, Uncertainty, etc. The data may be spatially distributed or Ńspatializedń (ie. non spatial data).

With proper variable selection, graphic design, and colorization Local Table Maps that have substantial information content and aesthetic appeal can be created. Local Table Maps represent an interesting table/map (in image fromat) hybrid information representation whose implementation can additionally mix in conventional, 3D, and icon pattern map constructs. The two research thrusts: Aggregate Cell Constructs and Spatialization represent the continuing evolution of research areas the author has been active in for most of this decade.



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Malczewski J., M. Pazner, M. Zaliwska (1997)., Visualization of Multicriteria Location Analysis Using Raster GIS: A Case Study, Cartography and Geographic Information Systems, pp. 80-90, Vol. 24, No. 2, Journal of American Congress of Surveying and Mapping, April 1997.

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Pazner, M. and W. Liu, Image Processing of Graphs Using GIS Functions and Procedures, in Proceedings GIS/LIS ╬92, pp. 636-645, San Jose, Ca.: AAG, ACSM, AM/FM International, ASPRS, URISA. November 10-12 1992.

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Research in aggregate cell constructs and spatialization was actively supported and funded in 1996-1997 by the US NSF through the National Center for Geographic Information and Analysis (NCGIA) at the University of California Santa Barbara. NATO's IST-13/TG-002 N/X Network of Experts on Visualization for Massive Military Datasets has provided an ongoing framework for conducting this research. This study is being conducted in collaboration with the Graduate School of Design at Harvard Unversity.


List of Illustrations

­ Figure 1 Local Table Map

­ Figure 2 Local Table Map Key

­ Figures 3 and 4: Small Multiples Input. One page shows the inputs in LTM color format. The second page shows these inputs colored individually using a variety of color schemes.

­ Figures 5, 6, 7: Local Table Map and the Environment. A 3-page spread of an LTM that is 'draped' over shaded relief, along with the water bodies.. The first page shows the whole map. The middle page reveals more detail in a zoomed-in subsection. The third page zooms in even further and provides the Key to the maps.

­ Figure 8: Local Table Map for Vegetated Areas.


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