Encuadre constitucional del fenómeno religioso

In the past one had to rely on traditional methods of cartographic expressions for visualisation of uncertainty. Today, it is possible to work in an interactive and dy- namic visualisation environment that incorporates new methods, as those proposed here, alongside traditional methods. Traditional methods were mainly based on the theory of semiology of graphics of Bertin (1967). For example, MacEachren (1992) investigated the use of these graphic variables for uncertainty depiction, noting the crucial importance of logically coupling visual variables with data scale. Of the extended set of Bertin’s variables, MacEachren suggested colour saturation as the most logical for uncertainty visualisation. Wel et al. (1997) proposed four static visualisation variables for conveying the quantitative character of uncertainty in remotely sensed image classification using probability vectors of individual pixels. Those variables being: value (grey-scale maps), colour saturation (bivariate maps), colour hue (associative ranking maps) and a combination of the latter two variables (dichotomy maps). An example is the traffic light principle: red, orange and green convey to a user prohibition, alertness, and permission respectively. Hootsmans (1996) proposed colour lightness and saturation to visualise uncertain information derived from fuzzy sets. Hootsmans combined colour hue to depict thematic class information and colour saturation or lightness to visualise uncertainty in one static map.

Techniques as described above focused on the extraction of uncertainty infor- mation from a classification, either as a probability vector or a membership vector per pixel, and presentation of this information to a user. The probability or mem- bership vectors are summarised in a single uncertainty number, for example by computing the maximum membership or probability, confusion index or entropy from these vectors. These uncertainty values were then visualised with one of the techniques describe above, either as an uncertainty map or a thematic map combined with uncertainty information. These types of visualisations can help in communicating uncertainty in the final classification product, however, they do not allow for interaction with the classification.

Developments in computer graphic technology introduced dynamic visualisa- tion techniques in cartography. For example, animation techniques were imple- mented to improve interpretation of large amounts of data, as is the case in visu- alisation of (classification) uncertainty. MacEachren (1994) distinguished between different uses of temporal graphic variables: to animate maps and to depict dy- namic processes in time. Sequential display of different uncertainty maps and different thematic maps derived from the same image may make up an anima-

2.3. Uncertainty visualisation

tion. For example, probabilities can be visualised sequentially, according to their ranking, thereby enabling the representation of all probabilities underlying a clas- sification. This animation can follow different schemes, such as simply sequential, progressive, cyclic and back-and-forth. Fisher (1994) proposed duration as a vari- able to depict uncertainty: the higher the probability, the longer the period of time the class colour is displayed. Wel et al. (1997) proposed a method to toggle a thematic map and associated uncertainty map to result in a combined sensation of classes and uncertainty. Hootsmans (1996) used animation techniques to represent uncertainty related to fuzzy series analysis. A sequence of maps was generated by processing a fuzzy series for a set of alpha-cuts. Ehlschlaeger et al. (1997) described a technique of visualising uncertainty in elevation data using animation.

These dynamic visualisation techniques offered a more advanced and flexible solution to visualising uncertainty information. They provided insight into (per- pixel) uncertainty in the classification result by means of visualising the entire vec- tor of probabilities or memberships. Most, if not all, of the mentioned techniques focused on visualising uncertainty in the classification result and did not allow for interaction with the classification. Another disadvantage of these techniques is that visualisation and interpretation of uncertainty becomes difficult when there is a large number of classes.

An interactive visualisation environment might be required to be able to im- prove the exploration of a classification and related uncertainty. The choice of a specific visualisation technique also depends on the user group. For decision makers, visualisation of uncertainty in the form of static maps might be sufficient, however, a scientific expert needs more in order to be able to improve the clas- sification process. Geographic visualisation (geovisualisation or GVis) techniques might be helpful in this sense (MacEachren and Kraak, 2001). These techniques focus on exploration as opposed to presentation. Interactive visualisation tech- niques such as dynamically linked views (Dykes, 1997; MacEachren, 1994) and geographic brushing (Monmonier, 1989) are essential for exploration of geospa- tial information. A special issue of the International Journal of Geographical Information Science was devoted to visualisation for exploration of spatial data (Kraak and MacEachren, 1999). Several authors showed that geovisualisation tools with dynamically linked views facilitate exploratory analysis and ‘visual thinking’ (Andrienko and Andrienko, 1999; MacEachren et al., 1999). Therefore, uncertainty visualisation should not just present expert users with meta-information on data quality but should also enable them to explore uncertainty and its relation to the original data.

ploratory geovisualisation tools can help to improve the expert’s understanding of uncertainty in a classified image scene. They proposed a combination of static, dynamic and interactive visualisations for exploration of classification uncertainty. Again, dynamically linked views and brushing functionality played a key role in these prototypes. The focus of these tools is on visual exploration of uncertainty in a classification result using linked displays of the original image, a parallel co- ordinate plot, a 2D feature space plot, the classified image with thematic classes, the uncertainty image displaying an uncertainty summary statistic per pixel and animation of alternative classifications. These tools provided better insight into classification uncertainty, however, they do not allow for interaction with the pa- rameters of a classification algorithm. A user should be able to visually interact with a classification algorithm to improve their knowledge of the nature and effects of the algorithm. Improved understanding may contribute to a superior classifi- cation. A feature space plot, dynamically linked with an image display and the classification result, may provide the best technique to visualise a classification. A user should be able to adapt the reference class clusters in a feature space plot to change the parameters of a fuzzy classification algorithm. Visual interaction with these parameters can help to gain insight into the origin and effect of uncer- tainty in a classification. Another advantage is that it can help to fine-tune the classification result.