Uncertainty in Remote Sensing

Introduction

The goal of remote sensing is to infer information about objects from measurements made from a remote location, frequently from space. The inference process is always less than perfect and thus there is an element of uncertainty regarding the results produced using remote sensing. When viewed from this perspective, the problem of uncertainty is central to remote sensing. However, the topic of uncertainty in remote sensing gets a relatively modest amount of attention. The reasons for this can be debated, but it is somewhat natural for people involved with remote sensing to focus on what can be done well with remote sensing rather than what cannot be done well. However, as a matter of the natural growth and maturity of the field of remote sensing, it is essential that the topic of uncertainty begins to demand more attention. The recent conference devoted to questions of uncertainty in remote sensing and GIS that formed the foundation for this topic was a good start toward raising awareness of the importance of uncertainty in remote sensing. This topic is devoted to outlining some of the issues related to uncertainty in remote sensing. As such, this topic is more about raising questions than attempting to answer them. Thehopeis that by making the issues more explicit, future work in remote sensing will devote more attention to uncertainty.

To start this discussion, consider as an example the following question, which is typical of the kind frequently asked by people in remote sensing:


Is it possible to map agricultural lands using remote sensing?


Of course, it is possible to make a map of agricultural lands using remote sensing. However, that is not really what is being asked. What is being asked is whether or not remote sensing can be used to provide someone with the information about agricultural lands they desire with suitable precision and at a level of accuracy which makes the map useful for their purposes. As such, this kind of question is inherently about uncertainty! As a result, answering such a question requires considerable clarification, careful qualification and the ability to make judgements about uncertainty. One reason it is difficult to answer such a question is that there are many dimensions to the remote sensing problem that contribute to the resulting uncertainty in a derived map. First, what kind of information about the agricultural area is desired and at what spatial scale? Is it enough to identify which areas are cultivated, or is more detailed information required about which crops are present in the individual fields, or the stage of crop development, or the moisture status of the crop, or any of many other characteristics of agricultural environments of interest. For thematic maps, as the categorical detail in the map (or the precision of the map) increases, the accuracy of the map typically decreases (or the uncertainty increases). While this general relationship is well known, the rate of decrease associated with increasing categorical detail is typically not well known.

A second factor concerns the nature and quality of the inputs used in the mapping process. In this context, both the remote sensing imagery to be used as well as other kinds of data, such as field data or laboratory spectra are important and might influence the ability to derive the desired information. As the quality of the imagery and other inputs increases, so will the accuracy of the resulting map.

A third consideration concerns the area to be mapped. In general, as the size of the area to be mapped increases, the accuracy of a map will decrease. And finally, answering the question posed requires a solid understanding of the requirements for the accuracy of the resulting map. Frequently, map users are, to some degree, willing to trade off the precision (detail) and accuracy of maps. Also, are the accuracy requirements the same for all categories in the map? For thematic maps, the accuracy of a few categories is often far more important than others.

While this list of factors that need consideration prior to answering our question is certainly not exhaustive, it does help illustrate that there are many factors involved and these factors are not independent. Thus, to answer a question about the feasibility of using remote sensing for various applications involves a complex calculus of many factors. One could say it is an exercise in evaluating uncertainty.

Characterizing Uncertainty

Perhaps the first challenge related to uncertainty in remote sensing is to adequately characterize uncertainty in maps derived from remote sensing. For thematic maps, the most conventional approach has been to provide estimates of overall map accuracy, where the percentage of sites mapped accurately is the most common metric used. However, there are a number of other metrics that have been developed and applied which attempt to improve on overall map accuracy such as the kappa statistic. Additionally, map accuracies are frequently reported for the individual classes as both user’s and producer’s accuracies, which is a significant improvement relative to overall map accuracies in many instances (Congalton, 1991).

In addition to knowing, on average, how likely errors are for the whole map, map users frequently would like to know where these errors are most likely to occur. Several recent studies have begun to explore the possibility of providing spatially explicit data on uncertainty, or mapping confidence.In such approaches each pixel is assigned both a class and then some measure of the confidence that the pixel actually belongs in the class. Many classification algorithms can be configured to provide such indications. This attention to providing spatially explicit uncertainty data is a very positive step and it is clear there is still much to be done and learned in this domain.

The methods used to report accuracy of maps representing continuously measured variables are inherently somewhat different from those for thematic maps. The most commonly used metric is the root mean square error (RMSE), although it is common for R2 values to be reported in the literature. It is worth noting that R2 values measure the strength of the relationship between an underlying remote sensing variable and the desired map variable and thus do not directly characterize accuracy. Thus, for the purposes of characterizing uncertainty in maps, the RMSE may be preferable. The RMSE is analogous to the overall map accuracy reported for thematic maps as it is a single value intended to characterize the accuracy for the entire map. Development of methods for spatially explicit characterization of uncertainty in maps of continuously measured variables would be highly desirable.

Understanding Uncertainty

A significant challenge is to better understand the nature and sources of uncertainty in maps derived from remote sensing. For example, a thorough understanding of the causes of uncertainty would allow for an informed answer to our hypothetical question at the beginning of this topic about the use of remote sensing to map agricultural lands. For a variety of reasons, remote sensing has been plagued by the tendency to study problems in ‘one place and one time’ rather than from a comprehensive perspective. Thus when interested in a specific application of remote sensing, one may find many relevant articles in the literature, but each is typically done in a single place using a single kind of imagery and a single set of methods. As a result it may be difficult to determine the best kind of imagery or methods to use in a new place for a similar application as a comprehensive understanding of the causes of uncertainty is unavailable.

One model for the remote sensing process is the image chain approach, as proposed by Schott (1997) and illustrated in Figure 2.1. One fundamental idea underlying the image chain approach is that the entire remote sensing process as applied in any situation is only as strong as the weakest link. In this context, the links in the chain represent various steps in the remote sensing process from image capture to image processing to image display or representation. The image chain approach is useful because it helps identify the many steps in the remote sensing process (or links in the chain) and illustrate that these steps are interrelated. Once the remote sensing process is viewed in this manner, it becomes easier to understand that limitations at each step limit the entire process. Improvements in the weakest links stand to improve the entire process the most. In the context of our discussion of uncertainty, a thorough understanding of the links in the chain should help us evaluate the various sources of uncertainty in a particular application.

Simplified image chain.

Figure 2.1 Simplified image chain.

It is interesting to consider the nature of the efforts in the remote sensing research community concerning uncertainty from the perspective of the image chain approach. Overwhelmingly, the primary step that has been evaluated with respect to its contribution to uncertainty in the final results (or map) has been the image classification step, and most particularly the effect of various classification algorithms on uncertainty. While this step is extremely important and certainly merits much attention, other steps in the remote sensing process may also contribute greatly to map uncertainty. For example, Song et al. (2001) have evaluated the effect of atmospheric correction on classification and change detection in cases where these mapping processes are calibrated using images from a different place and/or time to the images used to make the final maps. In such a situation, there are several steps in the remote sensing process (or links in the chain) that could limit the entire process, including image calibration and radiometric processing. As a community, we need to make sure that we are identifying the steps in the remote sensing process that contribute most to uncertainty (or the weakest links in the chain) and focusing our attention accordingly.

Future Challenges

What are some of the remaining challenges with respect to uncertainty in remote sensing?

(i) Reduce uncertainty in remote sensing products (i.e. make better maps!).

In one respect, this challenge is so obvious that it does not require mentioning. This goal is central to the entire field of remote sensing and researchers are constantly trying to find better ways to make better maps. However, it is worth noting here, from the perspective of the discussion of sources of uncertainty and the image chain approach, that one tendency of researchers is to focus their attention on the steps of the remote sensing process over which they have the most control, such as the selection of an image classification algorithm. However, to most effectively contribute to the larger goal of producing better maps from remote sensing we must find the weakest links in the image chain and devote our efforts to improving them. This charge may include more research on ways to improve sensing systems and the preprocessing of sensor data.

(ii) Improve the nature and quality of uncertainty information provided with maps derived from remote sensing.

The value, use and acceptance of maps derived from remote sensing will increase greatly if they have accompanying quantitative information on uncertainty.

Similarly, if spatially explicit data on uncertainty can be provided it will greatly benefit efforts to model uncertainty in analyses undertaken within a geographical information system.

(iii) Develop ways to characterize the sources of uncertainty in maps derived from remote sensing.

Again drawing from the image chain analogy, it would be very beneficial to know the sources of uncertainty in remote sensing maps. One can imagine trying to decompose the uncertainty in a map into the errors due to sensor limitations, preprocessing for calibration, radiometry or atmospheric effects, and mapping algorithms. Knowledge of this kind could greatly aid efforts to answer questions about the expected uncertainties for new maps of similar areas based on the proposed sensor and processing methods.

Concluding Comments

The question of uncertainty is central to the field of remote sensing. Essential to the process of increasing the quality of maps made using remote sensing is an understanding of the nature and sources of errors in maps. The image chain approach provides a valuable model for the remote sensing process that directs us to devote our efforts to strengthening the weakest link in the image chain. From the perspective of map users, accurate characterization of uncertainty greatly enhances the value of remote sensing products. In particular, spatially explicit data on map uncertainty promises to increase the utility of remote sensing products used in geographic information systems.

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