III. MATERIAL Y MÉTODOS
III.4. Procedimiento
Trial model of the Analytical Engine, proposed by Charles Babbage in 1837, and considered the first Turing- complete general-purpose computer, displayed at the Science Museum, London.
II.A Introduction
The data association problem, also known as the correspondence problem16, is that of finding the correspondence relations between new data available from the sensors and the previous data about the environment already present in the map. This means that the objective is to associate new uncertain data (under the guise of new measurements or
16 Within computer vision community the term correspondence problem is widely extended due the influence of the stereo vision field; at the same time the data association problem expression remains used in the SLAM community, probably inherited from the tracking methodologies in detection and ranging sensors.
observations) to known environmental landmarks, thus concluding that both measurements correspond to the same physical object/feature in the world.
For any given system which relies on solving the data association problem, there is a set of critical factors that define which will be the suitable approaches to solve it. The single most defining feature is the kind of sensor/s to be deployed. This will define how are the landmarks that can be detected as features, and in turn, configures the set of landmark parametrizations available. For example, it is common for multimodal systems having to address the data association in different spaces or multiple times in order to associate readings from the various sensors, as seen in (Atrey et al., 2010). Besides, the specifications of sensors and landmarks are the defining factors in two other problems: the landmark detection and, depending on the sensors, the filtering of false positives. The landmark detection problem is pretty straight forward for most of the approaches, as once it is clear what is defined as a landmark, it becomes just an issue of signal processing and feature detection in the sensor space.
On the other hand, filtering false positives is a harder challenge, as not only these false positives may arise in terms of landmark detection, but in the association step itself. The false positives for the landmark detection step may be produced by the spuriousness of the sensor, or by the characterization used to detect the landmark, e.g: in structured enviroments, like furnished rooms, it is usual that the Harris corner detector (Harris and Stephens, 1988) denotes as salient non-existent points where two orthogonal edges at different surfaces/depths overlap. The false positives due incorrect association tend to be an issue largely caused by the environment; if the detected landmarks are too similar or too close in sensor space, the probability of false associations grows. These can be the most disruptive cases for probabilistic SLAM, and many of the research in the association problem within SLAM is destined to pruning them, going as far as being preferable risk losing correct associations, as will be described in this chapter.
II.B Challenges on Data Association
In the probabilistic SLAM framework, the data association requires that the prediction step has been completed, and new sensor data are available. The problem itself can be considered as three different smaller problems or tasks: finding landmarks (as distinguishable data on the environment) in sensor reading; measurement of said landmarks, thus, interpreting their spatial relations with respect to the sensor or robot; and finally establish the correspondence relation with the previous landmarks on the map, if possible. FIGURE II.1 illustrates these tasks within the general EKF framework procedure.
The prediction of the observations (that is, how the known data are expected to be perceived by the sensor), is computed with the direct observation model h (equation 2.8), and although it is always a critical part on EKF-SLAM approaches, it is not a required step in many data association solutions. This theoretical division within the correspondence problem is rarely as clear in practice, and it is largely dependent on the approach, e.g.: in
LRF-based SLAM approaches the most common approach to data association is the ICP (Besl and McKay, 1992), where the whole sensors scan is matched, producing association without extracting landmarks.
FIGUREII.1: General EKF SLAM procedure and details on the processes considered within the Data Association Problem.
In the context of visual SLAM, the landmark measurement step is affected by the limitations of the camera sensors: without additional information, with cameras being bearing-only sensors, the depth is not directly observable, producing incomplete measurements. Also, as will be discussed along this chapter, the final association step depends largely on the parametrization model and the landmark initialization processes (seen in sections 2.7.1 and 3.5.6 respectively).
The methods to deal with landmark detection and observation problem can be classified in two large groups: model-based and appearance-based approaches. This division is related to the parametrization of the landmarks (seen in 2.7.1), as model-based approaches (Gee and Mayol-Cuevas, 2006) work with non-point geometric primitives17 used as geometric models, which allow modelling more complex elements of the environment with meaningful structure (Flint et al., 2010). On the other side, appearance-based approaches rely directly on the appearance of elements; thus, relying directly on the image data at pixel level. This means that the geometry, shape and size of an object is meaningless, but that the potentially relevant data are over the whole image, and a vision-based interpretation method is required to extract and reduce the information.
This information reduction is a way to remove irrelevant data, as an average camera sensor can yield hundreds of megabytes per second. The information that will be kept (let be it colour of a pixel/region, illumination, optical defocus, image-spatial relations, etc.) depends largely on the strategy used to produce the features. These strategies are usually divided in two wide categories: localized features, and whole-image features. The localized features involve sub-regions of a given image, generally denoting a pixel or/and its vicinity, while whole-image features are derived from full images (Lovegrove and Davison, 2010). Note that there are plenty of whole-image feature techniques relying on localized features to build upon using histograms (Dalal and Triggs, 2005) and other image classification techniques such as Bag of Words (Galvez-López and Tardós, 2012). These approaches are used frequently in the context of loop closing18, where the association problem has more relaxed real-time constraints. Several examples of the approaches taken to the association problem when dealing with loop closing can be found in (Williams et al., 2009).