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Recursive Construction of Models and Sub-models
We propose specifying models using an object-oriented mechanism. The target object in modeling
Hantavirus Pulmonary Syndrome is the location where the host/agent (i.e., mice) comes into contact with human beings. However, it is not possible to detect this object directly. Model substitution and
decomposition becomes necessary under such circumstances. Model substitution is the process of replacing a model or sub-model with another model or sub-model that is more observable. Model decomposition
is similar, but replaces a model or sub-model with two or more sub-models. For example, human beings are difficult to detect directly from satellite imagery, but it is possible to detect
the locations of houses. A model for locating houses can substitute a model for locating human beings. Similarly, it is not possible to directly detect the location of mice; however, models for identifying
favorable habitat, such as wet bushes in wet areas, can be constructed and substituted to the model for locating mice. These substitute models may, in turn, require further decomposition. For example, houses
cannot be directly located from older satellite imagery, due to poor resolution. In this case, ``flat regions'' near ``roads'' might be used as proxies for houses. Once a model is generated, a similarity
metric is used to measure the difference between the specified target model and a candidate from the data repository. Consequently, different candidate regions are
compared in terms of the similarity measure. In many cases, there are known results for the model specification - the ground truth. The ground truth is used to revise the specification of the similarity
measure through, for example, multidimensional scaling (to be described in a later section). Objects are represented as n-dimensional feature vectors  and  , where  and  , where  and  are the  feature in the feature vector. The most commonly used similarity metric is the Euclidean distance between these vectors: 
In general, the  distance metric is defined as
Furthermore, the components of the model can be referenced at different abstraction levels, as described below (shown in Fig. 4):
- Raw Pixels
: At the lowest abstraction level, object are simply aggregations of raw pixels from
the image. Comparison between objects or regions is done pixel-by-pixel, and commonly used similarity measures include the correlation coefficient and the distance. Comparison at the pixel level is very specific, and therefore is only used when relatively precise matches are required.
- Features
: A higher abstraction level for representing objects is the feature level. An image feature is a distinguishing primitive characteristic or attribute of an image [8]. Some features such as luminance, shape descriptor, and gray scale texture are natural since they correspond to the
visual appearance of an image. Other features such as amplitude histogram, color histogram, and spatial-frequency energy are algorithmic entities. Each image in an image archive is segmented
into regions consisting characterized by homogeneous feature vectors. Searching by similarity in the n-dimensional feature space involves the comparison of the query feature vector with the
feature vectors extracted from target images. These feature vectors are often predefined, pre-extracted, and stored in a database. Alternatively, they can be defined by the user and then
pre-extracted by the system. Finally, they can be defined by the user at run-time and then extracted during query processing. Various spatial indexing schemes such as R-trees facilitate
indexing the feature space.
- Semantics
: This is the highest abstraction level at which a content-based search is performed.
Semantic information from an image is usually extracted from a pre-trained classifier or is supplied through human interpretation. For satellite images, this information includes the type of
land cover of a specific area such as water, forest, or urban. A semantic network is constructed that groups similar semantic terms into categories. For example, pine trees and maple trees are
grouped into trees, rose and sunflower are grouped into flowers, corn and wheat are grouped into crops, and so forth. The purpose of constructing such a semantic network is to allow the
generalization of retrieval at the semantic level (retrieval of "trees" will retrieve both "pine trees" and "maple trees" simultaneously).
Figure 4: Abstraction levels of an image.
We distinguish between simple (or atomic) objects and composite objects. Both of these are used as
model components. The definition of a simple object reflects the three levels of abstraction defined above: a simple object is
- a connected region of raw pixels, or
- a connected region where selected features are homogeneous (e.g., texture feature), or
- a connected region with homogeneous semantics (e.g., forest, urban, water).
We also allow additional constraints to be imposed on the attributes of an simple object, such as the size, location.
A composite object consists of a set of simple objects and a set of spatial or temporal relationships. For example, suppose that we define the simple objects  ,  , and  . Then, the composite object  , shown in Fig. 5, consists of  and three spatial relationships:
- is to the north and east of ,
- is to the north and west of ,
- is to the west of .
Possible relationships include: direction, adjacency, distance, spatial containment, following or preceding in time, and many others. 
Figure 5: Example of a composite object.
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