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where I(x, y, t) is the image value at point (x, y) at time t, (u, v) are the horizontal and the vertical image velocities at (x, y), and t is considered to be small [55]. We note that in our model we have f = (u, v). If we assume that the motion eld (i.e., the pixel correspondences between the two images) is small at each pixel location, the motion estimator can be represented by the rst-order Taylor series expansion as ED = Ix u + Iy v + It dxdy, (8.5)

A database exists as a logical data model only until it is deployed on a specific database platform. Although all relational database platforms are basically similar, every database platform has its distinct capabilities and restrictions. So your database s physical model on Microsoft SQL Server is at least somewhat different from its physical model on Oracle 9i. In other words, a database has only one logical model and one physical model for every database platform on which it is deployed.

Physical data models are extracted from their logical counterparts by mapping logical objects to physical objects supported by the target database platform. The following table shows the relationship between logical and physical objects:

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where (Ix , Iy ) and It are the spatial and time derivatives of the image, and is an estimator. To resolve the above equation, it is necessary to add an additional constraint. The most common one is the spatial coherence constraint [55], which embodies the assumption that neighboring pixels in an image are likely to belong to the same surface, and therefore a smoothness in the ow is expected. The rst-order model of this second constraint is given by ES = ( (u, v)) dxdy, (8.6)

In many cases, your physical data model almost mirrors your logical data model because entities typically map directly to the tables that store them. Exceptions to this rule are logical data models that contain nonspecific relationships and entity subtypes. Although entity subtypes are an advanced topic, beyond the scope of this book, we do have a nonspecific relationship in Figure 8-14 that must be resolved into a physical database structure. Remember that the physical mechanism used to relate a child to its parent is the sharing of key values: The child s foreign key matches the parent s primary key. A nonspecific relationship doesn t migrate keys, so something must change between the structure of the logical data model and the physical data model extracted from it. To store these shared keys you must create a separate table a table with no entity counterpart as shown in Figure 8-14.

Logical Data Model (LDM) InventoryItem ItemNumber VARCHAR(15) NOT NULL ParentItemNumber VARCHAR(15) NULL Description VARCHAR(40) NOT NULL UnitPrice NUMERIC(12,2) NOT NULL

where represents the gradient. Visual motion is determined by minimizing the regularization problem E = ED + ES . (8.7)

completing the example. Barker et al. (1991) developed resistance factors for bearing capacity and sliding resistance of shallow footings supporting highway bridges, based on calibration using the FOSM approach. This procedure involved four steps: (1) estimating the inherent level of reliability in various methods of calculating footing capacity; (2) observing variations in reliability with bridge span length; (3) choosing target reliabilities based on the safety margin used in ASD; and (4) back calculating resistance factor using Equation (18.17). Partial results are shown in Table 18.7, suggesting the differences between the ASD and FOSM calibrations, and the effect of bridge span length. They suggest the values of resistance factors in the last column, in part to be more consistent with ASD experience. Resistance factors for overall slope stability under a shallow footing were also calculated by Barker et al. (1991) by direct calibration to the AASHTO code ASD requirements for factor of safety, using Equation (18.17). ASD calibration was used because it was thought that computer methods of slope stability analysis did not easily lend themselves to FOSM calibration procedures. More recent developments by Low (1996) using the Hasofer Lind method for slope stability analysis, however, suggest that a reliability-based calibration of resistance factor for slope stability design is straightforward, although yet to be reported in the literature.

Physical Data Model (PDM) InventoryItem ItemNumber (PK) ParentItemNumber Description UnitPrice varchar(15) NOT NULL varchar(15) NULL varchar(40) NOT NULL numeric(12,2) NOT NULL

Although the objective function E is nonlinear (and a direct solution does not exist for minimizing it), a convex approximation can be obtained [56]. The global minimum can then be determined iteratively. This procedure is most effective when the object displacements between consecutive images are small. When object displacements are large, a coarse-to- ne strategy

CategoryInventoryItem CategoryCode (PK)(FK) varchar(4) NOT NULL ItemNumber (PK)(FK) varchar(15) NOT NULL

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