**2.3.1 Applying physical restraints to generate additional MCEs**

A motion constraint equation alone is not sufficient to determine the optical flow, as indicated previously. It is proposed an refinement of the same given that its partial derivatives provide additional solutions to the flow working as multiple filters. Nagel (Nagel, 1983) was the pioneer in applying this method uses second-order differentiates, in fact, the differential operator is one of many that could be used to generate multiple MCES. Usually these operators are used numerically by convolutions as linear operators.

This process works because the convolution does not change the orientation of the spacetime structure. On the other hand, it is important to use filters that are linearly independent otherwise the produced MCES will degenerate and will not have won anything. The filters and their differentials can be estimated previously to achieve efficiency and, due to the locality of the operators, a massively parallel implementation of these structures.

It is possible also using neighborhood information from local regions to generate motion constraint equations extras (Lucas & Kanade, 1981; Simoncelli & Heeger, 1991). It is assumed, therefore, that the movement is a pure translation in a local region, where these constraints are modeled using a weight matrix so that the results are placed centered within a local region as for example, following a Gaussian distribution. It is rewritten then, the MCE as a minimization problem. The error term is minimized, or solved the set of equations generated by numerical methods.

Working with multicolored images, can be generated different functions of brightness. For example, the planes of red, green and blue of a standard camera can be treated as three separate images, producing three MCES to solve. As a counterpart to this multispectral method, it should be noted that the color planes are usually correlated, a fact, moreover, that is exploited by most compression algorithms. In these situations, the linear system of equations can be degenerate, so that ultimately there is no guarantee that the extra cost in computing lead to an improvement in the quality of flow.

A variation of this method is using additional invariance with respect small displacements and lighting changes, basing these measures in the proportion of different planes of color (spectral sensitivity functions) such as RGB or HSV commonly used. Using this last variant is obtained significant improvements over the use of a single plane RGB (Golland & Bruckstein, 1997).

274 Real-Time Systems, Architecture, Scheduling, and Application

There are different general methods for restricting MCE and improve optical flow measures: • Conducting global optimizations, such as smoothing (Horn & Schunck, 1981; Nagel,

• Restricting the optical flow to a model known, for example, the affine model (Liu *et al*.,

• Using multi-scale methods in a space and time domain (Anandan, 1989; Webber, 1994;

A motion constraint equation alone is not sufficient to determine the optical flow, as indicated previously. It is proposed an refinement of the same given that its partial derivatives provide additional solutions to the flow working as multiple filters. Nagel (Nagel, 1983) was the pioneer in applying this method uses second-order differentiates, in fact, the differential operator is one of many that could be used to generate multiple MCES.

This process works because the convolution does not change the orientation of the spacetime structure. On the other hand, it is important to use filters that are linearly independent otherwise the produced MCES will degenerate and will not have won anything. The filters and their differentials can be estimated previously to achieve efficiency and, due to the

It is possible also using neighborhood information from local regions to generate motion constraint equations extras (Lucas & Kanade, 1981; Simoncelli & Heeger, 1991). It is assumed, therefore, that the movement is a pure translation in a local region, where these constraints are modeled using a weight matrix so that the results are placed centered within a local region as for example, following a Gaussian distribution. It is rewritten then, the MCE as a minimization problem. The error term is minimized, or solved the set of equations

Working with multicolored images, can be generated different functions of brightness. For example, the planes of red, green and blue of a standard camera can be treated as three separate images, producing three MCES to solve. As a counterpart to this multispectral method, it should be noted that the color planes are usually correlated, a fact, moreover, that is exploited by most compression algorithms. In these situations, the linear system of equations can be degenerate, so that ultimately there is no guarantee that the extra cost in

A variation of this method is using additional invariance with respect small displacements and lighting changes, basing these measures in the proportion of different planes of color (spectral sensitivity functions) such as RGB or HSV commonly used. Using this last variant is obtained significant improvements over the use of a single plane RGB (Golland &

Usually these operators are used numerically by convolutions as linear operators.

locality of the operators, a massively parallel implementation of these structures.

• Using multispectral images (Golland & Bruckstein, 1997).

1997; Ong & Span, 1997; Fleet & Jepson, 2000).

• Exploiting temporal consistency (Giaccone & Jones, 1997, 1998).

**2.3.1 Applying physical restraints to generate additional MCEs** 

1983; Heitz & Bouthemy, 1993).

Yacoob & Davis, 1999).

generated by numerical methods.

Bruckstein, 1997).

computing lead to an improvement in the quality of flow.
