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By T. A. Chapman

Lecture notes in arithmetic No.1009

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Extra info for Controlled Simple Homotopy Theory and Applications

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The second advantage is that it requires much less memory to process the data when compared to non-linear methods, one of the major drawbacks which is the memory required to store the Jacobian matrix at each iteration. The proposed method can therefore be easily applied to large datasets without any requirement for high-end computation platforms. 2 Reducing Image Size Distortions As mentioned above, the cascading of sequential motion estimates leads to error accumulation, which affects the size of images.

The inclusion of the weight factor allows t x ∈η i j the result to be obtained faster (see Fig. 7), as the uncertainty estimation provides some information about error in the initial estimation. These two linear steps can be executed iteratively until a selected stopping criterion is fulfilled. A typical stopping criterion is to set a threshold on the decrease rate of error term ε2 . It should be noted that this approach has two main advantages over existing methods. First, it avoids non-linear optimisation by iterating two linear steps.

These two linear steps can be executed iteratively until a selected stopping criterion is fulfilled. A typical stopping criterion is to set a threshold on the decrease rate of error term ε2 . It should be noted that this approach has two main advantages over existing methods. First, it avoids non-linear optimisation by iterating two linear steps. This is relevant in the case of large-area mosaics. As non-linear optimisation is not required, its computational cost is very low, and minimisation is therefore faster.

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Controlled Simple Homotopy Theory and Applications by T. A. Chapman


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