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Each of these two-by-two matrices can be augmented back to a three-by-three matrix as follows without disrupting the validity of the equality:

Medical Image Processing

FIGURE 1 Illustration of the numerical example of two-dimensional rigid-body movements. To achieve a given result, different translations must be applied depending on whether translations are done before or after rotations. In the two-dimensional case, the amount of rotation is invariant, regardless of the order of transformations.

FIGURE 1 Illustration of the numerical example of two-dimensional rigid-body movements. To achieve a given result, different translations must be applied depending on whether translations are done before or after rotations. In the two-dimensional case, the amount of rotation is invariant, regardless of the order of transformations.

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