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The paper extended the concepts of expansive measures and N-expansive measures to group actions on compact metric spaces and proved that a group action is countably-expansive if and only if it is measure-expansive. It was shown that a group action of a compact metric space is N-expansive if and only if every Borel probability measure is N-expansive. These represented a group action version of the existing results. If the convex combination of Borel measures μ1,…,μn is 1-expansive, then μi is 1-expansive for every i=1,…,n. Finally the 1-expansive measures for continuous action was characterized as the convex sum of finitely many Dirac measures supported on expansive points. [ABSTRACT FROM AUTHOR]

Based on the very basic assumption in image motion estimation, i.e. the gray-lever invariant assumption, the global optimization solving model for digital speckle correlation method (DSCM), which is also named as digital image correlation(DIC) method was constructed by matching the whole speckle images, instead of subsets of speckled images. Then two kinds of solving schemes for DSCM, subset matching and FEM based DSCM, could be deduced from the global optimization solving model proposed in this paper. It is emphasized that the displacement representation mode is the key to DSCM solving, so different displacement representation modes could induce different DSCM solving schemes. [ABSTRACT FROM AUTHOR]