We have investigated critical scaling behavior of Barkhausen avalanches of two-dimensional Co and MnAs films using time-resolved magneto-optical microscopy, enabling to image Barkhausen avalanches at criticality. A stochastic analysis of the fluctuating size of Barkhausen jumps from numerous repetitive experiments shows a power-law scaling behavior in both systems. Strikingly, it is found that the variation of scaling exponent in the power-law distribution is closely correlated with the

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... n of the domain-evolution patterns. This result is understood by the fact that both the scaling exponent and the domain-evolution patterns strongly depend on the relative contribution between the dipolar interaction and domain wall energies.